Nonlinear stimulus representations in neural circuits with approximate excitatory-inhibitory balance.

Balanced excitation and inhibition is widely observed in cortex. How does this balance shape neural computations and stimulus representations? This question is often studied using computational models of neuronal networks in a dynamically balanced state. But balanced network models predict a linear relationship between stimuli and population responses. So how do cortical circuits implement nonlinear representations and computations? We show that every balanced network architecture admits stimuli that break the balanced state and these breaks in balance push the network into a “semi-balanced state” characterized by excess inhibition to some neurons, but an absence of excess excitation. The semi-balanced state produces nonlinear stimulus representations and nonlinear computations, is unavoidable in networks driven by multiple stimuli, is consistent with cortical recordings, and has a direct mathematical relationship to artificial neural networks. Several studies show that neurons in the cerebral cortex receive an approximate balance between excitatory (positive) and inhibitory (negative) synaptic input. What are the implications of this balance on neural representations? Earlier studies develop the theory of a “balanced state” that arises naturally in large scale computational models of neural circuits. This balanced state encourages simple, linear relationships between stimuli and neural responses. However, we know that the cortex must implement nonlinear representations. We show that the classical balanced state is fragile and easily broken in a way that produces a new state, which we call the “semi-balanced state.” In this semi-balanced state, input to some neurons is imbalanced by excessive inhibition—which transiently silences these neurons—but no neurons receive excess excitation and balance is maintained the sub-network of non-silenced neurons. We show that stimulus representations in the semi-balanced state are nonlinear, improve the network’s computational power, and have a direct relationship to artificial neural networks widely used in machine learning.