When and where do feed-forward neural networks learn localist representations?

TL;DR

This paper systematically investigates when and where localist representations emerge in feed-forward neural networks, revealing conditions that promote interpretable local codes contrary to traditional distributed coding assumptions.

Contribution

It provides the first systematic analysis of local code emergence in feed-forward networks using known input-output data, challenging the view that neural networks only learn distributed representations.

Findings

Local codes follow a well-defined distribution based on network and data parameters.

Using 1-hot output codes reduces local code emergence.

Dropout increases the number of local codes, indicating potential resilience to noise.

Abstract

According to parallel distributed processing (PDP) theory in psychology, neural networks (NN) learn distributed rather than interpretable localist representations. This view has been held so strongly that few researchers have analysed single units to determine if this assumption is correct. However, recent results from psychology, neuroscience and computer science have shown the occasional existence of local codes emerging in artificial and biological neural networks. In this paper, we undertake the first systematic survey of when local codes emerge in a feed-forward neural network, using generated input and output data with known qualities. We find that the number of local codes that emerge from a NN follows a well-defined distribution across the number of hidden layer neurons, with a peak determined by the size of input data, number of examples presented and the sparsity of input data. Using a 1-hot output code drastically decreases the number of local codes on the hidden layer. The number of emergent local codes increases with the percentage of dropout applied to the hidden layer, suggesting that the localist encoding may offer a resilience to noisy networks. This data suggests that localist coding can emerge from feed-forward PDP networks and suggests some of the conditions that may lead to interpretable localist representations in the cortex. The findings highlight how local codes should not be dismissed out of hand.