
==== Front
ArXiv
ArXiv
arxiv
ArXiv
2331-8422
Cornell University

arXiv:2302.10163v4
2302.10163
4
preprint
Article
Learning temporal relationships between symbols with Laplace Neural Manifolds
Howard Marc W.
Esfahani Zahra G.
Le Bao
Sederberg Per B.
22 9 2024
arXiv:2302.10163v420 2 2023
https://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License, which allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
http://arxiv.org/abs/2302.10163v4
nihpp-2302.10163v4.pdf
Firing across populations of neurons in many regions of the mammalian brain maintains a temporal memory, a neural timeline of the recent past. Behavioral results demonstrate that people can both remember the past and anticipate the future over an analogous internal timeline. This paper presents a mathematical framework for building this timeline of the future. We assume that the input to the system is a time series of symbols--sparse tokenized representations of the present--in continuous time. The goal is to record pairwise temporal relationships between symbols over a wide range of time scales. We assume that the brain has access to a temporal memory in the form of the real Laplace transform. Hebbian associations with a diversity of synaptic time scales are formed between the past timeline and the present symbol. The associative memory stores the convolution between the past and the present. Knowing the temporal relationship between the past and the present allows one to infer relationships between the present and the future. With appropriate normalization, this Hebbian associative matrix can store a Laplace successor representation and a Laplace predecessor representation from which measures of temporal contingency can be evaluated. The diversity of synaptic time constants allows for learning of non-stationary statistics as well as joint statistics between triplets of symbols. This framework synthesizes a number of recent neuroscientific findings including results from dopamine neurons in the mesolimbic forebrain.

Fixed a bunch of typos. This is the final version of this paper on arXiv
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