Robust exponential memory in Hopfield networks

TL;DR

This paper introduces a method to design Hopfield networks capable of exponentially increasing noise-tolerant memories by minimizing probability flow, enabling robust memory storage and solving complex computational problems.

Contribution

The authors develop a novel approach to create Hopfield networks with exponentially many noise-tolerant memories using probability flow minimization, advancing neural memory capacity.

Findings

Networks achieve exponential memory capacity.

Networks function as optimal error-correcting codes.

Efficiently solve the hidden clique problem.

Abstract

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have explored the potential of this network to solve combinatorial optimization problems and store memories as attractors of its deterministic dynamics, a basic open problem is to design a family of Hopfield networks with a number of noise-tolerant memories that grows exponentially with neural population size. Here, we discover such networks by minimizing probability flow, a recently proposed objective for estimating parameters in discrete maximum entropy models. By descending the gradient of the convex probability flow, our networks adapt synaptic weights to achieve robust exponential storage, even when presented with vanishingly small numbers of training patterns. In addition to providing a new set of error-correcting codes that achieve Shannon's channel capacity bound, these networks also efficiently solve a variant of the hidden clique problem in computer science, opening new avenues for real-world applications of computational models originating from biology.