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‎docs/_config.yml

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@@ -38,6 +38,7 @@ kramdown:
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exclude:
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- jekyllbook
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- en/index.md
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- vendor
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################################### English ####################################
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prologues:

‎docs/en/week11/11-1.md

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@@ -30,7 +30,7 @@ There are variations in ReLU. The Random ReLU (RReLU) is defined as follows.
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$$
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\text{RReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
@@ -47,7 +47,7 @@ Note that for RReLU, $a$ is a random variable that keeps samplings in a given ra
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$$
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\text{LeakyReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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a_\text{negative slope}x, & \text{otherwise}
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\end{cases}
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$$
@@ -66,7 +66,7 @@ LeakyReLU is necessary for skinny network, which is almost impossible to get gra
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$$
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\text{PReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
@@ -209,8 +209,8 @@ It is similar to the Sigmoid function but gets to the asymptote slowly and allev
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$$
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\text{HardTanh}(x) = \begin{cases}
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1, & \text{if $x > 1$}\\
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-1, & \text{if $x < -1$}\\
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1, & \text{if} x > 1\\
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-1, & \text{if} x < -1\\
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x, & \text{otherwise}
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\end{cases}
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$$
@@ -229,7 +229,7 @@ It works surprisingly well especially when weights are kept within the small val
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$$
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y = \begin{cases}
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x, & \text{if $x > \text{threshold}$}\\
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x, & \text{if} x > \text{threshold}\\
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v, & \text{otherwise}
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\end{cases}
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$$
@@ -255,8 +255,8 @@ It is rarely used except for sparse coding to compute the value of the latent va
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$$
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\text{SoftShrinkage}(x) = \begin{cases}
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x - \lambda, & \text{if $x > \lambda$}\\
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x + \lambda, & \text{if $x < -\lambda$}\\
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x - \lambda, & \text{if} x > \lambda\\
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x + \lambda, & \text{if} x < -\lambda\\
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0, & \text{otherwise}
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\end{cases}
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$$
@@ -273,8 +273,8 @@ This basically shrinks the variable by a constant towards 0, and forces to 0 if
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$$
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\text{HardShrinkage}(x) = \begin{cases}
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x, & \text{if $x > \lambda$}\\
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x, & \text{if $x < -\lambda$}\\
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x, & \text{if} x > \lambda\\
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x, & \text{if} x < -\lambda\\
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0, & \text{otherwise}
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\end{cases}
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$$

‎docs/en/week13/13-2.md

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@@ -156,7 +156,7 @@ Matrix representation being,
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$$h^{l+1} = \eta(\boldsymbol{D}^{-1}\boldsymbol{A}h^{l}\boldsymbol{W}^{l})$$
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where, \boldsymbol{A} has the dimensions $n \times n$, $h^{l}$ has dimensions $n \times d$ and $W^{l}$ has $d \times d$, which results in a $n \times d$ $h^{l+1}$ matrix.
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where, $\boldsymbol{A}$ has the dimensions $n \times n$, $h^{l}$ has dimensions $n \times d$ and $W^{l}$ has $d \times d$, which results in a $n \times d$ $h^{l+1}$ matrix.
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And the vectorial representation being,
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‎docs/es/week11/11-1.md

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@@ -62,15 +62,15 @@ Hay variaciones de la ReLU. La ReLU Aleatoria (RReLU, por sus siglas en inglés)
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<!--$$
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\text{RReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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-->
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$$
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\text{RReLU}(x) = \begin{cases}
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x, & \text{si $x \geq 0$}\\
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x, & \text{si} x \geq 0\\
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ax, & \text{en otro caso}
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\end{cases}
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$$
@@ -100,15 +100,15 @@ Recuerda que para la RReLU, $a$ es una variable aleatoria que se muestrea consta
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<!--$$
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\text{LeakyReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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a_\text{negative slope}x, & \text{otherwise}
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\end{cases}
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$$
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-->
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$$
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\text{LeakyReLU}(x) = \begin{cases}
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x, & \text{si $x \geq 0$}\\
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x, & \text{si} x \geq 0\\
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a_\text{pendiente negativa}x, & \text{en otro caso}
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\end{cases}
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$$
@@ -143,15 +143,15 @@ La LeakyReLU es necesaria para las redes neuronales delgadas, en las que es casi
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<!--$$
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\text{PReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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-->
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$$
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\text{PReLU}(x) = \begin{cases}
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x, & \text{si $x \geq 0$}\\
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x, & \text{si} x \geq 0\\
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ax, & \text{en otro caso}
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\end{cases}
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$$
@@ -469,17 +469,17 @@ Es similar a la función Sigmoide pero se acerca lentamente a la asíntota y has
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<!--$$
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\text{HardTanh}(x) = \begin{cases}
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1, & \text{if $x > 1$}\\
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-1, & \text{if $x < -1$}\\
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1, & \text{if} x > 1\\
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-1, & \text{if} x < -1\\
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x, & \text{otherwise}
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\end{cases}
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$$
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-->
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$$
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\text{Tanh dura}(x) = \begin{cases}
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1, & \text{si $x > 1$}\\
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-1, & \text{si $x < -1$}\\
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1, & \text{si} x > 1\\
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-1, & \text{si} x < -1\\
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x, & \text{en otro caso}
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\end{cases}
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$$
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<!--$$
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y = \begin{cases}
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x, & \text{if $x > \text{threshold}$}\\
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x, & \text{if} x > \text{threshold}\\
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v, & \text{otherwise}
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\end{cases}
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$$
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$$
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y = \begin{cases}
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x, & \text{si $x > \text{umbral}$}\\
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x, & \text{si} x > \text{umbral}\\
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v, & \text{en otro caso}
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\end{cases}
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$$
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<!--$$
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\text{SoftShrinkage}(x) = \begin{cases}
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x - \lambda, & \text{if $x > \lambda$}\\
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x + \lambda, & \text{if $x < -\lambda$}\\
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x - \lambda, & \text{if} x > \lambda\\
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x + \lambda, & \text{if} x < -\lambda\\
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0, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{Encogimiento suave}(x) = \begin{cases}
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x - \lambda, & \text{si $x > \lambda$}\\
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x + \lambda, & \text{si $x < -\lambda$}\\
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x - \lambda, & \text{si} x > \lambda\\
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x + \lambda, & \text{si} x < -\lambda\\
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0, & \text{en otro caso}
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\end{cases}
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$$
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<!--$$
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\text{HardShrinkage}(x) = \begin{cases}
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x, & \text{if $x > \lambda$}\\
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x, & \text{if $x < -\lambda$}\\
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x, & \text{if} x > \lambda\\
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x, & \text{if} x < -\lambda\\
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0, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{EncogimientoDuro}(x) = \begin{cases}
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x, & \text{si $x > \lambda$}\\
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x, & \text{si $x < -\lambda$}\\
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x, & \text{si} x > \lambda\\
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x, & \text{si} x < -\lambda\\
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0, & \text{en otro caso}
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\end{cases}
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$$

‎docs/fr/week11/11-1.md

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@@ -53,7 +53,7 @@ There are variations in ReLU. The Random ReLU (RReLU) is defined as follows.
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$$
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\text{RReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{RReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{LeakyReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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a_\text{negative slope}x, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{LeakyReLU}(x) = \begin{cases}
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x, & \text{if} x \geq 0\\
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a_\text{negative slope}x, & \text{otherwise}
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\end{cases}
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$$
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\text{PReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{PReLU}(x) = \begin{cases}
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x, & \text{if $x \geq 0$}\\
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x, & \text{if} x \geq 0\\
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ax, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{HardTanh}(x) = \begin{cases}
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1, & \text{if $x > 1$}\\
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-1, & \text{if $x < -1$}\\
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1, & \text{if} x > 1\\
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-1, & \text{if} x < -1\\
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x, & \text{otherwise}
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\end{cases}
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$$
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$$
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\text{HardTanh}(x) = \begin{cases}
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1, & \text{if $x > 1$}\\
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-1, & \text{if $x < -1$}\\
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1, & \text{if} x > 1\\
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-1, & \text{if} x < -1\\
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x, & \text{otherwise}
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\end{cases}
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$$
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$$
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y = \begin{cases}
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x, & \text{if $x > \text{threshold}$}\\
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x, & \text{if} x > \text{threshold}\\
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v, & \text{otherwise}
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\end{cases}
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$$
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$$
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y = \begin{cases}
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x, & \text{if $x > \text{threshold}$}\\
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x, & \text{if} x > \text{threshold}\\
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v, & \text{otherwise}
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\end{cases}
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$$
@@ -519,8 +519,8 @@ Elle est rarement utilisée sauf pour les codages épars afin de calculer la val
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$$
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\text{SoftShrinkage}(x) = \begin{cases}
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x - \lambda, & \text{if $x > \lambda$}\\
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x + \lambda, & \text{if $x < -\lambda$}\\
522+
x - \lambda, & \text{if} x > \lambda\\
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x + \lambda, & \text{if} x < -\lambda\\
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0, & \text{otherwise}
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\end{cases}
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$$
@@ -537,8 +537,8 @@ This basically shrinks the variable by a constant towards 0, and forces to 0 if
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$$
539539
\text{SoftShrinkage}(x) = \begin{cases}
540-
x - \lambda, & \text{if $x > \lambda$}\\
541-
x + \lambda, & \text{if $x < -\lambda$}\\
540+
x - \lambda, & \text{if} x > \lambda\\
541+
x + \lambda, & \text{if} x < -\lambda\\
542542
0, & \text{otherwise}
543543
\end{cases}
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$$
@@ -556,8 +556,8 @@ Essentiellement, cela réduit la variable d'une constante vers 0 et la force à
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$$
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\text{HardShrinkage}(x) = \begin{cases}
559-
x, & \text{if $x > \lambda$}\\
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x, & \text{if $x < -\lambda$}\\
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x, & \text{if} x > \lambda\\
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x, & \text{if} x < -\lambda\\
561561
0, & \text{otherwise}
562562
\end{cases}
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$$
@@ -574,8 +574,8 @@ It is rarely used except for sparse coding.
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$$
576576
\text{HardShrinkage}(x) = \begin{cases}
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x, & \text{if $x > \lambda$}\\
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x, & \text{if $x < -\lambda$}\\
577+
x, & \text{if} x > \lambda\\
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x, & \text{if} x < -\lambda\\
579579
0, & \text{otherwise}
580580
\end{cases}
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$$

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