The Difference Neuron-a new spiking neuron model

The previously proposed Neural Mode (J. Kanev, A. Koutsou, C. Christodoulou, K. Obermayer; 2016; Neural Computation, 28(10):2091-2128) quantifies to what extent spiking neurons use temporal integration or coincidence detection to calculate their output from their input. While the Neural Mode is easy to measure, parameterising a neuron model to show a certain level of coincidence detection or integration is not straightforward. We propose a new spiking neuron model - the Difference Neuron - that integrates or detects coincidences according to a predefined value of the Neural Mode. The Difference Neuron is a simple model without hidden states that depend on infinite input. It receives one or several input spike trains, and it can be configured to detect simple coincidences, gaps, or more complex patterns. It can exhibit spike bursting, and it covers areas of mathematical operation a biological neuron does not - it can spike without stimulus, it can operate purely on inhibition, and it can show inhibition and coincidence detection combinations that are unavailable to other neuron models. Sparsely connected networks of Difference Neurons can show different levels of regular and irregular synchronisation, depending on the Neural Mode of their neurons. We explore several single-neuron examples and investigate the neuron's behaviour. Because this new model does not include differential equations describing membrane potentials or ion concentrations, but computes its output spike times from simple time comparisons, we believe the Difference Neuron will simplify investigations into dynamics of spiking neurons and networks, and into spike patterns and the mechanisms of the neural code.