Linking connectivity, dynamics and computations in low-rank recurrent neural networks

TL;DR

This paper investigates how low-dimensional dynamics and computations emerge from the structure of recurrent neural networks with mixed connectivity, providing a geometric framework to relate connectivity to neural dynamics and computational capacity.

Contribution

It introduces a geometric approach to link low-rank connectivity structures with emergent low-dimensional dynamics and computational capabilities in recurrent neural networks.

Findings

Dynamics are low-dimensional and inferable from connectivity.

Minimal connectivity suffices for specific computations.

Computational capacity increases with connectivity dimensionality.

Abstract

Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how low-dimensional computations on mixed, distributed representations emerge from the structure of the recurrent connectivity and inputs to cortical networks is a major challenge. Here, we study a class of recurrent network models in which the connectivity is a sum of a random part and a minimal, low-dimensional structure. We show that, in such networks, the dynamics are low dimensional and can be directly inferred from connectivity using a geometrical approach. We exploit this understanding to determine minimal connectivity required to implement specific computations, and find that the dynamical range and computational capacity quickly increase with the dimensionality of the connectivity structure. This framework produces testable experimental predictions for the relationship between connectivity, low-dimensional dynamics and computational features of recorded neurons.