One-step secant backpropagation
net.trainFcn = 'trainoss'
[net,tr] = train(net,...)
trainoss is a network training function that updates weight and bias values according to the one-step secant method.
net.trainFcn = 'trainoss' sets the network trainFcn property.
[net,tr] = train(net,...) trains the network with trainoss.
Training occurs according to trainoss training parameters, shown here with their default values:
Maximum number of epochs to train
Maximum validation failures
Minimum performance gradient
Name of line search routine to use
Epochs between displays (NaN for no displays)
Generate command-line output
Show training GUI
Maximum time to train in seconds
Parameters related to line search methods (not all used for all methods):
Divide into delta to determine tolerance for linear search.
Scale factor that determines sufficient reduction in perf
Scale factor that determines sufficiently large step size
Initial step size in interval location step
Parameter to avoid small reductions in performance, usually set to 0.1 (see srch_cha)
Lower limit on change in step size
Upper limit on change in step size
Maximum step length
Minimum step length
Maximum step size
You can create a standard network that uses trainoss with feedforwardnet or cascadeforwardnet. To prepare a custom network to be trained with trainoss:
In either case, calling train with the resulting network trains the network with trainoss.
Here a neural network is trained to predict median house prices.
[x,t] = house_dataset; net = feedforwardnet(10,'trainoss'); net = train(net,x,t); y = net(x)
Because the BFGS algorithm requires more storage and computation in each iteration than the conjugate gradient algorithms, there is need for a secant approximation with smaller storage and computation requirements. The one step secant (OSS) method is an attempt to bridge the gap between the conjugate gradient algorithms and the quasi-Newton (secant) algorithms. This algorithm does not store the complete Hessian matrix; it assumes that at each iteration, the previous Hessian was the identity matrix. This has the additional advantage that the new search direction can be calculated without computing a matrix inverse.
The one step secant method is described in [Batt92]. This algorithm requires less storage and computation per epoch than the BFGS algorithm. It requires slightly more storage and computation per epoch than the conjugate gradient algorithms. It can be considered a compromise between full quasi-Newton algorithms and conjugate gradient algorithms.
trainoss can train any network as long as its weight, net input, and transfer functions have derivative functions.
Backpropagation is used to calculate derivatives of performance perf with respect to the weight and bias variables X. Each variable is adjusted according to the following:
X = X + a*dX;
where dX is the search direction. The parameter a is selected to minimize the performance along the search direction. The line search function searchFcn is used to locate the minimum point. The first search direction is the negative of the gradient of performance. In succeeding iterations the search direction is computed from the new gradient and the previous steps and gradients, according to the following formula:
dX = -gX + Ac*X_step + Bc*dgX;
where gX is the gradient, X_step is the change in the weights on the previous iteration, and dgX is the change in the gradient from the last iteration. See Battiti (Neural Computation, Vol. 4, 1992, pp. 141–166) for a more detailed discussion of the one-step secant algorithm.
Training stops when any of these conditions occurs:
The maximum number of epochs (repetitions) is reached.
The maximum amount of time is exceeded.
Performance is minimized to the goal.
The performance gradient falls below min_grad.
Validation performance has increased more than max_fail times since the last time it decreased (when using validation).
Battiti, R., "First and second order methods for learning: Between steepest descent and Newton's method," Neural Computation, Vol. 4, No. 2, 1992, pp. 141–166