A neural network can be trained to predict the distance to a spike, and this representation can be used to effectively predict spike times.
The auto-regressive prediction of a spike train using a spike distance model and Poisson-based models.
A spike distance function maps each point in time to a scalar representing the temporal distance to the nearest spike. This is either the time elapsed since the last spike or the time remaining until the next spike, whichever is less. This is an implicit representation of a set of spikes using contours.
Neural networks can be trained to approximate spike distance functions. The lost signal can be a distance such as Euclidean distance between the predicted and true spike distance functions. Spikes can be inferred from outputs of trained models. Intuitively, this is done by placing spikes at the troughs of the outputted array.
The task is to produce spike trains, so the evaluation metrics should measure the quality of the spike trains produced. High quality should correspond to a spike train that is close to the ground truth spike train. To measure this fidelity with respect to the ground truth, we use spike train similarity and difference metrics: Schreiber similarity and Van Rossum distance.
A neural network was trained multiple times: using the spike distance objective and using Poisson objectives with different summation interval lengths. The spike distance approach outperforms the Poisson approach across a wide range of smoothing parameters for the two evaluation metrics used. Spike prediction for the Poisson models utilized sampling to pick a spike count, then that number of spikes were tiled across the output interval. Other inference approaches were considered too, and for those, please check out the paper.
Approaches to predicting neuronal spike responses commonly use a Poisson learning objective. This objective quantizes responses into spike counts within a fixed summation interval, typically on the order of 10 to 100 milliseconds in duration; however, neuronal responses are often time accurate down to a few milliseconds, and at these timescales, Poisson models typically perform poorly. We demonstrate this limitation, and present a new learning objective to overcome it. We propose the concept of a spike distance function that maps points in time to the temporal distance to the nearest spike. We show that neural networks can be trained to approximate spike distance functions, and we present an efficient algorithm for inferring spike trains from the outputs of these models. Using recordings of chicken and frog retinal ganglion cells responding to visual stimuli, we compare the performance of our approach to Poisson models trained with various summation intervals. We show that our approach outperforms the use of Poisson models at spike train inference.
@misc{doran2023distance,
title={Spike distance function as a learning objective for spike prediction},
author={Kevin Doran and Marvin Seifert and Carola A. M. Yovanovich and Tom Baden},
year={2023},
eprint={2312.01966},
archivePrefix={arXiv},
primaryClass={q-bio.NC}
}