A Neuron as a Signal Processing Device

TL;DR

This paper models a neuron as a signal processing device that minimizes a cost function, reproducing physiological properties and enabling new insights into neuronal computation and neuromorphic design.

Contribution

It introduces an online algorithm that links neuronal physiology with computational modeling, unifying biological properties with a formal optimization framework.

Findings

Reproduces physiological properties like weighted summation and leaky integration.

Derives an Oja-like, parameter-free synaptic learning rule.

Makes testable predictions about neuronal behavior.

Abstract

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of synaptic weights scaled by an outgoing sparse activity vector. Formally, a neuron minimizes a cost function comprising a cumulative squared representation error and regularization terms. We derive an online algorithm that minimizes such cost function by alternating between the minimization with respect to activity and with respect to synaptic weights. The steps of this algorithm reproduce well-known physiological properties of a neuron, such as weighted summation and leaky integration of synaptic inputs, as well as an Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework makes several predictions, some of which can be verified by the existing data, others require further experiments. Such framework should allow modeling the function of neuronal circuits without necessarily measuring all the microscopic biophysical parameters, as well as facilitate the design of neuromorphic electronics.