Sample complexity results from computational learning theory, when applied to neural network learning for pattern classi cation problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classi cation problem and the learning algorithm nds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassi cation probability is no more than a certain error estimate (that is related to squared error on the training set) plus A 3 p (log n)=m (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training
For example, REF shows that for a neural network with small weights and small training set squared error, the true error depends on the size of its weights rather than the number of weights; this finding is similar in spirit to eq. (4).
The Sample Complexity of Pattern Classification With Neural Networks: The Size of the Weights is More Important Than the Size of the Network
Computer Science