We study the interaction between input distributions, learning algorithms, and finite sample sizes in the case of learning classification tasks. Focusing on the case of normal input distributions, we use statistical mechanics techniques to calculate the empirical and expected (or generalization) errors for several well-known algorithms learning the weights of a single-layer perceptron. In the case of spherically symmetric distributions within each class we find that the simple Hebb rule, corresponding to maximum-likelihood parameter estimation, outperforms the other more complex algorithms, based on error minimization. Moreover, we show that in the regime where the overlap between the classes is large, algorithms with low empirical error do worse in terms of generalization, a phenomenon known as overtraining.

Recent experimental findings (Gray et al. 1989; Eckhorn et al. 1988) seem to indicate that rapid oscillations and phase-lockings of different populations of cortical neurons play an important role in neural computations. In particular, global stimulus properties could be reflected in the correlated firing of spatially distant cells. Here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures. A specific demonstration is given for the problem of preattentive texture discrimination. Texture images are convolved with different sets of Gabor filters feeding into several corresponding arrays of coupled oscillators. After a brief transient, the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism. The importance of noise and of long range connections is briefly discussed.