Hopf algebras and Markov chains: Two examples and a theory · HackerPapers discussions

Hopf algebras and Markov chains: Two examples and a theory — mentioned by adamnemecek

Tue, 25 Apr 2023 19:02:04 GMT

Hopf algebra subsumes like all all currently fashionable architectures (transformers, convnets, SSM, diffusion models) and then some. Hopf convolution is a surprisingly general concept, Groebner bases are the thing used to calculate the antipode. Hopf algebra is tensor bialgebra, i.e. tensor with a built in feedback (which subsumes autodiff). I have written a paper on this recently https://arxiv.org/abs/2302.01834 This paper is also good https://arxiv.org/abs/1206.3620 I have a discord channel https://discord.cofunctional.ai.

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Hopf algebras and Markov chains: Two examples and a theory — mentioned by adamnemecek

Sun, 09 Apr 2023 23:11:22 GMT

I have written a paper on this recently viewing transformers as Hopf algebras https://arxiv.org/abs/2302.01834. This paper is very relevant https://arxiv.org/abs/1206.3620.

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Hopf algebras and Markov chains: Two examples and a theory — mentioned by adamnemecek

Fri, 10 Mar 2023 20:41:46 GMT

I don't know how to talk about this without some technical terms. Spend a little bit of time on it, it's a lot more understandable than you think. Peep this paper https://arxiv.org/abs/1206.3620. I have a discord channel if you want to learn more https://discord.cofunctional.ai.

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Hopf algebras and Markov chains: Two examples and a theory — mentioned by adamnemecek

Wed, 08 Mar 2023 16:06:33 GMT

Ok read the Persi Diaconis one https://arxiv.org/abs/1206.3620. You are right, it can be more polished but also it covers quite a lot and it was surprisingly hard to fit it all in. The main response I have been getting though is "I won't believe this until I see the implementation" so I have been concentrating on that.

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Hopf algebras and Markov chains: Two examples and a theory — mentioned by adamnemecek

Tue, 07 Mar 2023 21:01:25 GMT

I have recently written a paper on understanding machine learning via the lens of Hopf algebra https://arxiv.org/abs/2302.01834. Hopf algebras (which are really just tensors with recurrence relations built in) subsume convnets, transformers and diffusion model and also provide a theoretically better autodiff that operates within single layers as opposed to across entire graphs. Furthermore, there is a correspondence between Hopf algebra and cyclical linear logic and Hopf algebras are related to zonotopes, which are polyhedra that have been used in verified numerical computation. I'm strongly…

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Hopf algebras and Markov chains: Two examples and a theory — HN submission

Sun, 05 Mar 2023 15:46:26 GMT

Hopf algebras and Markov chains: Two examples and a theory (2012)

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.