wolffd@0: function g = mlpbkp(net, x, z, deltas)
wolffd@0: %MLPBKP	Backpropagate gradient of error function for 2-layer network.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	G = MLPBKP(NET, X, Z, DELTAS) takes a network data structure NET
wolffd@0: %	together with a matrix X of input vectors, a matrix  Z of hidden unit
wolffd@0: %	activations, and a matrix DELTAS of the  gradient of the error
wolffd@0: %	function with respect to the values of the output units (i.e. the
wolffd@0: %	summed inputs to the output units, before the activation function is
wolffd@0: %	applied). The return value is the gradient G of the error function
wolffd@0: %	with respect to the network weights. Each row of X corresponds to one
wolffd@0: %	input vector.
wolffd@0: %
wolffd@0: %	This function is provided so that the common backpropagation
wolffd@0: %	algorithm can be used by multi-layer perceptron network models to
wolffd@0: %	compute gradients for mixture density networks as well as standard
wolffd@0: %	error functions.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	MLP, MLPGRAD, MLPDERIV, MDNGRAD
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: % Evaluate second-layer gradients.
wolffd@0: gw2 = z'*deltas;
wolffd@0: gb2 = sum(deltas, 1);
wolffd@0: 
wolffd@0: % Now do the backpropagation.
wolffd@0: delhid = deltas*net.w2';
wolffd@0: delhid = delhid.*(1.0 - z.*z);
wolffd@0: 
wolffd@0: % Finally, evaluate the first-layer gradients.
wolffd@0: gw1 = x'*delhid;
wolffd@0: gb1 = sum(delhid, 1);
wolffd@0: 
wolffd@0: g = [gw1(:)', gb1, gw2(:)', gb2];