Vector< Matrix<double> > ProbabilisticLayer::calculate_probability_Hessian_form(const Vector<double>&) const
{
Vector< Matrix<double> > Hessian_form(1);
Hessian_form[0].set(1, 1, 0.0);
return(Hessian_form);
}
Vector< Matrix<double> > ScalingLayer::arrange_Hessian_form(const Vector<double>& second_derivative) const
{
const size_t scaling_neurons_number = get_scaling_neurons_number();
Vector< Matrix<double> > Hessian_form(scaling_neurons_number);
for(size_t i = 0; i < scaling_neurons_number; i++)
{
Hessian_form[i].set(scaling_neurons_number, scaling_neurons_number, 0.0);
Hessian_form[i](i,i) = second_derivative[i];
}
return(Hessian_form);
}
Vector< Matrix<double> > ProbabilisticLayer::calculate_softmax_Hessian_form(const Vector<double>& inputs) const
{
Vector< Matrix<double> > Hessian_form(probabilistic_neurons_number);
for(size_t i = 0; i < probabilistic_neurons_number; i++)
{
Hessian_form[i].set(probabilistic_neurons_number, probabilistic_neurons_number);
}
const Vector<double> outputs = inputs.calculate_softmax();
for(size_t i = 0; i < probabilistic_neurons_number; i++)
{
for(size_t j = 0; j < probabilistic_neurons_number; j++)
{
for(size_t k = 0; k < probabilistic_neurons_number; k++)
{
if(j == i && j == k && i == k)
{
Hessian_form[i](j, k) = outputs[i]*(1 - outputs[i] - 2*outputs[i]*(1 - outputs[i]));
}
else if(j == i && j != k && i != k)
{
Hessian_form[i](j, k) = -outputs[i]*outputs[k]*(1 - 2*outputs[i]);
}
else if(j != i && j == k && i != k)
{
Hessian_form[i](j, k) = outputs[i]*outputs[j]*outputs[k] - outputs[i]*outputs[j]*(1 - outputs[j]);
}
else if(j != i && i == k && j != k)
{
Hessian_form[i](j, k) = outputs[i]*outputs[j]*outputs[k] - outputs[i]*outputs[j]*(1 - outputs[i]);
}
else if(j != i && i != k && j != k)
{
Hessian_form[i](j, k) = 2*outputs[i]*outputs[j]*outputs[k];
}
}
}
}
return(Hessian_form);
}