Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Control

TL;DR

This paper investigates how low-rank and sparse recurrent connectivity in neural networks enhances robustness and efficiency in closed-loop control tasks, both theoretically and empirically.

Contribution

It introduces a parameterization of recurrent connectivity based on rank and sparsity, demonstrating improved robustness and efficiency in closed-form continuous-time neural networks.

Findings

Low-rank, sparse connectivity improves robustness under distribution shift.

Fewer parameters can outperform full-rank networks in online control.

Connectivity modulation influences network dynamics beneficially.

Abstract

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.