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\author{goldmist}
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  /Title (neural-network-theory.pdf)
  /Creator (Cheatography)
  /Author (goldmist)
  /Subject (Neural Network Theory Cheat Sheet)
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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Neural Network Theory Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{goldmist} via \textcolor{DarkBackground}{\uline{cheatography.com/32798/cs/10160/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}goldmist \\
  \uline{cheatography.com/goldmist} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 9th December, 2016.\\
   Updated 9th December, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Formal Systems}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Cognition, cognitive theory are formal systems, we use mathematics to study them} \tn 
% Row Count 2 (+ 2)
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\mymulticolumn{1}{x{5.377cm}}{Abstract concepts can be reasoned about precisely when situated in formal systems} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Neural networks are continuous systems} \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Constructing the continum}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Axiomatization} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Describe the basic properties and declare them to be true by definition} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Construction} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Use simpler objects and operations to explicitly define more complex models} \tn 
% Row Count 6 (+ 3)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Equivalence classes} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Partitions a set based on some rules} \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Dynamic Systems}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Recurrent ,learning, and biological neural networks} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Motor control is the effector of a dynamic system} \tn 
% Row Count 3 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{The mind is an abstract dynamical system with continuous state variables that are not activation values of units or representations} \tn 
% Row Count 6 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.09494 cm} x{3.88206 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{NNs as Probabilistic Models}}  \tn
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Used for & stochastically searching for global optima \tn 
% Row Count 2 (+ 2)
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 & representing and rationally coping with uncertainty \tn 
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 & measuring information \tn 
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\seqsplit{Deployed} in & neural network models \tn 
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 & symbolic modes with non-determinism and uncertainty (e.g. inferring knowledge from experience, using knowledge to infer outputs given inputs) \tn 
% Row Count 12 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Optimization}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Processing} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Activation dynamics.  Maximizes well-formedness (harmony) of the activation patter (depends on the connection weight).  Spreading activation dynamics is an optimization algorithm for the representation.} \tn 
% Row Count 6 (+ 6)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Learning} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Weight dynamics.  Minimizes error.  Weight-adjustment dynamics is an optimization algorithm for the knownledge in the weights: learning algorithm} \tn 
% Row Count 11 (+ 5)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Probabilistic modelling} \tn 
\mymulticolumn{1}{x{5.377cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Parameters of the statistical model change as more data is received.  Optimized based of likelihood according to data or Bayesian posterior probability of the data} \tn 
% Row Count 16 (+ 5)
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fourier analysis}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{f(x) = \textbackslash{}sum\_k c\_k e\textasciicircum{}\{ikx\} employs a basis of imaginary powers of x, \{e\textasciicircum{}\{ikx\}\}\_\{k \textbackslash{}in \textbackslash{}Z\}} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Also a basis of cos(kx) and sin(kx)} \tn 
% Row Count 3 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{Fourier coefficient states how strongly an oscillation of frequency 1/k is present in f} \tn 
% Row Count 5 (+ 2)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{\{f(t)\}\_t describe f in the time / spatial domain} \tn 
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% Row 4
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\mymulticolumn{1}{x{5.377cm}}{\{c\_k\}\_k describe f in the frequency / spatial-frequency domain} \tn 
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Support Vector Machines}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Use supervised learning to learn a region of activation space for each concept} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Classification driven only by training near the region boundary} \tn 
% Row Count 4 (+ 2)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Wide margin: error function favors a large margin between the training samples and the boundary it posits for separating the categories} \tn 
% Row Count 7 (+ 3)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{Slack variable: minimizes a variable for each training example that "picks up the slack" between the point and the category region it should be in} \tn 
% Row Count 10 (+ 3)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Kernel trick: implicitly maps the data into a high dimensional space in which classification conceptually takes places (implemented through a kernel function)} \tn 
% Row Count 14 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Discrete structures of distribution patterns}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{vectors v in R: distributed representation} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{With respect to an appropriate conceptual basis for V, components of a representation v indicate the strength of a set of basis concepts in v: gradient conceptual representation} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Eigen-basis re-scales components} \tn 
% Row Count 6 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{Analyse the entire distribution within V of the representations \{v\textasciicircum{}k\} of a set of represented items \{x\textasciicircum{}k\}} \tn 
% Row Count 9 (+ 3)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Clusters of \{v\textasciicircum{}k\} constitute a conceptual group and may be hierachically structured} \tn 
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% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Can construct is such that greater distance between v\textasciicircum{}\{k\} and v\textasciicircum{}\{t\} means greater mental distinguishability of x\textasciicircum{}\{k\} and x\textasciicircum{}\textbackslash{}\{t\}} \tn 
% Row Count 14 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Harmony}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Weight matrices, error functions, learning as optimization} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Activation vectors, well-formedness = harmony function, processing as optimzation} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{- Parallel, violable-constraint satisfaction} \tn 
% Row Count 5 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{- Schemas/prototypes in Harmony landscapes} \tn 
% Row Count 6 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Local optima is a deterministic problem, global optima require randomized/stochastic algorithms} \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Inductive learning}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Finding the best hypothesis within a hypothesis space about the word that the learning is trying to understand} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Goodness of a hypothesis is determined jointly by how well H fits the data that the learning has received about the world and how simple H is} \tn 
% Row Count 6 (+ 3)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{A hypothesis is a probabilistic data-generator} \tn 
% Row Count 7 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{Maximum Likelihood Principle} \tn 
% Row Count 8 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Maximum A Posteriori Principle: Bayesian principle that says pick the hypothesis that has highest a posteriori probability, balancing the likelihood of the data against the a priori probability of H.  Best not pick a H, maintain a degree of belief for every H in the H space} \tn 
% Row Count 14 (+ 6)
% Row 5
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\mymulticolumn{1}{x{5.377cm}}{Maximum Entropy Principle: Maxent.  Pick the H with the max missing information, among those H that are consistent with the known data} \tn 
% Row Count 17 (+ 3)
% Row 6
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\mymulticolumn{1}{x{5.377cm}}{Minimum Description Length Principle: shorter is better} \tn 
% Row Count 19 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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% That's all folks
\end{multicols*}

\end{document}