additional typos

doc/pub/NeuralNet/html/._NeuralNet-bs099.html

@@ -370,24 +370,24 @@ The idea of the gradient descent algorithm is to update parameters in
 direction where the cost function decreases goes to a minimum.
 
 <p>
-In general, the update of some parameters \( \vec \omega \) given a cost
-function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
+In general, the update of some parameters \( \hat{\omega} \) given a cost
+function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
 goes as follows:
 
 $$
-\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
+\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
 $$
 
 <p>
-for a number of iterations or until $ \big|\big| \vec
-\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
+for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) 
+is smaller than some
 given tolerance.
 
 <p>
 The value of \( \lambda \) decides how large steps the algorithm must take
-in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
-notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
-the elements in \( \vec \omega \).
+in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
+notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
+the elements in \( \hat{\omega} \).
 
 <p>
 <p>

doc/pub/NeuralNet/html/._NeuralNet-bs102.html

@@ -372,8 +372,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri
 The \( i \)-th neuron at layer \( l \) recieves the result
 \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
 \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec
-w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are
+\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
 elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
 \( b_i^{(l), \ \mathrm{hidden} } \):
 

doc/pub/NeuralNet/html/NeuralNet-reveal.html

@@ -4238,26 +4238,26 @@ The idea of the gradient descent algorithm is to update parameters in
 direction where the cost function decreases goes to a minimum.
 
 <p>
-In general, the update of some parameters \( \vec \omega \) given a cost
-function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
+In general, the update of some parameters \( \hat{\omega} \) given a cost
+function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
 goes as follows:
 
 <p>&nbsp;<br>
 $$
-\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
+\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
 $$
 <p>&nbsp;<br>
 
 <p>
-for a number of iterations or until $ \big|\big| \vec
-\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
+for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) 
+is smaller than some
 given tolerance.
 
 <p>
 The value of \( \lambda \) decides how large steps the algorithm must take
-in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
-notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
-the elements in \( \vec \omega \).
+in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
+notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
+the elements in \( \hat{\omega} \).
 </section>
 
 
@@ -4353,8 +4353,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri
 The \( i \)-th neuron at layer \( l \) recieves the result
 \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
 \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec
-w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are
+\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
 elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
 \( b_i^{(l), \ \mathrm{hidden} } \):
 

doc/pub/NeuralNet/html/NeuralNet-solarized.html

@@ -4090,24 +4090,24 @@ The idea of the gradient descent algorithm is to update parameters in
 direction where the cost function decreases goes to a minimum.
 
 <p>
-In general, the update of some parameters \( \vec \omega \) given a cost
-function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
+In general, the update of some parameters \( \hat{\omega} \) given a cost
+function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
 goes as follows:
 
 $$
-\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
+\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
 $$
 
 <p>
-for a number of iterations or until $ \big|\big| \vec
-\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
+for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) 
+is smaller than some
 given tolerance.
 
 <p>
 The value of \( \lambda \) decides how large steps the algorithm must take
-in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
-notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
-the elements in \( \vec \omega \).
+in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
+notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
+the elements in \( \hat{\omega} \).
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -4200,8 +4200,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri
 The \( i \)-th neuron at layer \( l \) recieves the result
 \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
 \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec
-w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are
+\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
 elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
 \( b_i^{(l), \ \mathrm{hidden} } \):
 

doc/pub/NeuralNet/html/NeuralNet.html

@@ -4095,24 +4095,24 @@ The idea of the gradient descent algorithm is to update parameters in
 direction where the cost function decreases goes to a minimum.
 
 <p>
-In general, the update of some parameters \( \vec \omega \) given a cost
-function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
+In general, the update of some parameters \( \hat{\omega} \) given a cost
+function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
 goes as follows:
 
 $$
-\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
+\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
 $$
 
 <p>
-for a number of iterations or until $ \big|\big| \vec
-\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
+for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) 
+is smaller than some
 given tolerance.
 
 <p>
 The value of \( \lambda \) decides how large steps the algorithm must take
-in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
-notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
-the elements in \( \vec \omega \).
+in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
+notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
+the elements in \( \hat{\omega} \).
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -4205,8 +4205,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri
 The \( i \)-th neuron at layer \( l \) recieves the result
 \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer
 \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in
-\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec
-w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are
+\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are
 elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
 \( b_i^{(l), \ \mathrm{hidden} } \):
 

doc/pub/NeuralNet/ipynb/NeuralNet.ipynb

@@ -4545,8 +4545,8 @@
     "The idea of the gradient descent algorithm is to update parameters in\n",
     "direction where the cost function decreases goes to a minimum.\n",
     "\n",
-    "In general, the update of some parameters $\\vec \\omega$ given a cost\n",
-    "function defined by some weights $\\vec \\omega$, $c(x, \\vec \\omega)$,\n",
+    "In general, the update of some parameters $\\hat{\\omega}$ given a cost\n",
+    "function defined by some weights $\\hat{\\omega}$, $c(x, \\hat{\\omega})$,\n",
     "goes as follows:"
    ]
   },
@@ -4555,7 +4555,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\vec \\omega_{\\mathrm{new} } = \\vec \\omega - \\lambda \\nabla_{\\vec \\omega} c(x, \\vec \\omega),\n",
+    "\\hat{\\omega}_{\\mathrm{new} } = \\hat{\\omega} - \\lambda \\nabla_{\\hat{\\omega}} c(x, \\hat{\\omega}),\n",
     "$$"
    ]
   },
@@ -4563,14 +4563,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "for a number of iterations or until $ \\big|\\big| \\vec\n",
-    "\\omega_{\\mathrm{new} } - \\vec \\omega \\big|\\big|$ is smaller than some\n",
+    "for a number of iterations or until $\\big|\\big| \\hat{\\omega}_{\\mathrm{new} } - \\hat{\\omega} \\big|\\big|$ \n",
+    "is smaller than some\n",
     "given tolerance.\n",
     "\n",
     "The value of $\\lambda$ decides how large steps the algorithm must take\n",
-    "in the direction of $ \\nabla_{\\vec \\omega} c(x, \\vec \\omega)$. The\n",
-    "notatation $\\nabla_{\\vec \\omega}$ denotes the gradient with respect to\n",
-    "the elements in $\\vec \\omega$.\n",
+    "in the direction of $ \\nabla_{\\hat{\\omega}} c(x, \\hat{\\omega})$. The\n",
+    "notatation $\\nabla_{\\hat{\\omega}}$ denotes the gradient with respect to\n",
+    "the elements in $\\hat{\\omega}$.\n",
     "\n",
     "\n",
     "## More on GD and cost function\n",
@@ -4671,8 +4671,7 @@
     "The $i$-th neuron at layer $l$ recieves the result\n",
     "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ from the $j$-th neuron at layer\n",
     "$l-1$. The $i$-th neuron at layer $l$ weights all of the elements in\n",
-    "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ with a weight vector $\\vec\n",
-    "w_{i,j}^{(l), \\ \\mathrm{hidden} }$ with as many weigths as there are\n",
+    "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \\ \\mathrm{hidden}}$ with as many weigths as there are\n",
     "elements in$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$, and adds a bias\n",
     "$b_i^{(l), \\ \\mathrm{hidden} }$:"
    ]

doc/src/NeuralNet/NeuralNet.do.txt

@@ -3436,24 +3436,24 @@ def cost_function(P, x):
 The idea of the gradient descent algorithm is to update parameters in
 direction where the cost function decreases goes to a minimum.
 
-In general, the update of some parameters $\vec \omega$ given a cost
-function defined by some weights $\vec \omega$, $c(x, \vec \omega)$,
+In general, the update of some parameters $\hat{\omega}$ given a cost
+function defined by some weights $\hat{\omega}$, $c(x, \hat{\omega})$,
 goes as follows:
 
 !bt
 \[
-\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
+\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
 \]
 !et
 
-for a number of iterations or until $ \big|\big| \vec
-\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
+for a number of iterations or until $\big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big|$ 
+is smaller than some
 given tolerance.
 
 The value of $\lambda$ decides how large steps the algorithm must take
-in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
-notatation $\nabla_{\vec \omega}$ denotes the gradient with respect to
-the elements in $\vec \omega$.
+in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
+notatation $\nabla_{\hat{\omega}}$ denotes the gradient with respect to
+the elements in $\hat{\omega}$.
 
 
 !split
@@ -3536,8 +3536,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri
 The $i$-th neuron at layer $l$ recieves the result
 $\hat{x}_j^{(l-1),\mathrm{hidden} }$ from the $j$-th neuron at layer
 $l-1$. The $i$-th neuron at layer $l$ weights all of the elements in
-$\hat{x}_j^{(l-1),\mathrm{hidden} }$ with a weight vector $\vec
-w_{i,j}^{(l), \ \mathrm{hidden} }$ with as many weigths as there are
+$\hat{x}_j^{(l-1),\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \ \mathrm{hidden}}$ with as many weigths as there are
 elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias
 $b_i^{(l), \ \mathrm{hidden} }$: