{"id":349,"date":"2022-07-22T12:14:29","date_gmt":"2022-07-22T04:14:29","guid":{"rendered":"https:\/\/www.lazybirds.top\/?p=349"},"modified":"2022-07-22T12:14:29","modified_gmt":"2022-07-22T04:14:29","slug":"d2l%e8%87%aa%e5%ad%a6%e7%ac%94%e8%ae%b0-8-%e5%be%aa%e7%8e%af%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c","status":"publish","type":"post","link":"https:\/\/www.lazybirds.top\/?p=349","title":{"rendered":"d2l\u81ea\u5b66\u7b14\u8bb0 &#8211; 8.\u5faa\u73af\u795e\u7ecf\u7f51\u7edc"},"content":{"rendered":"\n<p><a href=\"https:\/\/zh.d2l.ai\/\">\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b \u2014 \u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60 2.0.0-beta0 documentation (d2l.ai)<\/a><\/p>\n\n\n\n<!--more-->\n\n\n\n      <meta charset=\"utf-8\">\n      <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n      \n      <link rel=\"stylesheet\" href=\"https:\/\/www.lazybirds.top\/katex\/katex.min.css\">\n      \n      \n      \n      \n      \n      \n      \n      \n   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id=\"%E5%BA%8F%E5%88%97%E5%9B%9E%E5%BD%92%E6%A8%A1%E5%9E%8B\">&#x5E8F;&#x5217;&#x56DE;&#x5F52;&#x6A21;&#x578B;<\/h2>\n\n<ul>\n<li>&#x81EA;&#x56DE;&#x5F52;&#x6A21;&#x578B;&#xFF08;autoregressive models&#xFF09;&#xFF1A;&#x4F7F;&#x7528;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>x<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mi>&#x3C4;<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_{t-1}, \\ldots, x_{t-\\tau}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6389em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span 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models&#xFF09;&#xFF1A;&#x4FDD;&#x7559;&#x4E00;&#x4E9B;&#x5BF9;&#x8FC7;&#x53BB;&#x89C2;&#x6D4B;&#x7684;&#x603B;&#x7ED3;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">h_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x5E76;&#x540C;&#x65F6;&#x66F4;&#x65B0;&#x9884;&#x6D4B;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mover accent=\"true\"><mi>x<\/mi><mo>^<\/mo><\/mover><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\hat{x}_t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x548C;&#x603B;&#x7ED3;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">h_{t}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E4%B8%80%E4%BA%9B%E6%A6%82%E5%BF%B5\">&#x4E00;&#x4E9B;&#x6982;&#x5FF5;<\/h2>\n\n<ul>\n<li>\n<p>&#x52A8;&#x529B;&#x5B66;&#x9759;&#x6B62;&#xFF08;stationary&#xFF09;&#xFF1A;&#x5E8F;&#x5217;&#x672C;&#x8EAB;&#x7684;&#x52A8;&#x529B;&#x5B66;&#x4E0D;&#x968F;&#x65F6;&#x95F4;&#x6539;&#x53D8;<br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mi>T<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><msubsup><mo>&#x220F;<\/mo><mrow><mi>t<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>T<\/mi><\/msubsup><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P\\left(x_{1}, \\ldots, x_{T}\\right)=\\prod_{t=1}^{T} P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.2809em;vertical-align:-0.2997em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position:relative;top:0em;\">&#x220F;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9812em;\"><span style=\"top:-2.4003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.2029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2997em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>&#x9A6C;&#x5C14;&#x79D1;&#x592B;&#x6761;&#x4EF6;&#xFF08;Markov condition&#xFF09;&#xFF1A;&#x81EA;&#x56DE;&#x5F52;&#x6A21;&#x578B;&#x7684;&#x524D;&#x63D0;<\/p>\n<\/li>\n<li>\n<p>k&#x6B65;&#x9884;&#x6D4B;&#xFF08;k-step-ahead-prediction&#xFF09;<\/p>\n<\/li>\n<\/ul>\n<h1 class=\"mume-header\" id=\"%E8%AF%AD%E8%A8%80%E6%A8%A1%E5%9E%8B%E5%92%8C%E6%95%B0%E6%8D%AE%E9%9B%86\">&#x8BED;&#x8A00;&#x6A21;&#x578B;&#x548C;&#x6570;&#x636E;&#x96C6;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%B9%B3%E6%BB%91laplace-smoothing\">&#x62C9;&#x666E;&#x62C9;&#x65AF;&#x5E73;&#x6ED1;&#xFF08;Laplace smoothing&#xFF09;<\/h2>\n\n<p>&#x5F53;&#x6570;&#x636E;&#x96C6;&#x5F88;&#x5C0F;&#xFF0C;&#x6216;&#x5355;&#x8BCD;&#x975E;&#x5E38;&#x7F55;&#x89C1;&#x65F6;&#x4F7F;&#x7528;&#xFF0C;&#x6765;&#x5C06;&#x7F55;&#x89C1;&#x5355;&#x8BCD;&#x7EC4;&#x5408;&#x6307;&#x5B9A;&#x4E3A;&#x975E;&#x96F6;&#x8BA1;&#x6570;&#x3002;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mover accent=\"true\"><mi>P<\/mi><mo>^<\/mo><\/mover><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>1<\/mn><\/msub><mi mathvariant=\"normal\">\/<\/mi><mi>m<\/mi><\/mrow><mrow><mi>n<\/mi><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>1<\/mn><\/msub><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mover accent=\"true\"><mi>P<\/mi><mo>^<\/mo><\/mover><mrow><mo fence=\"true\">(<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo>&#x2223;<\/mo><mi>x<\/mi><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo fence=\"true\">)<\/mo><\/mrow><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msub><mover accent=\"true\"><mi>P<\/mi><mo>^<\/mo><\/mover><mrow><mo fence=\"true\">(<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msub><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mover accent=\"true\"><mi>P<\/mi><mo>^<\/mo><\/mover><mrow><mo fence=\"true\">(<\/mo><msup><mi>x<\/mi><mrow><mo mathvariant=\"normal\">&#x2032;<\/mo><mo mathvariant=\"normal\">&#x2032;<\/mo><\/mrow><\/msup><mo>&#x2223;<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo separator=\"true\">,<\/mo><msup><mi>x<\/mi><mrow><mo mathvariant=\"normal\">&#x2032;<\/mo><mo mathvariant=\"normal\">&#x2032;<\/mo><\/mrow><\/msup><mo fence=\"true\">)<\/mo><\/mrow><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>3<\/mn><\/msub><mover accent=\"true\"><mi>P<\/mi><mo>&#x2D9;<\/mo><\/mover><mrow><mo fence=\"true\">(<\/mo><msup><mi>x<\/mi><mrow><mo mathvariant=\"normal\">&#x2032;<\/mo><mo mathvariant=\"normal\">&#x2032;<\/mo><\/mrow><\/msup><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi>n<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><msup><mi>x<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo fence=\"true\">)<\/mo><\/mrow><mo>+<\/mo><msub><mi>&#x3F5;<\/mi><mn>3<\/mn><\/msub><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{aligned}\n\\hat{P}(x) &amp;=\\frac{n(x)+\\epsilon_{1} \/ m}{n+\\epsilon_{1}} \\\\\n\\hat{P}\\left(x^{\\prime} \\mid x\\right) &amp;=\\frac{n\\left(x, x^{\\prime}\\right)+\\epsilon_{2} \\hat{P}\\left(x^{\\prime}\\right)}{n(x)+\\epsilon_{2}}\\\\\n\\hat{P}\\left(x^{\\prime \\prime} \\mid x, x^{\\prime}\\right) &amp;=\\frac{n\\left(x, x^{\\prime}, x^{\\prime \\prime}\\right)+\\epsilon_{3} \\dot{P}\\left(x^{\\prime \\prime}\\right)}{n\\left(x, x^{\\prime}\\right)+\\epsilon_{3}}\n\\end{aligned}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:8.256em;vertical-align:-3.878em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:4.378em;\"><span style=\"top:-6.5747em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.815em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8019em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><span style=\"top:-0.9818em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8019em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8019em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.878em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:4.378em;\"><span style=\"top:-6.5747em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-3.815em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6238em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-0.9818em;\"><span class=\"pstrut\" style=\"height:3.6238em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5972em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6779em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9202em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.0556em;\"><span class=\"mord\">&#x2D9;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.878em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E9%A9%AC%E5%B0%94%E7%A7%91%E5%A4%AB%E6%A8%A1%E5%9E%8B%E4%B8%8En%E5%85%83%E8%AF%AD%E6%B3%95\">&#x9A6C;&#x5C14;&#x79D1;&#x592B;&#x6A21;&#x578B;&#x4E0E;n&#x5143;&#x8BED;&#x6CD5;<\/h2>\n\n<p>&#x6D89;&#x53CA;&#x4E00;&#x4E2A;&#x3001;&#x4E24;&#x4E2A;&#x548C;&#x4E09;&#x4E2A;&#x53D8;&#x91CF;&#x7684;&#x6982;&#x7387;&#x516C;&#x5F0F;&#x5206;&#x522B;&#x88AB;&#x79F0;&#x4E3A;&#x201C;&#x4E00;&#x5143;&#x8BED;&#x6CD5;&#x201D;&#xFF08;unigram&#xFF09;&#x3001;&#x201C;&#x4E8C;&#x5143;&#x8BED;&#x6CD5;&#x201D;&#xFF08;bigram&#xFF09;&#x3001;&#x201C;&#x4E09;&#x5143;&#x8BED;&#x6CD5;&#x201D;&#xFF08;trigram&#xFF09;&#x6A21;&#x578B;&#x3002;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>4<\/mn><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>3<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{aligned}\n&amp;P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2}\\right) P\\left(x_{3}\\right) P\\left(x_{4}\\right) \\\\\n&amp;P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2} \\mid x_{1}\\right) P\\left(x_{3} \\mid x_{2}\\right) P\\left(x_{4} \\mid x_{3}\\right) \\\\\n&amp;P\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)=P\\left(x_{1}\\right) P\\left(x_{2} \\mid x_{1}\\right) P\\left(x_{3} \\mid x_{1}, x_{2}\\right) P\\left(x_{4} \\mid x_{2}, x_{3}\\right) \n\\end{aligned}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:4.5em;vertical-align:-2em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.5em;\"><span style=\"top:-4.5em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-1.5em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.5em;\"><span style=\"top:-4.66em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.16em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><span style=\"top:-1.66em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E9%BD%90%E6%99%AE%E5%A4%AB%E5%AE%9A%E5%BE%8Bzipfs-law\">&#x9F50;&#x666E;&#x592B;&#x5B9A;&#x5F8B;&#xFF08;Zipf&apos;s law&#xFF09;<\/h2>\n\n<p>&#x7B2C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>i<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6595em;\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span>&#x4E2A;&#x6700;&#x5E38;&#x7528;&#x5355;&#x8BCD;&#x7684;&#x9891;&#x7387;&#x4E3A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>n<\/mi><mi>i<\/mi><\/msub><mo>&#x221D;<\/mo><mfrac><mn>1<\/mn><msup><mi>i<\/mi><mi>&#x3B1;<\/mi><\/msup><\/mfrac><mspace linebreak=\"newline\"><\/mspace><mi>log<\/mi><mo>&#x2061;<\/mo><msub><mi>n<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mo>&#x2212;<\/mo><mi>&#x3B1;<\/mi><mi>log<\/mi><mo>&#x2061;<\/mo><mi>i<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">n_i\\propto\\frac{1}{i^\\alpha}\\\\\n\\log n_{i}=-\\alpha \\log i+c<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x221D;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.0074em;vertical-align:-0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">i<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.5904em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x8FD9;&#x4E2A;&#x5206;&#x5E03;&#x4E0D;&#x4EC5;&#x9002;&#x7528;&#x4E8E;&#x4E00;&#x5143;&#x8BED;&#x6CD5;&#xFF0C;&#x8FD8;&#x9002;&#x7528;&#x4E8E;&#x5176;&#x4ED6;n&#x5143;&#x8BED;&#x6CD5;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E8%AF%BB%E5%8F%96%E9%95%BF%E5%BA%8F%E5%88%97%E6%95%B0%E6%8D%AE\">&#x8BFB;&#x53D6;&#x957F;&#x5E8F;&#x5217;&#x6570;&#x636E;<\/h2>\n\n<p>&#x5E8F;&#x5217;&#x6570;&#x636E;&#x7684;&#x4E0D;&#x540C;&#x91C7;&#x6837;&#x65B9;&#x6CD5;&#x5C06;&#x5BFC;&#x81F4;&#x9690;&#x72B6;&#x6001;&#x521D;&#x59CB;&#x5316;&#x7684;&#x5DEE;&#x5F02;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E9%87%87%E6%A0%B7random-sampling\">&#x968F;&#x673A;&#x91C7;&#x6837;&#xFF08;random sampling&#xFF09;<\/h3>\n\n<p>&#x5728;&#x8FED;&#x4EE3;&#x8FC7;&#x7A0B;&#x4E2D;&#xFF0C;&#x6765;&#x81EA;&#x4E24;&#x4E2A;&#x76F8;&#x90BB;&#x7684;&#x3001;&#x968F;&#x673A;&#x7684;&#x3001;&#x5C0F;&#x6279;&#x91CF;&#x4E2D;&#x7684;&#x5B50;&#x5E8F;&#x5217;&#x4E0D;&#x4E00;&#x5B9A;&#x5728;&#x539F;&#x59CB;&#x5E8F;&#x5217;&#x4E0A;&#x76F8;&#x90BB;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E9%A1%BA%E5%BA%8F%E5%88%86%E5%8C%BAsequential-partitioning\">&#x987A;&#x5E8F;&#x5206;&#x533A;&#xFF08;sequential partitioning&#xFF09;<\/h3>\n\n<p>&#x4E24;&#x4E2A;&#x76F8;&#x90BB;&#x7684;&#x5C0F;&#x6279;&#x91CF;&#x4E2D;&#x7684;&#x5B50;&#x5E8F;&#x5217;&#x5728;&#x539F;&#x59CB;&#x5E8F;&#x5217;&#x4E0A;&#x4E5F;&#x662F;&#x76F8;&#x90BB;&#x7684;&#x3002;<\/p>\n<h1 class=\"mume-header\" id=\"%E5%BE%AA%E7%8E%AF%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C-1\">&#x5FAA;&#x73AF;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;<\/h1>\n\n<p>RNN&#x662F;&#x5177;&#x6709;<strong>&#x9690;&#x72B6;&#x6001;&#xFF08;hidden state&#xFF09;<\/strong> &#x7684;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x3002;<\/p>\n<p><img src=\"https:\/\/zh.d2l.ai\/_images\/rnn.svg\" alt><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi mathvariant=\"bold\">H<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><mi>&#x3D5;<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">X<\/mi><mi>t<\/mi><\/msub><msub><mi mathvariant=\"bold\">W<\/mi><mrow><mi>x<\/mi><mi>h<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi mathvariant=\"bold\">H<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><msub><mi mathvariant=\"bold\">W<\/mi><mrow><mi>h<\/mi><mi>h<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi mathvariant=\"bold\">b<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mspace linebreak=\"newline\"><\/mspace><msub><mi mathvariant=\"bold\">O<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><msub><mi mathvariant=\"bold\">H<\/mi><mi>t<\/mi><\/msub><msub><mi mathvariant=\"bold-italic\">W<\/mi><mrow><mi>h<\/mi><mi>q<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi mathvariant=\"bold\">b<\/mi><mi>q<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{H}_{t}=\\phi\\left(\\mathbf{X}_{t} \\mathbf{W}_{x h}+\\mathbf{H}_{t-1} \\mathbf{W}_{h h}+\\mathbf{b}_{h}\\right) \n\\\\\n\\mathbf{O}_{t}=\\mathbf{H}_{t} \\boldsymbol{W}_{h q}+\\mathbf{b}_{q}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8361em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">&#x3D5;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">hh<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8361em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">O<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.9722em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right:0.15972em;\">W<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.9805em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><img src=\"https:\/\/zh.d2l.ai\/_images\/rnn-train.svg\" alt><\/p>\n<h2 class=\"mume-header\" id=\"%E5%9B%B0%E6%83%91%E5%BA%A6perplexity\">&#x56F0;&#x60D1;&#x5EA6;&#xFF08;perplexity&#xFF09;<\/h2>\n\n<p>&#x7528;&#x4E8E;&#x8BC4;&#x4EF7;&#x8BED;&#x8A00;&#x6A21;&#x578B;&#x7684;&#x8D28;&#x91CF;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>exp<\/mi><mo>&#x2061;<\/mo><mrow><mo fence=\"true\">(<\/mo><mo>&#x2212;<\/mo><mfrac><mn>1<\/mn><mi>n<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>t<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><mi>log<\/mi><mo>&#x2061;<\/mo><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo>&#x2223;<\/mo><msub><mi>x<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\exp \\left(-\\frac{1}{n} \\sum_{t=1}^{n} \\log P\\left(x_{t} \\mid x_{t-1}, \\ldots, x_{1}\\right)\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:3.0171em;vertical-align:-1.2671em;\"><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">(<\/span><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6514em;\"><span style=\"top:-1.8829em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2671em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x5176;&#x4E2D;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><\/span><\/span><\/span>&#x7531;&#x8BED;&#x8A00;&#x6A21;&#x578B;&#x7ED9;&#x51FA;&#xFF0C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>x<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_{t}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x662F;&#x5728;&#x65F6;&#x95F4;&#x6B65;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span>&#x4ECE;&#x8BE5;&#x5E8F;&#x5217;&#x4E2D;&#x89C2;&#x6D4B;&#x5230;&#x7684;&#x5B9E;&#x9645;&#x8BCD;&#x5143;&#x3002;<\/p>\n<p>&#x8FD9;&#x6837;&#x7684;&#x5EA6;&#x91CF;&#x786E;&#x4FDD;&#x4E86;&#x4E0D;&#x540C;&#x957F;&#x5EA6;&#x7684;&#x5E8F;&#x5217;&#x5177;&#x6709;&#x53EF;&#x6BD4;&#x6027;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E7%8B%AC%E7%83%AD%E7%BC%96%E7%A0%81\">&#x72EC;&#x70ED;&#x7F16;&#x7801;<\/h2>\n\n<p>&#x5C06;&#x6BCF;&#x4E2A;&#x8BCD;&#x5143;&#x8868;&#x793A;&#x4E3A;&#x66F4;&#x5177;&#x8868;&#x73B0;&#x529B;&#x7684;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x3002;<\/p>\n<p>&#x4F7F;&#x7528;&#x4E86;&#x4EE5;&#x4E0B;&#x51FD;&#x6570;<\/p>\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">F<span class=\"token punctuation\">.<\/span>one_hot\n<\/pre><h2 class=\"mume-header\" id=\"%E9%A2%84%E6%B5%8B\">&#x9884;&#x6D4B;<\/h2>\n\n<p>&#x9884;&#x70ED;&#xFF08;warm-up&#xFF09;&#x671F;&#xFF1A;&#x5FAA;&#x73AF;&#x904D;&#x5386;prefix&#x4E2D;&#x7684;&#x5B57;&#x7B26;&#xFF0C;&#x4E0D;&#x65AD;&#x5C06;&#x9690;&#x72B6;&#x6001;&#x4F20;&#x9012;&#x5230;&#x4E0B;&#x4E00;&#x4E2A;&#x65F6;&#x95F4;&#x6B65;&#xFF0C;&#x4F46;&#x4E0D;&#x751F;&#x6210;&#x4EFB;&#x4F55;&#x8F93;&#x51FA;&#x3002;&#x5728;&#x6B64;&#x671F;&#x95F4;&#x6A21;&#x578B;&#x4F1A;&#x81EA;&#x6211;&#x66F4;&#x65B0;&#xFF08;&#x4F8B;&#x5982;&#xFF0C;&#x66F4;&#x65B0;&#x9690;&#x72B6;&#x6001;&#xFF09;&#xFF0C;&#x4F46;&#x4E0D;&#x4F1A;&#x8FDB;&#x884C;&#x9884;&#x6D4B;&#x3002;<\/p>\n<p>&#x9884;&#x70ED;&#x671F;&#x7ED3;&#x675F;&#x540E;&#xFF0C;&#x9690;&#x72B6;&#x6001;&#x7684;&#x503C;&#x901A;&#x5E38;&#x6BD4;&#x521D;&#x59CB;&#x503C;&#x66F4;&#x9002;&#x5408;&#x9884;&#x6D4B;&#x3002;&#x7ECF;&#x9884;&#x70ED;&#x540E;&#x518D;&#x8FDB;&#x884C;&#x9884;&#x6D4B;&#x3002;<\/p>\n<p>&#x9884;&#x6D4B;&#x65F6;&#xFF0C;&#x5C06;&#x6BCF;&#x6B65;&#x9884;&#x6D4B;&#x7684;&#x8F93;&#x51FA;&#x5B57;&#x7B26;&#x4F5C;&#x4E3A;&#x4E0B;&#x4E00;&#x6B65;&#x7684;&#x8F93;&#x5165;&#x5B57;&#x7B26;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E6%A2%AF%E5%BA%A6%E8%A3%81%E5%89%AA\">&#x68AF;&#x5EA6;&#x88C1;&#x526A;<\/h2>\n\n<p>&#x5BF9;&#x4E8E;&#x957F;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span>&#x7684;&#x5E8F;&#x5217;&#xFF0C;&#x5728;&#x53CD;&#x5411;&#x4F20;&#x64AD;&#x8FC7;&#x7A0B;&#x4E2D;&#x4F1A;&#x4EA7;&#x751F;&#x957F;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"script\">O<\/mi><mo stretchy=\"false\">(<\/mo><mi>T<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\mathcal{O}(T)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathcal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">T<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x7684;&#x77E9;&#x9635;&#x4E58;&#x6CD5;&#x94FE;&#x3002;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span>&#x8F83;&#x5927;&#x65F6;&#xFF0C;&#x4F1A;&#x5BFC;&#x81F4;&#x6570;&#x503C;&#x4E0D;&#x7A33;&#x5B9A;&#x3002;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x68AF;&#x5EA6;&#x88C1;&#x526A;&#x6765;&#x7A33;&#x5B9A;&#x8BAD;&#x7EC3;&#x3002;<\/p>\n<p>&#x82E5;&#x76EE;&#x6807;&#x51FD;&#x6570;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>f<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><\/span><\/span><\/span>&#x6EE1;&#x8DB3;Lipschitz&#x8FDE;&#x7EED;&#xFF0C;&#x5219;&#x901A;&#x8FC7;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3B7;<\/mi><mi mathvariant=\"bold\">g<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\eta\\mathbf{g}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3B7;<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><\/span><\/span><\/span>&#x66F4;&#x65B0;&#x53C2;&#x6570;&#x5411;&#x91CF;&#x65F6;&#xFF0C;&#x6709;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo>&#x2212;<\/mo><mi>&#x3B7;<\/mi><mi mathvariant=\"bold\">g<\/mi><mo stretchy=\"false\">)<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2264;<\/mo><mi>L<\/mi><mi>&#x3B7;<\/mi><mi mathvariant=\"normal\">&#x2225;<\/mi><mi mathvariant=\"bold\">g<\/mi><mi mathvariant=\"normal\">&#x2225;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">|f(\\mathbf{x})-f(\\mathbf{x}-\\eta \\mathbf{g})| \\leq L \\eta\\|\\mathbf{g}\\|<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3B7;<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3B7;<\/span><span class=\"mord\">&#x2225;<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><span class=\"mord\">&#x2225;<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x6B64;&#x65F6;&#xFF0C;&#x901A;&#x8FC7;&#x63A7;&#x5236;&#x68AF;&#x5EA6;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"bold\">g<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{g}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><\/span><\/span><\/span>&#x7684;&#x6A21;&#x957F;&#x53EF;&#x4EE5;&#x9650;&#x5236;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>f<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><\/span><\/span><\/span>&#x7684;&#x53D8;&#x5316;&#x3002;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"bold\">g<\/mi><mo>&#x2190;<\/mo><mi>min<\/mi><mo>&#x2061;<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mfrac><mi>&#x3B8;<\/mi><mrow><mi mathvariant=\"normal\">&#x2225;<\/mi><mi mathvariant=\"bold\">g<\/mi><mi mathvariant=\"normal\">&#x2225;<\/mi><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"bold\">g<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{g} \\leftarrow \\min \\left(1, \\frac{\\theta}{\\|\\mathbf{g}\\|}\\right) \\mathbf{g}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2190;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.4em;vertical-align:-0.95em;\"><\/span><span class=\"mop\">min<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">&#x2225;<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><span class=\"mord\">&#x2225;<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">&#x3B8;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">g<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>&#x68AF;&#x5EA6;&#x88C1;&#x526A;&#x7684;&#x574F;&#x5904;&#xFF1A;&#x9650;&#x5236;&#x4E86;&#x53D6;&#x5F97;&#x8FDB;&#x5C55;&#x7684;&#x8FDB;&#x5EA6;<\/li>\n<li>&#x68AF;&#x5EA6;&#x88C1;&#x526A;&#x7684;&#x597D;&#x5904;&#xFF1A;&#x9650;&#x5236;&#x4E86;&#x4E8B;&#x60C5;&#x53D8;&#x7CDF;&#x7684;&#x7A0B;&#x5EA6;<\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E8%AE%AD%E7%BB%83\">&#x8BAD;&#x7EC3;<\/h2>\n\n<p>&#x6838;&#x5FC3;&#x4EE3;&#x7801;&#xFF1A;<\/p>\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">rnn_layer <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>RNN<span class=\"token punctuation\">(<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>vocab<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> num_hiddens<span class=\"token punctuation\">)<\/span>\nY<span class=\"token punctuation\">,<\/span> state_new <span class=\"token operator\">=<\/span> rnn_layer<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> state<span class=\"token punctuation\">)<\/span>\n<span class=\"token comment\"># rnn_layer&#x7684;&#x201C;&#x8F93;&#x51FA;&#x201D;Y&#x4E0D;&#x6D89;&#x53CA;&#x8F93;&#x51FA;&#x5C42;&#x7684;&#x8BA1;&#x7B97;&#xFF1A;<\/span>\n<span class=\"token comment\"># &#x5B83;&#x662F;&#x6307;&#x6BCF;&#x4E2A;&#x65F6;&#x95F4;&#x6B65;&#x7684;&#x9690;&#x72B6;&#x6001;&#xFF0C;&#x8FD9;&#x4E9B;&#x9690;&#x72B6;&#x6001;&#x53EF;&#x7528;&#x4F5C;&#x540E;&#x7EED;&#x8F93;&#x51FA;&#x5C42;&#x7684;&#x8F93;&#x5165;<\/span>\n<span class=\"token comment\"># rnn_layer&#x53EA;&#x5305;&#x62EC;&#x9690;&#x85CF;&#x7684;&#x5FAA;&#x73AF;&#x5C42;&#xFF0C;&#x8FD8;&#x9700;&#x521B;&#x5EFA;&#x4E00;&#x4E2A;&#x5355;&#x72EC;&#x7684;&#x8F93;&#x51FA;&#x5C42;<\/span>\n<\/pre><h2 class=\"mume-header\" id=\"%E9%80%9A%E8%BF%87%E6%97%B6%E9%97%B4%E5%8F%8D%E5%90%91%E4%BC%A0%E6%92%AD\">&#x901A;&#x8FC7;&#x65F6;&#x95F4;&#x53CD;&#x5411;&#x4F20;&#x64AD;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>L<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mn>1<\/mn><mi>T<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>t<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>T<\/mi><\/munderover><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>l<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>y<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>o<\/mi><mi>t<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mn>1<\/mn><mi>T<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>t<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>T<\/mi><\/munderover><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mrow><mo fence=\"true\">(<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi>y<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>o<\/mi><mi>t<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>o<\/mi><mi>t<\/mi><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>g<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>h<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>o<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{aligned}\n\\frac{\\partial L}{\\partial w_{h}} &amp;=\\frac{1}{T} \\sum_{t=1}^{T} \\frac{\\partial l\\left(y_{t}, o_{t}\\right)}{\\partial w_{h}} \\\\\n&amp;=\\frac{1}{T} \\sum_{t=1}^{T} \\frac{\\partial\\left(\\left(y_{t}, o_{t}\\right)\\right.}{\\partial o_{t}} \\frac{\\partial g\\left(h_{t}, w_{o}\\right)}{\\partial h_{t}} \\frac{\\partial h_{t}}{\\partial w_{h}}\n\\end{aligned}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.7909em;vertical-align:-3.1454em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.6454em;\"><span style=\"top:-5.6454em;\"><span class=\"pstrut\" style=\"height:3.8283em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-2.25em;\"><span class=\"pstrut\" style=\"height:3.8283em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.1454em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.6454em;\"><span style=\"top:-5.6454em;\"><span class=\"pstrut\" style=\"height:3.8283em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8283em;\"><span style=\"top:-1.8829em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2671em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-2.25em;\"><span class=\"pstrut\" style=\"height:3.8283em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8283em;\"><span style=\"top:-1.8829em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2671em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">o<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">o<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.1454em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\partial h_{t}}{\\partial w_{h}}=\\frac{\\partial f\\left(x_{t}, h_{t-1}, w_{h}\\right)}{\\partial w_{h}}+\\frac{\\partial f\\left(x_{t}, h_{t-1}, w_{h}\\right)}{\\partial h_{t-1}} \\frac{\\partial h_{t-1}}{\\partial w_{h}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.2074em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.263em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.3213em;vertical-align:-0.8943em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8943em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mi>t<\/mi><\/msub><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/munderover><mrow><mo fence=\"true\">(<\/mo><munderover><mo>&#x220F;<\/mo><mrow><mi>j<\/mi><mo>=<\/mo><mi>i<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><mi>t<\/mi><\/munderover><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>j<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>j<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mrow><mi>j<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mrow><mi>i<\/mi><mo separator=\"true\">,<\/mo><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>i<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\partial h_{t}}{\\partial w_{h}}=\\frac{\\partial f\\left(x_{t}, h_{t-1}, w_{h}\\right)}{\\partial w_{h}}+\\sum_{i=1}^{t-1}\\left(\\prod_{j=i+1}^{t} \\frac{\\partial f\\left(x_{j}, h_{j-1}, w_{h}\\right)}{\\partial h_{j-1}}\\right) \\frac{\\partial f\\left(x_{i,}, h_{i-1}, w_{h}\\right)}{\\partial w_{h}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.2074em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.263em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:3.2149em;vertical-align:-1.4138em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8011em;\"><span style=\"top:-1.8723em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2777em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">(<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7806em;\"><span style=\"top:-1.8723em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x220F;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4138em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9721em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x4E2D;&#x95F4;&#x503C;&#x4F1A;&#x88AB;&#x7F13;&#x5B58;&#x3001;&#x91CD;&#x590D;&#x4F7F;&#x7528;&#xFF0C;&#x4EE5;&#x907F;&#x514D;&#x91CD;&#x590D;&#x8BA1;&#x7B97;&#x3002;<\/p>\n<p>&#x77E9;&#x9635;&#x9AD8;&#x6B21;&#x5E42;&#x53EF;&#x80FD;&#x5BFC;&#x81F4;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x7279;&#x5F81;&#x503C;&#x7684;&#x53D1;&#x6563;&#x6216;&#x6D88;&#x5931;&#xFF0C;&#x5C06;&#x4EE5;&#x68AF;&#x5EA6;&#x7206;&#x70B8;&#x6216;&#x68AF;&#x5EA6;&#x6D88;&#x5931;&#x7684;&#x5F62;&#x5F0F;&#x8868;&#x73B0;&#x3002;<\/p>\n<p>&#x622A;&#x65AD;&#x662F;&#x8BA1;&#x7B97;&#x65B9;&#x4FBF;&#x6027;&#x548C;&#x6570;&#x503C;&#x7A33;&#x5B9A;&#x6027;&#x7684;&#x9700;&#x8981;&#xFF0C;&#x5305;&#x62EC;&#xFF1A;<\/p>\n<h3 class=\"mume-header\" id=\"%E6%88%AA%E6%96%AD%E6%97%B6%E9%97%B4%E6%AD%A5\">&#x622A;&#x65AD;&#x65F6;&#x95F4;&#x6B65;<\/h3>\n\n<p>&#x5728;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3C4;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\tau<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1132em;\">&#x3C4;<\/span><\/span><\/span><\/span>&#x6B65;&#x540E;&#x622A;&#x65AD;&#x5F0F;&#x4E2D;&#x7684;&#x6C42;&#x548C;&#x8BA1;&#x7B97;&#x3002;<\/p>\n<p>&#x8FD9;&#x6837;&#x505A;&#x5BFC;&#x81F4;&#x8BE5;&#x6A21;&#x578B;&#x4E3B;&#x8981;&#x4FA7;&#x91CD;&#x4E8E;&#x77ED;&#x671F;&#x5F71;&#x54CD;&#xFF0C;&#x800C;&#x975E;&#x957F;&#x671F;&#x5F71;&#x54CD;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E6%88%AA%E6%96%AD\">&#x968F;&#x673A;&#x622A;&#x65AD;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>z<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><msub><mi>&#x3BE;<\/mi><mi>t<\/mi><\/msub><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mi>t<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><mo separator=\"true\">,<\/mo><msub><mi>w<\/mi><mi>h<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mrow><mi>t<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">z_{t}=\\frac{\\partial f\\left(x_{t}, h_{t-1}, w_{h}\\right)}{\\partial w_{h}}+\\xi_{t} \\frac{\\partial f\\left(x_{t}, h_{t-1}, w_{h}\\right)}{\\partial h_{t-1}} \\frac{\\partial h_{t-1}}{\\partial w_{h}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.263em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.3213em;vertical-align:-0.8943em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04601em;\">&#x3BE;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.046em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8943em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x5176;&#x4E2D;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>&#x3BE;<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><msub><mi>&#x3C0;<\/mi><mi>t<\/mi><\/msub><mtext>&#xA0;&#x4E14;&#xA0;<\/mtext><mi>P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>&#x3BE;<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><msubsup><mi>&#x3C0;<\/mi><mi>t<\/mi><mrow><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msubsup><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><msub><mi>&#x3C0;<\/mi><mi>t<\/mi><\/msub><mspace linebreak=\"newline\"><\/mspace><mi>E<\/mi><mrow><mo fence=\"true\">[<\/mo><msub><mi>z<\/mi><mi>t<\/mi><\/msub><mo fence=\"true\">]<\/mo><\/mrow><mo>=<\/mo><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>h<\/mi><mi>t<\/mi><\/msub><mi mathvariant=\"normal\">\/<\/mi><mi mathvariant=\"normal\">&#x2202;<\/mi><msub><mi>w<\/mi><mi>h<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">P\\left(\\xi_{t}=0\\right)=1-\\pi_{t} \\text { &#x4E14; } P\\left(\\xi_{t}=\\pi_{t}^{-1}\\right)=\\pi_{t}\n\\\\\nE\\left[z_{t}\\right]=\\partial h_{t} \/ \\partial w_{h}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04601em;\">&#x3BE;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.046em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.2141em;vertical-align:-0.35em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C0;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord text\"><span class=\"mord\">&#xA0;<\/span><span class=\"mord cjk_fallback\">&#x4E14;<\/span><span class=\"mord\">&#xA0;<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04601em;\">&#x3BE;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.046em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C0;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C0;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">]<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x5728;&#x5B9E;&#x8DF5;&#x4E2D;&#x5E76;&#x4E0D;&#x6BD4;&#x5E38;&#x89C4;&#x622A;&#x65AD;&#x597D;&#xFF01;<\/p>\n\n      <\/div>\n      \n    \n","protected":false},"excerpt":{"rendered":"<p>\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b \u2014 \u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60 2.0.0-beta0 documentation (d2l.ai)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[31,20],"tags":[32,33,26,25],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/349"}],"collection":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=349"}],"version-history":[{"count":1,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/349\/revisions"}],"predecessor-version":[{"id":350,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/349\/revisions\/350"}],"wp:attachment":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}