  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.
