Optimal sparsity in autoencoder memory models of the hippocampus

Storing complex correlated memories is significantly more efficient when memories are recoded to obtain compressed representations. Previous work has shown that compression can be implemented in a simple neural circuit, which can be described as a sparse autoencoder. The activity of the encoding units in these models recapitulates the activity of hippocampal neurons recorded in multiple experiments. However, these investigations have assumed that the level of sparsity is fixed and that inputs have the same statistics and, hence, that they are uniformly compressible. In contrast, biological agents encounter environments with vastly different memory demands and compressibility. Here, we investigate whether the compressibility of inputs determines optimal sparsity in sparse autoencoders. We find 1) that as the compressibility of inputs increases, the optimal coding level decreases, 2) that the desired coding level diverges from the observed coding level as a function of both memory demand and input compressibility, and 3) that optimal memory capacity is achieved when sparsity is weakly enforced. In addition, we characterize how sparsity and the strength of sparsity enforcement jointly control optimal performance. These results provide predictions for how sparsity in the hippocampus should change in response to environmental statistics and theoretical grounds for why sparsity is dynamically tuned in the brain.