Short Term Memory Capacity in Networks via the Restricted Isometry Property

TL;DR

This paper analyzes the capacity of randomly connected linear networks for short-term memory using compressed sensing, showing superlinear scaling and optimal recovery conditions across various network topologies.

Contribution

It introduces a rigorous framework leveraging the Restricted Isometry Property to quantify and optimize short-term memory capacity in neural networks.

Findings

Network capacity can scale superlinearly with nodes.

STM capacities can exceed network size under certain conditions.

Optimal recovery length balances errors in finite and infinite sequences.

Abstract

Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from compressed sensing to provide rigorous non asymptotic recovery guarantees, quantifying the impact of the input sparsity level, the input sparsity basis, and the network characteristics on the system capacity. Our analysis demonstrates that network memory capacities can scale superlinearly with the number of nodes, and in some situations can achieve STM capacities that are much larger than the network size. We provide perfect recovery guarantees for finite sequences and recovery bounds for infinite sequences. The latter analysis predicts that network STM systems may have an optimal recovery length that balances errors due to omission and recall mistakes. Furthermore, we show that the conditions yielding optimal STM capacity can be embodied in several network topologies, including networks with sparse or dense connectivities.