Simulating leaky integrate and fire neuron with integers

TL;DR

This paper introduces a novel integer-based simulation method for leaky integrate and fire neurons, enabling exact state comparisons and potentially improving the accuracy of neuronal network simulations.

Contribution

The authors propose a new integer-based simulation paradigm for LIF neurons that replicates standard behavior while allowing precise state comparisons.

Findings

Exact state comparison enabled by integer representation

Simulation matches standard floating point LIF neuron behavior

Potential for improved accuracy in neuronal network analysis

Abstract

The leaky integrate and fire (LIF) neuron represents standard neuronal model used for numerical simulations. The leakage is implemented in the model as exponential decay of trans-membrane voltage towards its resting value. This makes inevitable the usage of machine floating point numbers in the course of simulation. It is known that machine floating point arithmetic is subjected to small inaccuracies, which prevent from exact comparison of floating point quantities. In particular, it is incorrect to decide whether two separate in time states of a simulated system composed of LIF neurons are exactly identical. However, decision of this type is necessary, e.g. to figure periodic dynamical regimes in a reverberating network. Here we offer a simulation paradigm of a LIF neuron, in which neuronal states are described by whole numbers. Within this paradigm, the LIF neuron behaves exactly the same way as does the standard floating point simulated LIF, although exact comparison of states becomes correctly defined.