Short-Term Memory Capacity in Networks via the Restricted Isometry Property

• Published in: Neural computation Vol. 26; no. 6; pp. 1198 - 1235
• Main Authors: Charles, Adam S., Yap, Han Lun, Rozell, Christopher J.
• Format: Journal Article
• Language: English
• Published: One Rogers Street, Cambridge, MA 02142-1209, USA MIT Press 01.06.2014; MIT Press Journals, The
• Subjects: Cerebral Cortex; Compressed; Error analysis; Humans; Letters; Mathematical analysis; Memory; Memory, Short-Term - physiology; Models, Neurological; Nerve Net - physiology; Network topologies; Networks; Neural Networks (Computer); Nonlinear Dynamics; Optimization; Recall; Recovery; Scanning tunneling microscopy
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/NECO_a_00590

Cortical networks are hypothesized to rely on transient network activity to support short-term memory (STM). In this letter, 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 nonasymptotic 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.