Internal Anthropic model refuted the 3SUM and APSP hypotheses: first truly subquadratic 3SUM and truly subcubic APSP (Alman & Vassilevska Williams)

A new preprint by Alman & Vassilevska Williams presents deterministic O(n^1.9992) 3SUM and O(n^2.9995) integer-weight APSP, marking the first polynomial improvements over the textbook n2 and n3 bounds. This breakthrough relies on a novel thin matrix product algorithm, which also accelerates Exact Triangle, Zero-Weight k-Clique, and Tree Edit Distance. Interestingly, an internal Anthropic research model independently discovered the core algorithm, and the main theorems are formalized in Lean.

This paper is notable as an internal Anthropic research model independently discovered the core algorithm, unlike typical human-led algorithmic breakthroughs.