func_t *func_poly_monic(func_t *f)
{
func_t *a=NULL;
if(!(func_is_poly(f))){ FUNC_ERROR_ARG1("func_poly_monic",f); }
a=func_poly_get_lc(f);
if(a==NULL || func_is_one(a)){ return f; }
return func_expand(func_mul(func_inv(FR(a)),f));
}
void Neuron::reverse_activate()
{
value = func_inv(value);
}
void back_propagate(NeuralNetwork& nn, const values_t& input, const values_t& expected_output, std::vector<values_matrix_t>& delta_W, values_matrix_t& delta_b)
{
//algorithm from http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks/
//Neuron(W) -> z -> func() -> a
//input -> NN -> output/y
//step 1
values_t output;
nn.process(input, output);
values_t& prev = output;
TYPE tmp;
int lyr;
int num_lyrs, num_neurons, num_connections;
values_matrix_t error;
error.resize(nn.net.size());
//step 2
//output layer first
lyr = error.size()-1;
num_neurons = nn.net[lyr].size();
error[lyr].resize(num_neurons);
for(int n=0; n<num_neurons; n++){
error[lyr][n] = func_deriv( func_inv(output[n]) ); //->f'(z)
error[lyr][n] *= (output[n] - expected_output[n]); //-> -(y-a) = (a-y)
}
prev = error[lyr];
//step 3
//from output layer to layer 1 (layer after the input layer), but counting from output-1 to 0
for(; --lyr >=0;){
num_neurons = nn.net[lyr].size();
error[lyr].resize(num_neurons);
for(int n=0; n<num_neurons; n++){
error[lyr][n] = func_deriv( func_inv( nn.net[lyr][n].value ) ); //->f'(z)
tmp = 0;
for(int j=0; j<prev.size(); j++){ //-> W^T*error[lyr+1] = W^T*prev
tmp += prev[j] * nn.net[lyr+1][j][n];
}
error[lyr][n] *= tmp;
}
prev = error[lyr];
}
//step 4
//add to delta W, delta b
num_lyrs = error.size();
for(lyr=0; lyr<num_lyrs; lyr++){
num_neurons = error[lyr].size();
for(int neu=0; neu<num_neurons; neu++){
num_connections = nn.net[lyr][neu].size();
delta_b[lyr][neu] += error[lyr][neu];
for(int con=0; con<num_connections; con++){
//nn.net[lyr-1] -> lyr before current layer
//nn.net[lyr-1][con] -> specific neuron before current layer (num_neurons of [lyr-1] = num_connections of [lyr])
if(lyr == 0)
delta_W[lyr][neu][con] += error[lyr][neu]*input[con];
else
delta_W[lyr][neu][con] += error[lyr][neu]*nn.net[lyr-1][con].value;
}
}
}
}
