What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation

One of the most important aspects of any machine learning paradigm is how i t scales according to problem size and complexity. Using a task with known optimal train ing error, and a pre-specified maximum number of training updates, we investigate the convergence of th backpropagation algorithm with respect to a) the complexity of the required function approximatio n, b) the size of the network in relation to the size required for an optimal solution, and c) the degree o f noise in the training data. In general, for a) the solution found is worse when the function to be app roximated is more complex, for b) oversized networks can result in lower training and generalization error in certain cases, and for c) the use of committee or ensemble techniques can be more beneficial as the level o f noise in the training data is increased. For the experiments we performed, we do not obtain the optimal solution in any case. We further support the observation that larger networks can produce bett er training and generalization error using a face recognition example where a network with many more par ameters than training points generalizes better than smaller networks.