## Resumo

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.

## Resumo Limpo

cortic network hypothes reli transient network activ support shortterm memori stm letter studi capac random connect recurr linear network perform stm input signal approxim spars basi leverag result compress sens provid rigor nonasymptot recoveri guarante quantifi impact input sparsiti level input sparsiti basi network characterist system capac analysi demonstr network memori capac can scale superlinear number node situat can achiev stm capac much larger network size provid perfect recoveri guarante finit sequenc recoveri bound infinit sequenc latter analysi predict network stm system may optim recoveri length balanc error due omiss recal mistak furthermor show condit yield optim stm capac can embodi sever network topolog includ network spars dens connect