An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
Reinforced generation of combinatorial structures: Hardness of approximation
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Litvak's conjecture on minimizing moments of Gaussian minima is disproved by a cosine-based correlation matrix for small n and p, with a new conjecture proposed that this matrix is the general minimizer, supported conditionally via a volumetric extension of Fejes Tóth's zone conjecture.
LLM-reinforced evolutionary search produces exact values Z(11,21,3,3)=116, Z(11,22,3,3)=121, Z(12,22,3,3)=132 and lower bounds for 41 additional Zarankiewicz numbers.
k-server-bench formulates potential-function discovery for the k-server conjecture as a code-based inequality-satisfaction task; current agents fully solve the resolved k=3 case and reduce violations on the open k=4 case.
Code evolution produces link prediction algorithms with average AUC of 0.915 versus 0.783 for human-designed methods across 580 networks, with better scalability.
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
Glia deploys a multi-agent LLM workflow with reasoning, experimentation, and analysis agents to generate interpretable algorithms for request routing, scheduling, and auto-scaling in distributed GPU clusters, reaching human-expert performance levels.
citing papers explorer
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Advancing Mathematics Research with AI-Driven Formal Proof Search
An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
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A revision of Litvak's conjecture on Gaussian minima and a volumetric zone conjecture
Litvak's conjecture on minimizing moments of Gaussian minima is disproved by a cosine-based correlation matrix for small n and p, with a new conjecture proposed that this matrix is the general minimizer, supported conditionally via a volumetric extension of Fejes Tóth's zone conjecture.
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New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Search
LLM-reinforced evolutionary search produces exact values Z(11,21,3,3)=116, Z(11,22,3,3)=121, Z(12,22,3,3)=132 and lower bounds for 41 additional Zarankiewicz numbers.
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$k$-server-bench: Automating Potential Discovery for the $k$-Server Conjecture
k-server-bench formulates potential-function discovery for the k-server conjecture as a code-based inequality-satisfaction task; current agents fully solve the resolved k=3 case and reduce violations on the open k=4 case.
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Code evolution for link prediction in complex networks
Code evolution produces link prediction algorithms with average AUC of 0.915 versus 0.783 for human-designed methods across 580 networks, with better scalability.
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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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Glia: A Human-Inspired AI for Automated Systems Design and Optimization
Glia deploys a multi-agent LLM workflow with reasoning, experimentation, and analysis agents to generate interpretable algorithms for request routing, scheduling, and auto-scaling in distributed GPU clusters, reaching human-expert performance levels.