-In order to minimize it, an optimalization method must be chosen. +In order to minimize it, an optimization method must be chosen.
Here, gradient descent with a constant step size has been chosen. diff --git a/doc/pub/NeuralNet/html/NeuralNet-reveal.html b/doc/pub/NeuralNet/html/NeuralNet-reveal.html index 9ec93ee5b..30803e519 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-reveal.html +++ b/doc/pub/NeuralNet/html/NeuralNet-reveal.html @@ -1367,7 +1367,7 @@ where the superscript \( l-1 \) indicates that these are the outputs from layer Our cost function at the final layer \( l=L \) is now
$$
-\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
+\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
$$
@@ -4048,7 +4048,7 @@ $$
-In order to minimize it, an optimalization method must be chosen. +In order to minimize it, an optimization method must be chosen.
Here, gradient descent with a constant step size has been chosen. diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html index f5c9407fe..95c8c283e 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html +++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html @@ -1362,7 +1362,7 @@ $$ where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \). Our cost function at the final layer \( l=L \) is now $$ -\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right), +\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right), $$ 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 @@ -3909,7 +3909,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 $$
-In order to minimize it, an optimalization method must be chosen. +In order to minimize it, an optimization method must be chosen.
Here, gradient descent with a constant step size has been chosen. diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html index 67f62dbb7..37461c5ce 100644 --- a/doc/pub/NeuralNet/html/NeuralNet.html +++ b/doc/pub/NeuralNet/html/NeuralNet.html @@ -1367,7 +1367,7 @@ $$ where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \). Our cost function at the final layer \( l=L \) is now $$ -\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right), +\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right), $$ 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 @@ -3914,7 +3914,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 $$
-In order to minimize it, an optimalization method must be chosen. +In order to minimize it, an optimization method must be chosen.
Here, gradient descent with a constant step size has been chosen. diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb index 4a8251538..097b9083c 100644 --- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb +++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb @@ -1549,7 +1549,7 @@ "metadata": {}, "source": [ "$$\n", - "\\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", + "\\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", "$$" ] }, @@ -4352,7 +4352,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In order to minimize it, an optimalization method must be chosen. \n", + "In order to minimize it, an optimization method must be chosen. \n", "\n", "Here, gradient descent with a constant step size has been chosen. \n", "\n", diff --git a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz index e098aee2c..8412488c5 100644 Binary files a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz and b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz differ diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf index 108191e10..cbe373bc0 100644 Binary files a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf and b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf differ diff --git a/doc/src/NeuralNet/NeuralNet.do.txt b/doc/src/NeuralNet/NeuralNet.do.txt index 5c0da3c04..0735a92d2 100644 --- a/doc/src/NeuralNet/NeuralNet.do.txt +++ b/doc/src/NeuralNet/NeuralNet.do.txt @@ -995,7 +995,7 @@ where the superscript $l-1$ indicates that these are the outputs from layer $l-1 Our cost function at the final layer $l=L$ is now !bt \[ -\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right), +\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right), \] !et 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 @@ -3281,7 +3281,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 \] !et -In order to minimize it, an optimalization method must be chosen. +In order to minimize it, an optimization method must be chosen. Here, gradient descent with a constant step size has been chosen.