ANC Workshop - William Berg

Speaker: William Berg

Title:

Towards gradient-based spiking neural network parameter inference

Abstract:

ML and gradient-descent based approaches have long been successful in optimising parameters for various neural network architectures by minimising over differentiable loss functions, resulting in high-performance inferred network models that approximate the functional mapping of the training data.

However, application to networks where the neuron-models mimic biophysical properties, including membrane potential and often associated nonlinear internal dynamics, is limited.

Firstly, the output of each node is usually of a binary nature, making the signal non-differentiable, and secondly, each network node has temporal dependencies with one-another, as well as to the data-domain.

With the goal of inferring models that exhibit spiking behaviour similar to that of in vivo recordings, we outline a methodology for leveraging gradient-based methods to train and infer spiking models that capture independent higher-order statistics of the recorded site, as well as biophysically interpretable parameters.

A key ingredient in this is to either use a surrogate-gradient for spike detection and gradient-propagation through time, or to use a synaptic model where continuous sub-threshold currents are induced inside of a defined active zone as a function of the membrane potential.  Further, because the input to a recorded site is unknown, we assume an input generator function which is a Poisson density function.

Lastly, we assess and compare functional ensembles in the target spike train and inferred model spike trains by non-negative matrix factorisation.