Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptation

TL;DR

This paper demonstrates that interneurons in recurrent neural networks facilitate faster and more robust adaptation to changing input statistics, acting as an implicit acceleration mechanism similar to overparameterized models.

Contribution

It introduces a theoretical comparison showing interneurons improve learning speed and robustness over direct recurrent connections in linear neural networks.

Findings

Interneuron-mediated networks converge faster than direct recurrent networks.

Convergence time scales logarithmically with initialization spectrum for interneuron networks.

Interneuron networks are overparameterized solutions to whitening objectives.

Abstract

Early sensory systems in the brain rapidly adapt to fluctuating input statistics, which requires recurrent communication between neurons. Mechanistically, such recurrent communication is often indirect and mediated by local interneurons. In this work, we explore the computational benefits of mediating recurrent communication via interneurons compared with direct recurrent connections. To this end, we consider two mathematically tractable recurrent linear neural networks that statistically whiten their inputs -- one with direct recurrent connections and the other with interneurons that mediate recurrent communication. By analyzing the corresponding continuous synaptic dynamics and numerically simulating the networks, we show that the network with interneurons is more robust to initialization than the network with direct recurrent connections in the sense that the convergence time for the synaptic dynamics in the network with interneurons (resp. direct recurrent connections) scales logarithmically (resp. linearly) with the spectrum of their initialization. Our results suggest that interneurons are computationally useful for rapid adaptation to changing input statistics. Interestingly, the network with interneurons is an overparameterized solution of the whitening objective for the network with direct recurrent connections, so our results can be viewed as a recurrent linear neural network analogue of the implicit acceleration phenomenon observed in overparameterized feedforward linear neural networks.