typos typos typos grrrr
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@@ -263,7 +263,7 @@ MathJax.Hub.Config({
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In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation \( z_i^l \), that is we need
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$$
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\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l}.
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
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$$
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For the Softmax function we have
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@@ -1388,7 +1388,7 @@ In case we employ the more general case given by the Softmax equation, we need t
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<p> <br>
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$$
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\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l}.
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
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$$
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<p> <br>
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@@ -1321,7 +1321,7 @@ In case we use another activation function than the logistic one, we need to eva
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In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation \( z_i^l \), that is we need
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$$
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\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l}.
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
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$$
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For the Softmax function we have
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@@ -1326,7 +1326,7 @@ In case we use another activation function than the logistic one, we need to eva
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In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation \( z_i^l \), that is we need
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$$
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\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l}.
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
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$$
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For the Softmax function we have
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@@ -1586,7 +1586,7 @@
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"source": [
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"$$\n",
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"\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
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"\\frac{\\partial f(z_i^l)}{\\partial z_j^l} \\frac{\\partial z_j^l}{\\partial w_{jk}^l}= \\frac{\\partial f(z_i^l)}{\\partial z_j^l}a_k^{l}.\n",
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"\\frac{\\partial f(z_i^l)}{\\partial z_j^l} \\frac{\\partial z_j^l}{\\partial w_{jk}^l}= \\frac{\\partial f(z_i^l)}{\\partial z_j^l}a_k^{l-1}.\n",
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"$$"
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]
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},
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@@ -1013,7 +1013,7 @@ In case we employ the more general case given by the Softmax equation, we need t
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!bt
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\[
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\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l}.
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\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
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\]
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!et
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For the Softmax function we have
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