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additional typos

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mhjensen
2018-10-19 06:30:26 +02:00
parent 092fdecd9b
commit 97ee7402a8
9 changed files with 54 additions and 60 deletions
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doc/pub/NeuralNet/html/NeuralNet.html
+9 -10
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@@ -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
\( b_i^{(l), \ \mathrm{hidden} } \):