RNNs of RNNs: Recursive Construction of Stable Assemblies of Recurrent Neural Networks

TL;DR

This paper develops a theoretical framework for constructing stable assemblies of multiple interacting recurrent neural networks, enabling complex distributed processing while maintaining stability, with applications to neuroscience and machine learning.

Contribution

It introduces conditions for the stability of combined RNNs, parameterizes these conditions for optimization, and demonstrates their effectiveness on benchmark tasks.

Findings

Stable RNN assemblies can be constructed with feedback connections.

Stability conditions are optimized using gradient-based methods.

Networks of RNNs perform well on sequential tasks.

Abstract

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.