From 619717e18e02dbeaf63fa84485b1acd3e6cd2fca Mon Sep 17 00:00:00 2001
From: Petr Baudis <pasky@ucw.cz>
Date: Sun, 14 Mar 2010 03:20:38 +0100
Subject: [PATCH] tex: Typeset nits

---
 tex/gostyle.tex | 9 ++-------
 1 file changed, 2 insertions(+), 7 deletions(-)

diff --git a/tex/gostyle.tex b/tex/gostyle.tex
index c5d5028..e46b041 100644
--- a/tex/gostyle.tex
+++ b/tex/gostyle.tex
@@ -685,9 +685,8 @@ where $J$ is the previous layer, while $y_j$ is the activation for neurons from
 Function $f()$ is a~so-called \emph{activation function}
 and its purpose is to bound the outputs of neurons.
 A typical example of an activation function is the sigmoid function.%
-\footnote{A special case of the logistic function, defined by the formula
-$\sigma(x)=\frac{1}{1+e^{-(rx+k)}}$; parameters control the growth rate ($r$)
-and the x-position ($k$).}
+\footnote{A special case of the logistic function $\sigma(x)=(1+e^{-(rx+k)})^{-1}$.
+Parameters control the growth rate $r$ and the x-position $k$.}
 
 \subsubsection{Training}
 Training of the feed-forward neural network usually involves some
@@ -752,15 +751,11 @@ When training the classifier for $\vec O$ element $o_i$
 of class $c = \lfloor o_i/k \rfloor$,
 we assume the $\vec R$ elements are normally distributed and
 feed the classifier information in the form
-
 $$ \vec R \mid c $$
-
 estimating the mean $\mu_c$ and standard deviation $\sigma_c$
 of each $\vec R$ element for each encountered $c$.
 Then, we can query the built probability model on
-
 $$ \max_c P(c \mid \vec R) $$
-
 obtaining the most probable class $i$ for an arbitrary $\vec R$.
 Each probability is obtained using the normal distribution formula:
 $$ P(c \mid x) = {1\over \sqrt{2\pi\sigma_c^2}}\exp{-(x-\mu_c)^2\over2\sigma_c^2} $$
-- 
2.11.4.GIT