Modeling Higher-Order Interactions in Sparse and Heavy-Tailed Neural Population Activity.

Area of Science:

• Computational Neuroscience
• Statistical Physics
• Machine Learning

Background:

• Neurons exhibit sparse, variable spiking with higher-order interactions.
• Population activity is often silent, punctuated by synchronous bursts, leading to heavy-tailed distributions.
• The origin of these population-level patterns from individual neuron nonlinearities is not well understood.

Purpose of the Study:

• To derive conditions for sparse, heavy-tailed firing rate distributions in large homogeneous binary neural networks.
• To propose a class of distributions capturing these patterns and their underlying neural mechanisms.
• To connect these findings to recurrent neural networks and memory capacity.

Main Methods:

• Derivation of sufficient conditions for sparse, heavy-tailed distributions in infinite binary neural networks.
• Proposal of an exponential family subclass with specific interaction structures.
• Analysis of recurrent neural networks exhibiting these distributions.

Main Results:

• Identified conditions for generating sparse and heavy-tailed population firing rate distributions.
• Characterized a distribution class with alternating higher-order interactions and a base-measure function.
• Found that individual neurons with threshold-like and supralinear activation facilitate sparse, synchronous activity.

Conclusions:

• Individual neuron nonlinearities are key to generating population-level sparse and heavy-tailed firing patterns.
• These patterns are linked to memory capacity in networks like modern Hopfield networks.
• The theoretical framework supports the development of energy-efficient, spike-based learning machines.