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updating week 41
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‎doc/pub/week41/html/week41-bs.html‎

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‎doc/pub/week41/html/week41-reveal.html‎

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‎doc/pub/week41/html/week41-solarized.html‎

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‎doc/pub/week41/html/week41.html‎

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‎doc/pub/week41/ipynb/ipynb-week41-src.tar.gz‎

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‎doc/pub/week41/ipynb/week41.ipynb‎

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‎doc/src/week41/.ipynb_checkpoints/week41-checkpoint.ipynb‎

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‎doc/src/week41/_minted/65E03FF20B6B3DC1E8F8756667419FF9.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{\PYGZus{}\PYGZus{}future\PYGZus{}\PYGZus{}}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{n}{division}
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{sympy}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{o}{*}
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\PYG{n}{x} \PYG{o}{=} \PYG{n}{symbols}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{x}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{expr} \PYG{o}{=} \PYG{n}{sqrt}\PYG{p}{(}\PYG{n}{x}\PYG{o}{*}\PYG{n}{x}\PYG{o}{+}\PYG{n}{exp}\PYG{p}{(}\PYG{n}{x}\PYG{o}{*}\PYG{n}{x}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{simplify}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{)}
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\PYG{n}{derivative} \PYG{o}{=} \PYG{n}{diff}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{,}\PYG{n}{x}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{derivative}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week41/_minted/93B9C4D3B722A5D46E6B643B143D1A87.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{numpy}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{np}
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\PYG{c+c1}{\PYGZsh{} We use the Sigmoid function as activation function}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{sigmoid}\PYG{p}{(}\PYG{n}{z}\PYG{p}{)}\PYG{p}{:}
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\PYG{k}{return} \PYG{l+m+mf}{1.0}\PYG{o}{/}\PYG{p}{(}\PYG{l+m+mf}{1.0}\PYG{o}{+}\PYG{n}{np}\PYG{o}{.}\PYG{n}{exp}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{n}{z}\PYG{p}{)}\PYG{p}{)}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{forwardpropagation}\PYG{p}{(}\PYG{n}{x}\PYG{p}{)}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} weighted sum of inputs to the hidden layer}
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\PYG{n}{z\PYGZus{}1} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matmul}\PYG{p}{(}\PYG{n}{x}\PYG{p}{,} \PYG{n}{w\PYGZus{}1}\PYG{p}{)} \PYG{o}{+} \PYG{n}{b\PYGZus{}1}
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\PYG{c+c1}{\PYGZsh{} activation in the hidden layer}
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\PYG{n}{a\PYGZus{}1} \PYG{o}{=} \PYG{n}{sigmoid}\PYG{p}{(}\PYG{n}{z\PYGZus{}1}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} weighted sum of inputs to the output layer}
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\PYG{n}{z\PYGZus{}2} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matmul}\PYG{p}{(}\PYG{n}{a\PYGZus{}1}\PYG{p}{,} \PYG{n}{w\PYGZus{}2}\PYG{p}{)} \PYG{o}{+} \PYG{n}{b\PYGZus{}2}
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\PYG{n}{a\PYGZus{}2} \PYG{o}{=} \PYG{n}{z\PYGZus{}2}
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\PYG{k}{return} \PYG{n}{a\PYGZus{}1}\PYG{p}{,} \PYG{n}{a\PYGZus{}2}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{backpropagation}\PYG{p}{(}\PYG{n}{x}\PYG{p}{,} \PYG{n}{y}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{a\PYGZus{}1}\PYG{p}{,} \PYG{n}{a\PYGZus{}2} \PYG{o}{=} \PYG{n}{forwardpropagation}\PYG{p}{(}\PYG{n}{x}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} parameter delta for the output layer, note that a\PYGZus{}2=z\PYGZus{}2 and its derivative wrt z\PYGZus{}2 is just 1}
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\PYG{n}{delta\PYGZus{}2} \PYG{o}{=} \PYG{n}{a\PYGZus{}2} \PYG{o}{\PYGZhy{}} \PYG{n}{y}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+m+mf}{0.5}\PYG{o}{*}\PYG{p}{(}\PYG{p}{(}\PYG{n}{a\PYGZus{}2}\PYG{o}{\PYGZhy{}}\PYG{n}{y}\PYG{p}{)}\PYG{o}{*}\PYG{o}{*}\PYG{l+m+mi}{2}\PYG{p}{)}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} delta for the hidden layer}
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\PYG{n}{delta\PYGZus{}1} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matmul}\PYG{p}{(}\PYG{n}{delta\PYGZus{}2}\PYG{p}{,} \PYG{n}{w\PYGZus{}2}\PYG{o}{.}\PYG{n}{T}\PYG{p}{)} \PYG{o}{*} \PYG{n}{a\PYGZus{}1} \PYG{o}{*} \PYG{p}{(}\PYG{l+m+mi}{1} \PYG{o}{\PYGZhy{}} \PYG{n}{a\PYGZus{}1}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} gradients for the output layer}
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\PYG{n}{output\PYGZus{}weights\PYGZus{}gradient} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matmul}\PYG{p}{(}\PYG{n}{a\PYGZus{}1}\PYG{o}{.}\PYG{n}{T}\PYG{p}{,} \PYG{n}{delta\PYGZus{}2}\PYG{p}{)}
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\PYG{n}{output\PYGZus{}bias\PYGZus{}gradient} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{sum}\PYG{p}{(}\PYG{n}{delta\PYGZus{}2}\PYG{p}{,} \PYG{n}{axis}\PYG{o}{=}\PYG{l+m+mi}{0}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} gradient for the hidden layer}
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\PYG{n}{hidden\PYGZus{}weights\PYGZus{}gradient} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{matmul}\PYG{p}{(}\PYG{n}{x}\PYG{o}{.}\PYG{n}{T}\PYG{p}{,} \PYG{n}{delta\PYGZus{}1}\PYG{p}{)}
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\PYG{n}{hidden\PYGZus{}bias\PYGZus{}gradient} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{sum}\PYG{p}{(}\PYG{n}{delta\PYGZus{}1}\PYG{p}{,} \PYG{n}{axis}\PYG{o}{=}\PYG{l+m+mi}{0}\PYG{p}{)}
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\PYG{k}{return} \PYG{n}{output\PYGZus{}weights\PYGZus{}gradient}\PYG{p}{,} \PYG{n}{output\PYGZus{}bias\PYGZus{}gradient}\PYG{p}{,} \PYG{n}{hidden\PYGZus{}weights\PYGZus{}gradient}\PYG{p}{,} \PYG{n}{hidden\PYGZus{}bias\PYGZus{}gradient}
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\PYG{c+c1}{\PYGZsh{} ensure the same random numbers appear every time}
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\PYG{n}{np}\PYG{o}{.}\PYG{n}{random}\PYG{o}{.}\PYG{n}{seed}\PYG{p}{(}\PYG{l+m+mi}{0}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} Input variable}
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\PYG{n}{x} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mf}{4.0}\PYG{p}{]}\PYG{p}{,}\PYG{n}{dtype}\PYG{o}{=}\PYG{n}{np}\PYG{o}{.}\PYG{n}{float64}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} Target values}
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\PYG{n}{y} \PYG{o}{=} \PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{x}\PYG{o}{+}\PYG{l+m+mf}{1.0}
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\PYG{c+c1}{\PYGZsh{} Defining the neural network, only scalars here}
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\PYG{n}{n\PYGZus{}inputs} \PYG{o}{=} \PYG{n}{x}\PYG{o}{.}\PYG{n}{shape}
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\PYG{n}{n\PYGZus{}features} \PYG{o}{=} \PYG{l+m+mi}{1}
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\PYG{n}{n\PYGZus{}hidden\PYGZus{}neurons} \PYG{o}{=} \PYG{l+m+mi}{1}
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\PYG{n}{n\PYGZus{}outputs} \PYG{o}{=} \PYG{l+m+mi}{1}
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\PYG{c+c1}{\PYGZsh{} Initialize the network}
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\PYG{c+c1}{\PYGZsh{} weights and bias in the hidden layer}
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\PYG{n}{w\PYGZus{}1} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{random}\PYG{o}{.}\PYG{n}{randn}\PYG{p}{(}\PYG{n}{n\PYGZus{}features}\PYG{p}{,} \PYG{n}{n\PYGZus{}hidden\PYGZus{}neurons}\PYG{p}{)}
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\PYG{n}{b\PYGZus{}1} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n}{n\PYGZus{}hidden\PYGZus{}neurons}\PYG{p}{)} \PYG{o}{+} \PYG{l+m+mf}{0.01}
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\PYG{c+c1}{\PYGZsh{} weights and bias in the output layer}
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\PYG{n}{w\PYGZus{}2} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{random}\PYG{o}{.}\PYG{n}{randn}\PYG{p}{(}\PYG{n}{n\PYGZus{}hidden\PYGZus{}neurons}\PYG{p}{,} \PYG{n}{n\PYGZus{}outputs}\PYG{p}{)}
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\PYG{n}{b\PYGZus{}2} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n}{n\PYGZus{}outputs}\PYG{p}{)} \PYG{o}{+} \PYG{l+m+mf}{0.01}
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\PYG{n}{eta} \PYG{o}{=} \PYG{l+m+mf}{0.1}
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\PYG{k}{for} \PYG{n}{i} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{l+m+mi}{50}\PYG{p}{)}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} calculate gradients}
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\PYG{n}{derivW2}\PYG{p}{,} \PYG{n}{derivB2}\PYG{p}{,} \PYG{n}{derivW1}\PYG{p}{,} \PYG{n}{derivB1} \PYG{o}{=} \PYG{n}{backpropagation}\PYG{p}{(}\PYG{n}{x}\PYG{p}{,} \PYG{n}{y}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} update weights and biases}
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\PYG{n}{w\PYGZus{}2} \PYG{o}{\PYGZhy{}}\PYG{o}{=} \PYG{n}{eta} \PYG{o}{*} \PYG{n}{derivW2}
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\PYG{n}{b\PYGZus{}2} \PYG{o}{\PYGZhy{}}\PYG{o}{=} \PYG{n}{eta} \PYG{o}{*} \PYG{n}{derivB2}
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\PYG{n}{w\PYGZus{}1} \PYG{o}{\PYGZhy{}}\PYG{o}{=} \PYG{n}{eta} \PYG{o}{*} \PYG{n}{derivW1}
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\PYG{n}{b\PYGZus{}1} \PYG{o}{\PYGZhy{}}\PYG{o}{=} \PYG{n}{eta} \PYG{o}{*} \PYG{n}{derivB1}
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\end{MintedVerbatim}

‎doc/src/week41/_minted/FCC7426E301CBCF11A668C5057AF3D1A.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{\PYGZus{}\PYGZus{}future\PYGZus{}\PYGZus{}}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{n}{division}
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{sympy}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{o}{*}
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\PYG{n}{x} \PYG{o}{=} \PYG{n}{symbols}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{x}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{expr} \PYG{o}{=} \PYG{n}{exp}\PYG{p}{(}\PYG{n}{x}\PYG{o}{*}\PYG{n}{x}\PYG{p}{)}
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\PYG{n}{simplify}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{)}
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\PYG{n}{derivative} \PYG{o}{=} \PYG{n}{diff}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{,}\PYG{n}{x}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{expr}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{python}\PYG{p}{(}\PYG{n}{derivative}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

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