# Mathematic in HTM

Hello,
please i wonder whether this question has been answered but i wanted to know if there is any comprehensive mathematical framework on HTM
THANKS

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This is some of the deep underpinnings of the HTM theory:

This puts these SDRs to work so you can see some context:

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Iâ€™ve also found two non-Numenta papers of note that examine the mathematics:

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What do you mean by â€śMathematical Frameworkâ€ť? Can you please cite an analogy?

If youâ€™re looking for formalization of the HTM theory, the closest I have read so far is the one posted above by @jacobeverist, specifically the first resource about the spatial pooler.

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i meant the mathematical base where we can stand for further modification in order to match it to other algorithms

so far thank @Bitking @jacobeverist for sharing great insight

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I think one of the things to note when dealing with the spatial pooler and temporal memory in HTM is that they exhibit behavior of a complex system wherein it is not straightforward to reduce the emergent behavior (e.g. learning) to its tinier rules and formulate a mathematical framework out of it. Firstly IMO the HTM was mainly biological-constraints-driven and computation is only second. Of course you can approximate the HTMâ€™s operations using math and in my experience there are related posts about this in this forum if youâ€™ll have a search about (objective functions, learning, cost function, linear combinations, etc).

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That said, I do think that set theory may have the right tools to analyze the behavior of sparse systems in general, and HTM in particular.

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I have actually put together a nice mathematical framework using set theory focused on conceptualizing the computational and representational properties of HTM-like systems. It actually lends itself well to understanding what is actually going on with the distributed representation, what is being achieved with a spatial pooler/temporal learner, how you would construct systems using modular components, and how you would construct algorithms that do other types of operations.

I am currently working on a paper about this that I hope to release in a month or two. I think you will find it very interesting.

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I find using set theory and graph theory very convenient in describing and analyzing the SP.

I look forward to it. Awesome. Iâ€™m also trying to come up with a narrative about whatâ€™s really going on in an SP. But no guarantee on its progress yet. Iâ€™m also currently reading about Judea Pearlâ€™s causal framework and see if I can relate this to HTM. This is of course done in my spare time.

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Some of the papers cited above rely on this paper from 2015: Encoding Reality: Prediction-Assisted Cortical Learning Algorithm in Hierarchical Temporal Memory which gives a pretty rigorous treatment of the CLA machinery. There have been a number of theses which also base their treatment on the paper Citations

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It sounds like there are a number of us trying to come up with a more formal mathematical description and/or narrative of the HTM algorithms. Would any of you be interested in collaborating on a paper where we all bring our specific interests and expertise to bear on the problem? I think one benefit of such a collaboration might be to come up with a consistent set of notations and nomenclature that would allow us to talk to each other in common terms rather than referring to our own respective silos.

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Post what you currently have?

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Okay. Iâ€™ve got a rough start on a paper here. Let me know if you want to edit it, and I will add you as a collaborator. (DM me the email address you use to register on the Overleaf site.)

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@fergalbyrne Itâ€™s been a while since I read your papers and I appreciate being reminded about where they situate in the larger context. I will have to return to them with fresh eyes again to see what insights I can get again.

Thanks!

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Hi, I hope Iâ€™m not too late to the party . So Iâ€™m doing my masters (In mathematics) on this topic and would like to know if there is any existing research that I can maybe have a look at to get myself up to speed with you guys on this. Iâ€™m excited to see how this area of research will progress.

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Hi,

Check here:

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Hey thanks. Looking forward to seeing some of your previous work too, as Jacob Everist mentioned. Exciting business.

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@Thoriso_Molefe

Hi. My white paper is still a work in progress. Iâ€™m about 50% done. Thereâ€™s lots of visuals that Iâ€™m struggling with since they require python scripts to generate. Hopefully it will be ready in 2 months.