Fwd: PatternBoost: AI for (current) Maths

[Siddhartha Gadgil]

---------- Forwarded message ---------
From: Siddhartha Gadgil <gad...@iisc.ac.in>
Date: Mon, 11 Nov 2024 at 07:38
Subject: PatternBoost: AI for (current) Maths
To: ALL @ MATH <all....@iisc.ac.in>

Dear All,

         Could not resist sharing a paper: https://arxiv.org/pdf/2411.00566, which shows how AI can be used to help current mathematics (at least in some domain) and even has code which they explain can be used almost in a plug-and-play mode for other problems. The authors have in the past done separate work advancing mathematics using AI (notably https://arxiv.org/abs/2410.08304 which is also very interesting).

         The main idea here is to search for "patterns", say graphs with special properties by combining:

• A local search, specific to the problem to generate a bunch of good candidates.
• Getting a "transformer", essentially a specially trained GPT-2, to suggest candidates "globally similar" to the good candidates.

The transformer is based on the code "morelikethis" (by Andrej Karpathy). This is a demonstration code where you train a model with a bunch of stuff, and it generates more "similar" stuff.

The idea of the search is to generate an initial set of candidates using local search, then train a transformer to generate more patterns, which are then optimized by local search to give fresh patterns. This is data for more training, so we iterate.

Trying this for other problems is a great project in my view and I am happy to discuss with anyone who wants to give this a shot.

regards,

Siddhartha