Comments on: Deep learning and toposes https://lievenlebruyn.github.io/neverendingbooks/deep-learning-and-toposes/ Sat, 31 Aug 2024 11:08:25 +0000 hourly 1 https://wordpress.org/?v=6.6.1 By: Shiva https://lievenlebruyn.github.io/neverendingbooks/deep-learning-and-toposes/#comment-130 Tue, 18 Jan 2022 04:38:58 +0000 http://www.neverendingbooks.org/?p=10027#comment-130 Hi Mr. Bruyn,
I really enjoy reading your blog as an aspiring mathematician currently pursuing a Masters.
Here is another paper that may interest you: https://arxiv.org/abs/2006.15136: Homotopy Theoretic and Categorical Models of Neural Information Networks by Manin-Marcolli.
Entropy seems to pop up a lot in all of this. So I thought I might mentione some highly unlikely places where it crops up.

It appears in the work on Connes-Consani’s approach to the “Field with one element” :https://arxiv.org/abs/0911.3537- Characteristic one, entropy, and the absolute point

It also occurs in constructing real analogs of P-adic period rings of P-adic Hodge theory: https://arxiv.org/abs/1202.4377
The universal thickening of the field of real numbers

This latter one seems to be related to the condensed mathematics of Scholze and Clausen. Scholze talks about it in both the Condensed mathematics and Analytic Geometry lecture notes, as well here: https://www.ams.org/journals/notices/202007/rnoti-p1010.pdf – This one is a tribute to Fontiane

It might have connections to a geometry below Spec(Z) is what Scholze seems to be saying.

Hope you find all of this interesting and worth writing about.

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