Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)
Rishidev Chaudhuri, Ila Fiete
Neural network models of memory and error correction famously include the Hopfield network, which can directly store---and error-correct through its dynamics---arbitrary N-bit patterns, but only for ~N such patterns. On the other end of the spectrum, Shannon's coding theory established that it is possible to represent exponentially many states (~e^N) using N symbols in such a way that an optimal decoder could correct all noise upto a threshold. We prove that it is possible to construct an associative content-addressable network that combines the properties of strong error correcting codes and Hopfield networks: it simultaneously possesses exponentially many stable states, these states are robust enough, with large enough basins of attraction that they can be correctly recovered despite errors in a finite fraction of all nodes, and the errors are intrinsically corrected by the network’s own dynamics. The network is a two-layer Boltzmann machine with simple neural dynamics, low dynamic-range (binary) pairwise synaptic connections, and sparse expander graph connectivity. Thus, quasi-random sparse structures---characteristic of important error-correcting codes---may provide for high-performance computation in artificial neural networks and the brain.