Toward a Theory for Macroscopic Neural Computation Based on Laplace Transform

Back to Main BRAIN TMM page





Title:  Toward a Theory for Macroscopic Neural Computation Based on Laplace Transform

Effective cognition requires us to orient ourselves in space and time.  A great deal of neural evidence suggests that the hippocampus and related brain structures maintain a cognitive map of the world using spatial and temporal coordinates.  We describe a computational theory to estimate continuous variables such as space and time using the cooperative activity of many neurons.  According to this hypothesis, functions over space and time are not estimated directly but via estimating the Laplace transform of those functions.  The inverse transform can be computed using a well-known neural circuit, resulting in a close correspondence with well-known neural findings from place cells and time cells.  Recent evidence from rodent and monkey recordings provide dramatic evidence that the entorhinal cortex maintains an estimate of the Laplace transform of functions of time, confirming a unique prediction of this computational approach.

Grant #: EB022864

Status:  Completed  2019/08/31

This review article provides a high level review of theoretical and empirical work suggesting a theoretical framework for how the brain might think.   The basic idea is that populations of neurons represent information over continuous dimensions such as time and space, but also other more abstract dimensions. The theory suggests that the brain uses the Laplace transform to build and manipulate these representations. 
Howard, M.W. and Hasselmo, M.E. (submitted). Cognitive computation using neural representations of time and space in the Laplace domain.

This paper shows evidence for the real Laplace transform of time in entorhinal cortex, confirming a prediction of the theory going back more than a decade.
Bright, I.M.*, Meister, M.L.R.*, Cruzado, N.A., Tiganj, Z., Buffalo, E.A.*, and Howard, M.W.* (In press). 
A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortexPNAS…

BRAIN Math Project - Howard.pdf


2020 BRAIN PI meeting - Labroots poster and audio track,

2019 BRAIN PI Meeting - poster

Marc Howard at poster 2019


















Link to Data/Model Reuse abstract, [Link] 

Abstract for U19 Data match:
We have worked on a theory for how populations of neurons represent information and manipulate information.  The theory interfaces well with cognitive models, especially for working memory tasks.   The theory predicts that neural populations come in pairs.  The optimal data for us has spikes from many simultaneously recorded neurons from more than one brain region during a complex behavior that we can analyze.  The model is scale-invariant so very ``slow'' tasks (extended over more than a minute per trial) are of special interest.


2021 Brain PI Meeting


Link to Poster:



Back to Main BRAIN TMM page





Table sorting checkbox