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Early sensory systems in the brain rapidly adapt to fluctuating inputstatistics, which requires recurrent communication between neurons.Mechanistically, such recurrent communication is often indirect and mediated bylocal interneurons. In this work, we explore the computational benefits ofmediating recurrent communication via interneurons compared with directrecurrent connections. To this end, we consider two mathematically tractablerecurrent linear neural networks that statistically whiten their inputs -- onewith direct recurrent connections and the other with interneurons that mediaterecurrent communication. By analyzing the corresponding continuous synapticdynamics and numerically simulating the networks, we show that the network withinterneurons is more robust to initialization than the network with directrecurrent connections in the sense that the convergence time for the synapticdynamics in the network with interneurons (resp. direct recurrent connections)scales logarithmically (resp. linearly) with the spectrum of theirinitialization. Our results suggest that interneurons are computationallyuseful for rapid adaptation to changing input statistics. Interestingly, thenetwork with interneurons is an overparameterized solution of the whiteningobjective for the network with direct recurrent connections, so our results canbe viewed as a recurrent linear neural network analogue of the implicitacceleration phenomenon observed in overparameterized feedforward linear neuralnetworks.

Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptation