perhaps last typo...grrr
This commit is contained in:
@@ -390,7 +390,7 @@ $$
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where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \).
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Our cost function at the final layer \( l=L \) is now
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$$
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
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$$
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where we have defined the targets \( t_i \). The derivatives of the cost function with respect to the output \( a_i^L \) are then easily calculated and we get
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@@ -369,7 +369,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
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$$
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<p>
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In order to minimize it, an optimalization method must be chosen.
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In order to minimize it, an optimization method must be chosen.
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<p>
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Here, gradient descent with a constant step size has been chosen.
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@@ -1367,7 +1367,7 @@ where the superscript \( l-1 \) indicates that these are the outputs from layer
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Our cost function at the final layer \( l=L \) is now
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<p> <br>
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$$
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
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$$
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<p> <br>
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@@ -4048,7 +4048,7 @@ $$
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<p> <br>
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<p>
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In order to minimize it, an optimalization method must be chosen.
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In order to minimize it, an optimization method must be chosen.
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<p>
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Here, gradient descent with a constant step size has been chosen.
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@@ -1362,7 +1362,7 @@ $$
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where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \).
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Our cost function at the final layer \( l=L \) is now
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$$
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
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$$
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where we have defined the targets \( t_i \). The derivatives of the cost function with respect to the output \( a_i^L \) are then easily calculated and we get
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@@ -3909,7 +3909,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
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$$
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<p>
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In order to minimize it, an optimalization method must be chosen.
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In order to minimize it, an optimization method must be chosen.
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<p>
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Here, gradient descent with a constant step size has been chosen.
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@@ -1367,7 +1367,7 @@ $$
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where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \).
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Our cost function at the final layer \( l=L \) is now
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$$
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
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$$
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where we have defined the targets \( t_i \). The derivatives of the cost function with respect to the output \( a_i^L \) are then easily calculated and we get
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@@ -3914,7 +3914,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
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$$
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<p>
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In order to minimize it, an optimalization method must be chosen.
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In order to minimize it, an optimization method must be chosen.
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<p>
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Here, gradient descent with a constant step size has been chosen.
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@@ -1549,7 +1549,7 @@
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"metadata": {},
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"source": [
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"$$\n",
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"\\mathcal{C}(\\hat{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(i-t_i)\\log{(1-a_i^L)}\\right),\n",
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"\\mathcal{C}(\\hat{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
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"$$"
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]
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},
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@@ -4352,7 +4352,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In order to minimize it, an optimalization method must be chosen. \n",
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"In order to minimize it, an optimization method must be chosen. \n",
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"\n",
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"Here, gradient descent with a constant step size has been chosen. \n",
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"\n",
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@@ -995,7 +995,7 @@ where the superscript $l-1$ indicates that these are the outputs from layer $l-1
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Our cost function at the final layer $l=L$ is now
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!bt
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\[
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
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\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
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\]
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!et
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where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get
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@@ -3281,7 +3281,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
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\]
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!et
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In order to minimize it, an optimalization method must be chosen.
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In order to minimize it, an optimization method must be chosen.
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Here, gradient descent with a constant step size has been chosen.
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