The impact of sparsity in low-rank recurrent neural networks.

The impact of sparsity in low-rank recurrent neural networks.

Blog Article

Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces.How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics.This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse.

Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank.We first analyse the battery wire impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics.We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity Transformer T1 matrices composed of a low-rank and a full-rank random component.

This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters.Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.