This posting contains links to and explanations for C code developed for our research in the 1990's.

## C Code for Error Backpropagation

train.c is a C program for training multilayer, feedforward neural networks with error backpropagation using early stopping and cross-validation. The program includes the option of training the networks on a CNAPS Server (see the section above on Parallel Algorithms). The results are written to stdout in either short format or long format. If in short format, the results can be summarized and sorted by summshort.awk, an awk script. If in long format, use nnlong-to-short.awk to first convert the file to short format. This tutorial describes how to use the train.c program and awk scripts. It also describes how to run train.c from within Matlab using functions described below.

## A Matlab Wrapper for train.c

Since much of the work in any neural network experiment goes into data manipulation, we have written a suite of Matlab functions for preparing data, launching the train.c program, and displaying the results. For starters, here is nnTrain.m, a function that accepts arguments like the name of the data matrix, writes data files to be read by the train.c program, and starts a background process running the train.c program. This has evolved to include many features we find handy, such as running remotely on another machine, including on our CNAPS Server. As mentioned above, this tutorial describes how to use train.c, nnTrain.m and other Matlab functions mentioned below. The LaTeX source file and associated figure files are available in this tar file an example for inexperienced LaTeX'ers.

In addition to summarizing the output of train.c with the awk scripts, you may plot histograms of test error for each set of parameter values included in the short format output file using the Matlab functions nnRuns.m, to load into Matlab a matrix containing results of all runs, and nnPlotRuns.m to display one histogram for each set of parameter values. nnRuns.m needs meanNoNaN.m.

Long format output includes information for learning curves, network responses to test data, and the best weight values for each training run. These can be extracted from the output file and displayed within Matlab using nnResults.m. nnResults calls these Matlab functions: nnParseResults.m, nnPlotCurve.m, nnPlotOuts.m, nnPlotOutsScat.m, nnShowWeights.m, nnDrawBoxes.m, fskipwords.m.

## Matlab Code for Real-Time Recurrent Learning

rtrlinit.m and rtrl.m are two Matlab functions for initializing and training a recurrent neural network using Williams and Zipser's Real-Time Recurrent Learning algorithm. These functions and others that demonstrate their use are contained in rtrl.tar.gz. See the README file in this tar file. rfir.m is a Matlab function for training recurrent networks using a generalization of Williams and Zipser's real-time recurrent learning modified for networks with FIR synapses, based on the work of Eric Wan. An example of its use is in xorrfir.m that trains a recurrent network to form the exclusive-or of two input bits.

## Matlab and Octave Code for Error Backpropagation with Early Stopping

As an experiment in Octave's compatability with Matlab, I have written a short bit of Octave/Matlab code for training feedforward neural networks with a single hidden layer using error backpropagation with early stopping. Here is a gzipped tar file containing several m-files. The README very briefly explains how to run the two-bit exclusive-or example included in the tar file.