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.

研究了随机连接的线性网络对于执行近似稀疏输入信号的短期记忆（STM）的容量，利用了压缩感知结果提供了严格的非渐近恢复保证，量化了输入稀疏级别、输入稀疏基、网络特性对系统容量的影响，证明网络内存容量可以与节点数量超线性地扩展，并且在某些情况下可以实现远大于网络大小的 STM 容量。