AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
An information theoretic approach to Sidorenko's conjecture
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abstract
We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type conditions allow us to extend Sidorenko's conjecture to large families of $k$-uniform hypergraphs. This is somewhat unexpected since the conjecture fails for $k$ uniform hypergraphs in general.
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Caterpillar-based homomorphism counts yield pessimistic join size estimates that overestimate by roughly m to the power 3/5 in simulations, improving on prior star and bi-star exponents.
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Mathematical exploration and discovery at scale
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
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Sidorenko-Inspired Pessimistic Estimation
Caterpillar-based homomorphism counts yield pessimistic join size estimates that overestimate by roughly m to the power 3/5 in simulations, improving on prior star and bi-star exponents.