The interplay between randomness and structure during learning in RNNs

TL;DR

This study investigates how learning in RNNs involves low-rank connectivity changes influenced by task structure and initial randomness, providing insights into the learning process and network organization.

Contribution

It reveals that RNN learning induces low-rank connectivity modifications driven by task structure, enhancing understanding of neural network adaptation.

Findings

Low-rank matrices describe connectivity changes in trained RNNs.

Low-dimensional task structure leads to low-rank connectivity modifications.

Random initial connectivity accelerates learning due to low-rank dynamics.

Abstract

Recurrent neural networks (RNNs) trained on low-dimensional tasks have been widely used to model functional biological networks. However, the solutions found by learning and the effect of initial connectivity are not well understood. Here, we examine RNNs trained using gradient descent on different tasks inspired by the neuroscience literature. We find that the changes in recurrent connectivity can be described by low-rank matrices, despite the unconstrained nature of the learning algorithm. To identify the origin of the low-rank structure, we turn to an analytically tractable setting: training a linear RNN on a simplified task. We show how the low-dimensional task structure leads to low-rank changes to connectivity. This low-rank structure allows us to explain and quantify the phenomenon of accelerated learning in the presence of random initial connectivity. Altogether, our study opens a new perspective to understanding trained RNNs in terms of both the learning process and the resulting network structure.