# How the Brain Creates a Timeline of the Past

**URL:** <https://discourse.numenta.org/t/how-the-brain-creates-a-timeline-of-the-past/7008>\
**Category:** General Neuroscience\
**Tags:** time\
**Created:** [January 5, 2020, 4:23pm UTC](https://discourse.numenta.org/t/how-the-brain-creates-a-timeline-of-the-past/7008 "2020-01-05T16:23:50Z")\
**Posts on this page:** 1\
**Showing post:** 6

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**Author:** ![mthiboust](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.numenta.org/mthiboust/32/4509_2.png) [@mthiboust](https://discourse.numenta.org/u/mthiboust)\
**Post date:** [January 7, 2020, 10:16pm UTC](https://discourse.numenta.org/t/how-the-brain-creates-a-timeline-of-the-past/7008/6 "2020-01-07T22:16:03Z")

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Thanks Mark for the info. I didn’t know about the “inverse Laplace transform” time coding theory. I quickly scanned the first paper (Howard 2014) and it looks intriguing.

@MabuManaileng: yes, we are speaking of the mathematical Laplace transform that the brain is approximating with neural networks (according to Howard’s theory).

Looking at Howard’s more recent papers, I came across this one that retained my attention: _Predicting the Future with Multi-scale Successor Representations (Momennejad & Howard, 2018):_  
[https://www.biorxiv.org/content/biorxiv/early/2018/10/22/449470.full.pdf](https://www.biorxiv.org/content/biorxiv/early/2018/10/22/449470.full.pdf)

> _In what follows we show that a neurally plausible linear operation, namely the inverse of the Laplace transform, can be used to compute the derivative of multi-scale SR.  
> […]  
> We have shown that a multi-scale SR ensemble is equivalent to the real Laplace transform of a given states timeline of successor states. The inverse of this Laplace transform computes the derivative of the SR ensemble, recovering which future states lie within given temporal horizons of a given state (e.g., the present state, or the goal state)._

In short, mixing ideas from Laplace transform & Successor Representation (SR) help to overcome limitations of SR when modeling place and grid cells. This combination is called multi-scale SR ensemble and I really like the idea!

Some more info on SR in this post:

> [@Grid cells - not necessarily all about space!](https://discourse.numenta.org/t/grid-cells-not-necessarily-all-about-space/6918/3):
>
> Interesting that you naturally evoke eigenvalues for formalizing the grid cell “thing”. Did you know that a theory explains grid cell patterns by eigenvalues? Place cells can be modeled with Successor Representations (a technique from Reinforcement Learning). And surprisingly, grid cell patterns look accurately similar to the eigendecomposition of those Successor Representations. A good and not too technical blog post on Successor Representations: [https://medium.com/@awjuliani/the-present-in…](https://medium.com/@awjuliani/the-present-in-terms-of-the-future-successor-representations-in-reinforcement-learning-316b78c5fa3)

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