Correlated Weights in Infinite Limits of Deep Convolutional Neural Networks
This work is significant for researchers studying the theoretical properties and practical applications of infinite-width neural networks, particularly in understanding and preserving the defining characteristics of CNNs.
This paper addresses the issue of spatial correlations disappearing in infinite-width limits of Convolutional Neural Networks (CNNs) when using independent weight priors. By introducing correlated weight priors, the authors demonstrate that spatial correlations in activations are maintained, and varying this correlation allows interpolation between independent-weight limits and mean-pooling.
Infinite width limits of deep neural networks often have tractable forms. They have been used to analyse the behaviour of finite networks, as well as being useful methods in their own right. When investigating infinitely wide convolutional neural networks (CNNs), it was observed that the correlations arising from spatial weight sharing disappear in the infinite limit. This is undesirable, as spatial correlation is the main motivation behind CNNs. We show that the loss of this property is not a consequence of the infinite limit, but rather of choosing an independent weight prior. Correlating the weights maintains the correlations in the activations. Varying the amount of correlation interpolates between independent-weight limits and mean-pooling. Empirical evaluation of the infinitely wide network shows that optimal performance is achieved between the extremes, indicating that correlations can be useful.