


The Cascade Correlation AlgorithmDeveloped in 1990 by Fahlman, the cascade correlation algorithm provides a solution. Cascade correlation neural networks are similar to traditional networks in that the neuron is the most basic unit. Training the neurons, however, is rather novel. An untrained cascade correlation network is a blank slate; it has no hidden units. A cascade correlation network’s output weights are trained until either the solution is found, or progress stagnates. If a single layered network will suffice, training is complete.
If further training yields no appreciable reduction of error, a hidden neuron is ‘recruited.’ A pool of hidden neurons (generally 8) is created and trained until their error reduction halts. The hidden neuron with the greatest correspondence to the overall error (the one that will affect it the most) is then installed in the network and the others are discarded. The new hidden neuron ‘rattles’ the network and significant error reduction is accomplished after each hidden neuron is added. This ingenious design prevents the moving target problem by training feature detectors one by one and only accepting the best. The weights of hidden neurons are static; once they are initially trained, they are not touched again. The features they identify are permanently cast into the memory of the network. Preserving the orientation of hidden neurons allows cascade correlation to accumulate experience after its initial training session. Few neural network architectures allow this. If a backpropagation network is retrained, it ‘forgets’ its initial training. The size step problem contributes greatly to error stagnation. When a network takes steps that are too small, the error value reaches an asymptote. Cascade correlation avoids this by using the quickprop algorithm. Quickprop finds the second derivative (change of slope) of the error function. With each epoch it takes a different size step corresponding to the change of the error slope. If the error is reducing rapidly, quickprop descends quickly. Once the slope flattens out, quickprop slows down so that it does not pass the minimum. Quickprop is like a person searching for a house. If the person knows he is far away, he drives fast. Once he approaches the house, he slows down and looks more carefully
The difference in training speeds is unmistakably clear from an analysis of backpropagation’s error graph versus that of cascadecorrelation. Backpropagation slowly converges on a solution as the moving target problem and sizestep problem strike. In some trials the hidden neurons become locked on the same feature, and the network never attains a solution. As visible in the graph, cascade correlation faces this same problem except that when the error reduction stagnates, cascade correlation recruits a new hidden neuron that will promote further error reduction. Cascade correlation aggressively seeks to reduce error at the fastest possible rate. The cascade correlation algorithm trains substantially faster then virtually any other existing algorithm. A classic classification benchmark, the two spirals problem developed by Alexis Wieland, clearly illustrates this. The two spirals problem consists of 194 points arranged in a circular pattern; half the points are of type A, the other half are type B. A heavily modified version of backpropagation took 20,000 epochs and 1.2 billion weight modifications to converge on a solution. Cascade correlation takes an average of 1700 epochs and a mere 19 million alterations. 