What Can a Single Neuron Compute?

What can a single neuron compute? Abstract In this paper we formulate a description of the computation performed by a neuron as a combination of dimensional reduction and nonlinearity. 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 or perceptron 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.