additional typos

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
 $b_i^{(l), \ \mathrm{hidden} }$: