Dense Associative Memory for Pattern Recognition

TL;DR

This paper introduces a dense associative memory model that can store and retrieve many more patterns than neurons, establishing a duality with deep neural networks and exploring new activation functions for pattern recognition tasks.

Contribution

It proposes a duality between associative memory models and neural networks, enabling analysis of unconventional activation functions like higher rectified polynomials.

Findings

Memory models outperform traditional networks in pattern storage

Duality allows energy-based analysis of neural network properties

Higher rectified polynomials improve recognition accuracy

Abstract

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of models that smoothly interpolates between two limiting cases can be constructed. One limit is referred to as the feature-matching mode of pattern recognition, and the other one as the prototype regime. On the deep learning side of the duality, this family corresponds to feedforward neural networks with one hidden layer and various activation functions, which transmit the activities of the visible neurons to the hidden layer. This family of activation functions includes logistics, rectified linear units, and rectified polynomials of higher degrees. The proposed duality makes it possible to apply energy-based intuition from associative memory to analyze computational properties of neural networks with unusual activation functions - the higher rectified polynomials which until now have not been used in deep learning. The utility of the dense memories is illustrated for two test cases: the logical gate XOR and the recognition of handwritten digits from the MNIST data set.