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@@ -196,7 +196,7 @@ |
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" & = & -a_j a_i\n", |
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"\\end{eqnarray}\n", |
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"\n", |
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"当u,v都是变量的函数时的导数推导公式:\n", |
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"当$u$,$v$都是变量的函数时的导数推导公式:\n", |
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"$$\n", |
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"(\\frac{u}{v})' = \\frac{u'v - uv'}{v^2} \n", |
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"$$\n", |
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@@ -222,21 +222,41 @@ |
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"cell_type": "markdown", |
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"metadata": {}, |
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"source": [ |
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"参数更新方程为\n", |
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"### 3.4 参数更新\n", |
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"\n", |
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"误差与参数的偏导为:\n", |
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"$$\n", |
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"\\frac{\\partial C}{\\partial w_{ij}} = (-y_i + a_i) x_i\n", |
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"$$\n", |
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"\n", |
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"误差项为:\n", |
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"$$\n", |
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"\\delta_i = -(-y_i + a_i)\n", |
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"$$\n", |
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"\n", |
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"参数跟新公式为:\n", |
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"$$\n", |
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"w_{ij} = w_{ij} + \\eta \\delta_i x_i\n", |
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"$$\n", |
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"\n", |
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"\n", |
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"其中\n", |
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"$$\n", |
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"a_i = \\frac{e^{z_i}}{\\sum_k e^{z_k}}\n", |
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"$$\n", |
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"\n", |
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"$$\n", |
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"z_i = \\sum_{j} w_{ij} x_{j} + w_b\n", |
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"$$\n" |
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"$$\n", |
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"\n" |
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] |
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}, |
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{ |
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"cell_type": "markdown", |
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"metadata": {}, |
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"source": [ |
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"### 3.4 二次代价函数的更行方程\n", |
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"\n", |
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"最为对比,使用二次代价函数的更新方程为:\n", |
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"\n", |
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"$$\n", |
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@@ -245,7 +265,9 @@ |
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"\n", |
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"$$\n", |
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"w_{ji} = w_{ji} + \\eta \\delta_j x_{ji}\n", |
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"$$" |
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"$$\n", |
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"\n", |
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"需要注意这里 $w_{ji}$ 和上面的定义不太一样!" |
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] |
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}, |
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{ |
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@@ -286,7 +308,7 @@ |
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"name": "python", |
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"nbconvert_exporter": "python", |
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"pygments_lexer": "ipython3", |
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"version": "3.5.4" |
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"version": "3.7.9" |
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} |
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}, |
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"nbformat": 4, |
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