Post #2500974

2025-05-14 20:17 UTC

I&#39;ve been working (together with Javier Gomez-Serrano) with a group at Google Deepmind to explore potential mathematical applications of their tool &quot;AlphaEvolve&quot;, a successor of their earlier tool &quot;Funsearch&quot; that was publicly announced today: https://deepmind.google/discover/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/ . Very roughly speaking, this is a tool that can attempt to extremize functions F(x) with x ranging over a high dimensional parameter space Omega, that can outperform more traditional optimization algorithms when the parameter space is very high dimensional and the function F (and its extremizers) have non-obvious structural features. Some of the preliminary problems we have tried this on, including problems involving harmonic analysis inequalities, additive combinatorics, and packing, were already mentioned in the announcement; we are now gradually moving on to more challenging problems where the parameter space has a sparser set of good solutions. The work is still ongoing, but I hope to be able to report more upon it when we are closer to completion (probably a few months from now).

Replies (8)

@highergeometer@mathstodon.xyz 2025-05-14 21:25

@tao@mathstodon.xyz People are talking about this construction https://math.stackexchange.com/a/662382/3835 that claimed back in 2014 to do 4x4 matrix multiplication in 48 scalar multiplications. Thoughts? And just while typing this I got pinged with a result from 1970: https://mathstodon.xyz/@fredrikj/114508287537669113

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@sahak@xn--69aa8bzb.xn--y9a3aq 2025-05-15 01:44

@tao@mathstodon.xyz AlphaExplore or AlphaEvolve?

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@TomL@mathstodon.xyz 2025-05-15 08:35

@tao@mathstodon.xyz sounds like it would help to quantify the roughness of the function. Smooth analytic functions are easier to extremise than fractals, which are easier than even rougher functions. Comes down to the asymptotic behaviour of its power spectrum. They typically require different optimisers. On the other hand, this roughness may very in space and with scale, making the problem harder. It may even vary non-smoothly with these!

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@allendist57@mathstodon.xyz 2025-05-15 19:23

@tao@mathstodon.xyz from what if understand you both specificity the problem and gave it an action space in the form of a class of functions for example step function. Is this correct and how important was that to the process

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@kailuowang@mathstodon.xyz 2025-05-16 14:21

@tao@mathstodon.xyz do you see it as a possible step towards a tool (or generally speaking, "algorithm", ) that can eventually replace optimizers such as gradient descent or adam in large neural network training?

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@battaglia01@mathstodon.xyz 2025-05-17 23:54

@tao@mathstodon.xyz very neat - is x supposed to be some high dimensional R^n, or could this also work if x is in some other domain, e.g. Z^n?

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@ReD_CoDE@mathstodon.xyz 2025-05-20 21:46

@tao@mathstodon.xyz I'm developing a new paradigm, called generator paradigm, also generative learning (GL) Would be happy to know your view: (A,W) = G(z), G ∈ G_type, type ∈ {symbolic, neural, RL-based, procedural, neuro-symbolic, . . . }. where: - z is a semantic seed encoding the task, environment, or behavior description. - A is the architecture, specifying the computational graph, structure, or symbolic program of the model. - W are the parameters (e.g., weights, rules, constants) instantiated within A. - G belongs to a class of generators G_type, indexed by their realization type (e.g., symbolic, neural, procedural, RL-based, etc.). It sidesteps "symbolic traps," like the EA used in AlphaEvolve, but is even better

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@ReD_CoDE@mathstodon.xyz 2025-05-21 22:40

@tao@mathstodon.xyz https://zenodo.org/records/15478507

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