Neural Network Toolbox™

Calculate weight and bias performance gradient as single vector

Syntax

• [gX,normgX] = calcgx(net,X,Pd,BZ,IWZ,LWZ,N,Ac,El,perf,Q,TS);
  

Description

This function calculates the gradient of a network's performance with respect to its vector of weight and bias values X.

If the network has no layer delays with taps greater than 0, the result is the true gradient.

If the network has layer delays greater than 0, the result is the Elman gradient, an approximation of the true gradient.

[gX,normgX] = calcgx(net,X,Pd,BZ,IWZ,LWZ,N,Ac,El,perf,Q,TS) takes

net	Neural network
X	Vector of weight and bias values
Pd	Delayed inputs
BZ	Concurrent biases
IWZ	Weighted inputs
LWZ	Weighted layer outputs
N	Net inputs
Ac	Combined layer outputs
El	Layer errors
perf	Network performance
Q	Concurrent size
TS	Time steps

and returns

gX	Gradient dPerf/dX
normgX	Norm of gradient

Examples

Here is a linear network with a single input element ranging from 0 to 1, two neurons, and a tap delay on the input with taps at 0, 2, and 4 time steps. The network is also given a recurrent connection from layer 1 to itself with tap delays of [1 2].

• net = newlin([0 1],2);
  net.layerConnect(1,1) = 1;
  net.layerWeights{1,1}.delays = [1 2];
  

Here is a single (Q = 1) input sequence P with five time steps (TS = 5), and the four initial input delay conditions Pi, combined inputs Pc, and delayed inputs Pd.

• P = {0 0.1 0.3 0.6 0.4};
  Pi = {0.2 0.3 0.4 0.1};
  Pc = [Pi P];
  Pd = calcpd(net,5,1,Pc);
  

Here the two initial layer delay conditions for each of the two neurons and the layer targets for the two neurons over five time steps are defined.

• Ai = {[0.5; 0.1] [0.6; 0.5]};
  Tl = {[0.1;0.2] [0.3;0.1], [0.5;0.6] [0.8;0.9], [0.5;0.1]};
  

Here the network's weight and bias values are extracted, and the network's performance and other signals are calculated.

• X = getx(net);
  [perf,El,Ac,N,BZ,IWZ,LWZ] = calcperf(net,X,Pd,Tl,Ai,1,5);
  

Finally you can use calcgz to calculate the gradient of performance with respect to the weight and bias values X.

• [gX,normgX] = calcgx(net,X,Pd,BZ,IWZ,LWZ,N,Ac,El,perf,1,5);
  

See Also

calcjx, calcjejj

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