Evidence accumulation in a Laplace domain decision space

TL;DR

This paper introduces a neural implementation of evidence accumulation in the Laplace domain, predicting exponential growth in firing rates and a novel neural representation of accumulated evidence, aligning with recent neural findings.

Contribution

It proposes a Laplace transform-based neural model for evidence accumulation, offering a new mathematical framework and neural predictions for decision-making processes.

Findings

Neural firing rates grow exponentially to a bound during decision tasks.

Two neural populations encode the Laplace transform and its inverse, representing evidence.

Model aligns with recent neural recordings from rodent studies.

Abstract

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially, across neurons there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform, these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a "decision axis." This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.