perhaps last typo...grrr

This commit is contained in:
mhjensen
2018-10-19 06:47:47 +02:00
parent d5af6f12c1
commit 5af12ffde4
9 changed files with 12 additions and 12 deletions
@@ -390,7 +390,7 @@ $$
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
@@ -369,7 +369,7 @@ c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2
$$
<p>
In order to minimize it, an optimalization method must be chosen.
In order to minimize it, an optimization method must be chosen.
<p>
Here, gradient descent with a constant step size has been chosen.
+2 -2
View File
@@ -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
<p>&nbsp;<br>
$$
\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(i-t_i)\log{(1-a_i^L)}\right),
\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
$$
<p>&nbsp;<br>
@@ -4048,7 +4048,7 @@ $$
<p>&nbsp;<br>
<p>
In order to minimize it, an optimalization method must be chosen.
In order to minimize it, an optimization method must be chosen.
<p>
Here, gradient descent with a constant step size has been chosen.
@@ -1362,7 +1362,7 @@ $$
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
$$
<p>
In order to minimize it, an optimalization method must be chosen.
In order to minimize it, an optimization method must be chosen.
<p>
Here, gradient descent with a constant step size has been chosen.
+2 -2
View File
@@ -1367,7 +1367,7 @@ $$
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
$$
<p>
In order to minimize it, an optimalization method must be chosen.
In order to minimize it, an optimization method must be chosen.
<p>
Here, gradient descent with a constant step size has been chosen.
+2 -2
View File
@@ -1549,7 +1549,7 @@
"metadata": {},
"source": [
"$$\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",
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+2 -2
View File
@@ -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.