What Can a Single Neuron Compute?

We implement this description for the Hodgkin Huxley model, identify the most relevant dimensions and find the nonlinearity. A two dimensional description already captures a significant fraction of the information that spikes carry about dynamic inputs.This description also shows that computation in the Hodgkin-Huxley model is more complex than a simple integrateand-fire orperceptron model. 1 Introduction Classical neural network models approximate neurons as devices that sum their inputs and generate a nonzero output if the sum exceeds a threshold. From our current state of knowledge in neurobiology it is easy to criticize these models as oversimplified: whereis the complex geometry of neurons, or the many different kinds of ion channel, each with its own intricate multistate kinetics? Indeed, progress at this more microscopic level of description has led us to the point where we can write (almost) exact models for the electrical dynamics of neurons, at least on short time scales. These nearly exact models are complicated by any measure, including tens if not hundreds of differential equations to describe the states of different channels in different spatial compartments of the cell. Faced with this detailed microscopic description, we need to answer a question which goes well beyond the biological context: given a continuous dynamical system, what does it compute? Our goal in this paper is to make this question about what a neuron computes somewhat moreprecise, and then to explore what we take to be the simplest example, namely the Hodgkin-Huxley model [1],[2] (and refs therein).