C++ Library for Neural Networks — Use libneuron to design neural networks with back propagation and evolution.
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221 lines
8.0 KiB
221 lines
8.0 KiB
/*! @file |
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@id $Id$ |
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*/ |
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// 1 2 3 4 5 6 7 8 |
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// 45678901234567890123456789012345678901234567890123456789012345678901234567890 |
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#include <matrix.hxx> |
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#include <cmath> |
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/** @mainpage Neural Network with Hidden Layers |
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@section neuro-intro Overview |
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@subsection nature Natural Neural Network |
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From <a href="https://en.wikipedia.org/wiki/Neuron">Wikipedia</a>: |
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«A neuron is an electrically excitable cell that processes and |
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transmits information through electrical and chemical |
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signals. These signals between neurons occur via synapses, |
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specialized connections with other cells. Neurons can connect to |
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each other to form neural networks. Neurons are the core |
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components of the brain and spinal cord of the central nervous |
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system, and of the ganglia of the peripheral nervous system.» The |
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neuron connects with dendrites to the world or to the axon of |
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other neuirons. The neurites (dendrite or axon) transport |
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electrical stimulation to the cell, which emits the signal to the |
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dendrites if the activation reaches a certain level. |
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@dot |
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digraph g { |
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rankdir=LR; |
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ranksep=0.8; |
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node [shape=hexagon]; |
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edge [arrowhead=none]; |
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subgraph clusterInput { |
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label="sensors"; |
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color="white"; |
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node [shape=point]; |
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I0; I1; I2; I3; I4; I5; I6; I7; I8 I9; |
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} |
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subgraph clusterOutput { |
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label="actors"; |
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color="white"; |
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node [shape=point]; |
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O0; O1; O2; O3; O4; O5; O6; |
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} |
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I1 -> Cell1 [label="axon";taillabel="synapse"]; |
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{ I2; I3; I4; } -> Cell1; |
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{ I5; I6; I7; I8; } -> Cell2; |
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{ I4; I6; I9; I0; } -> Cell3; |
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Cell1 -> Cell8 [label="axon / dendrite"]; |
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Cell1 -> { Cell2; Cell4; Cell5; } |
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Cell2 -> { Cell4; Cell5; Cell6; Cell8; } |
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Cell3 -> { Cell4; Cell6; Cell7; Cell8; } |
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{ Cell4; Cell5; Cell6 } -> { Cell7; Cell8; } |
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Cell7 -> { O0; O1; O2 }; |
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Cell8 -> { O3; O4; O5; }; |
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Cell8 -> O6 [label="dendrite"]; |
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} |
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@enddot |
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@subsection art Artificial Neural Network |
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A complex neural network can be imitiated as a vector @c I of @c i |
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input values, a vector @c O of @c o output values and any number |
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@c l of hidden layers, where each of them contains @c h |
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neurons. |
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A neural network with double precision is initialized as: |
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@code |
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NeuroNet<double, i, o, l, h> net; |
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@endcode |
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@dot |
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digraph g { |
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rankdir=LR; |
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ranksep=1.5; |
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subgraph clusterInput { |
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label="Input Layer"; |
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I1 [label=<I<SUB>1</SUB>>]; |
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I2 [label=<I<SUB>2</SUB>>]; |
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Ix [label=<I<SUB>…</SUB>>]; |
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Ii [label=<I<SUB>i</SUB>>]; |
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} |
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subgraph clusterHidden1 { |
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label="First Hidden Layer"; |
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H11 [label=<H<SUB>11</SUB>>]; |
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H12 [label=<H<SUB>12</SUB>>]; |
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H1x [label=<H<SUB>1…</SUB>>]; |
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H1h [label=<H<SUB>1h</SUB>>]; |
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} |
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subgraph clusterHidden2 { |
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label="Second Hidden Layer"; |
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H21 [label=<H<SUB>21</SUB>>]; |
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H22 [label=<H<SUB>22</SUB>>]; |
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H2x [label=<H<SUB>2…</SUB>>]; |
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H2h [label=<H<SUB>2h</SUB>>]; |
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} |
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subgraph clusterHiddenx { |
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label="More Hidden Layers"; |
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Hx1 [label=<H<SUB>…1</SUB>>]; |
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Hx2 [label=<H<SUB>…2</SUB>>]; |
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Hxx [label=<H<SUB>……</SUB>>]; |
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Hxh [label=<H<SUB>…h</SUB>>]; |
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} |
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subgraph clusterHiddenl { |
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label="Last Hidden Layer"; |
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Hl1 [label=<H<SUB>l1</SUB>>]; |
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Hl2 [label=<H<SUB>l2</SUB>>]; |
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Hlx [label=<H<SUB>l…</SUB>>]; |
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Hlh [label=<H<SUB>lh</SUB>>]; |
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} |
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subgraph clusterOutput { |
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label="Output Layer"; |
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O1 [label=<O<SUB>1</SUB>>]; |
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O2 [label=<O<SUB>2</SUB>>]; |
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Ox [label=<O<SUB>…</SUB>>]; |
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Oo [label=<O<SUB>o</SUB>>]; |
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} |
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{ I1; I2; Ix; Ii; } |
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-> { H11; H12; H1x; H1h; } |
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-> { H21; H22; H2x; H2h; } |
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-> { Hx1; Hx2; Hxx; Hxh; } |
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-> { Hl1; Hl2; Hlx; Hlh; } |
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-> { O1; O2; Ox; Oo; } |
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} |
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@enddot |
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@section neuro-forward Forward Propagation |
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The connections between two layers can be modelled as a |
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Matrix. Then Matrix H<sub>1</sub> contains the weights from @c I |
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to the first hidden layer, @c H<sub>2</sub> from the first to the |
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second, and so on, until @c H<sub>l+1</sub> contains the weights |
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from layer @c l to the output @c O. |
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There is also an activation function @f. For back propagation, |
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this function needs a first derivation @c f'. |
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To get the activation of the first hidden layer, the input vector |
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is multiplied with the weight matrix of the first hidden layer, |
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this results in an output vector. Then the activation function is |
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applied to all values of the output vector: |
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<pre> |
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V<sub>1</sub> = f(I×H<sub>1</sub>) |
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</pre> |
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This is done for all layers, up to the output. The output vector |
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is then calculated as: |
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<pre> |
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O = f(f(f(f(I×H<sub>1</sub>)×H<sub>2</sub>)×H<sub>…</sub>)×H<sub>l+1</sub>) |
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</pre> |
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@code |
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const size_type i(4); |
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const size_type o(2); |
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NeuroNet<double, i, o> net; |
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Matrix<1, i> input(1.0, 2.0, 0.0, -1.0); |
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Matrix<1, o> output = feed(input); |
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@endcode |
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@section neuro-backward Back Propagation |
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@page biblio Bibliography |
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- <a href="http://briandolhansky.com/blog/2014/10/30/artificial-neural-networks-matrix-form-part-5">Artificial Neural Networks: Matrix Form (Part 5)</a> |
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- <a href="http://briandolhansky.com/blog/2013/9/27/artificial-neural-networks-backpropagation-part-4">Artificial Neural Networks: Mathematics of Backpropagation (Part 4)</a> |
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- <a href="http://www.tornau.name/wp-content/uploads/2009/04/studiumsmaterialien/neuronale_netze_zusammefassung.pdf">Vorlesung Neuronale Netze - Zusammenfassung - Christoph Tornau</a> |
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- <a href="http://www.neuronalesnetz.de/">Neuronale Netze — Eine Einführung</a> |
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- <a href="http://alphard.ethz.ch/hafner/Vorles/Optim/ANN/Artificial%20Neural%20Network%20based%20Curve%20Prediction%20Documentation.pdf">Artificial Neural Network based Curve Prediction</a> |
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- <a href="http://cs231n.github.io/convolutional-networks/">Convolutional Neural Networks (CNNs / ConvNets)</a> |
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- <a href="https://www.tensorflow.org/versions/r0.9/tutorials/index.html">TensorFlow Tutorials</a> |
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- <a href="http://alphard.ethz.ch/hafner/Vorles/Optim/ANN/Artificial%20Neural%20Network%20based%20Curve%20Prediction%20Documentation.pdf">Artificial Neural Network based Curve Prediction</a> |
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*/ |
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namespace math { |
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// tangens hyperbolicus as standard activation function |
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template<typename TYPE> TYPE tanh(const TYPE& v) { |
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return ::tanh((long double)v); |
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} |
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// derivate of activation function for back propagation |
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template<typename TYPE> TYPE tanh_diff(const TYPE& v) { |
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TYPE ch(::cosh((long double)v)); |
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return 1/(ch*ch); |
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} |
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} |
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template |
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<typename TYPE, |
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size_t INPUT_LAYERS, |
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size_t OUTPUT_LAYERS, |
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size_t HIDDEN_LAYERS = INPUT_LAYERS+OUTPUT_LAYERS, |
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size_t HIDDEN_LAYER_SIZE = INPUT_LAYERS+OUTPUT_LAYERS, |
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TYPE(*ACTIVATION)(const TYPE&) = math::tanh<TYPE>, |
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TYPE(*ACTIVATION_DIFF)(const TYPE&) = math::tanh_diff<TYPE>> |
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class NeuroNet { |
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public: |
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NeuroNet() { |
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} |
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Matrix<TYPE, 1, OUTPUT_LAYERS> operator()(const Matrix<TYPE, 1, INPUT_LAYERS>& in) { |
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Matrix<TYPE, 1, HIDDEN_LAYER_SIZE> l((in*_wi).apply(ACTIVATION)); |
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for (int i(0); i<HIDDEN_LAYERS-1; ++i) |
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l = (l*_wh[i]).apply(ACTIVATION); |
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Matrix<TYPE, 1, OUTPUT_LAYERS> out((l*_wo).apply(ACTIVATION)); |
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return out; |
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} |
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Matrix<TYPE, 1, OUTPUT_LAYERS> learn(const Matrix<TYPE, 1, INPUT_LAYERS>& in, |
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const Matrix<TYPE, 1, OUTPUT_LAYERS>& expect) { |
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Matrix<TYPE, 1, OUTPUT_LAYERS> out((*this)(in)); |
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Matrix<TYPE, 1, OUTPUT_LAYERS> diff(expect-out); |
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return diff; |
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} |
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private: |
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Matrix<TYPE, INPUT_LAYERS, HIDDEN_LAYER_SIZE> _wi; |
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Matrix<TYPE, HIDDEN_LAYER_SIZE, HIDDEN_LAYER_SIZE> _wh[HIDDEN_LAYERS-1]; |
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Matrix<TYPE, HIDDEN_LAYER_SIZE, OUTPUT_LAYERS> _wo; |
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};
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