Transient chaotic dimensionality expansion by recurrent networks

Abstract

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these two forms of signaling? We develop a unified mean-field theory for large random networks to show that first- and second-order statistics in rate and binary networks are in fact identical if rate neurons receive the right amount of noise. Their response to presented stimuli, however, can be radically different. We quantify these differences by studying how nearby state trajectories evolve over time, asking to what extent the dynamics is chaotic. Chaos in the two models is found to be qualitatively different. In binary networks we find a network-size-dependent transition to chaos and a chaotic submanifold whose dimensionality expands stereotypically with time, while rate networks with matched statistics are nonchaotic. Dimensionality expansion in chaotic binary networks aids classification in reservoir computing and optimal performance is reached within about a single activation per neuron; a fast mechanism for computation that we demonstrate also in spiking networks. A generalization of this mechanism extends to rate networks in their respective chaotic regimes.

Final, shortened post-print version. (see v3 for extended material on microscopic and macroscopic chaos)

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Cited by in corpus (7)

• Dimension of activity in random neural networks
• Self-learning Machines based on Hamiltonian Echo Backpropagation
• Large Deviations Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions
• Extended Anderson Criticality in Heavy-Tailed Neural Networks
• Evolving to learn: discovering interpretable plasticity rules for spiking networks
• Irreversibility in Non-reciprocal Chaotic Systems
• Discontinuous transition to chaos in a canonical random neural network