AlphaEvolve: A coding agent for scientific and algorithmic discovery

DeepMind white paper (June 2025) for the discovery-by-evolution pillar of AI4Math: an evolutionary coding agent where frontier LLMs are the mutation operator over entire codebases, and a programmatic evaluator grounds every generation. The loop: a program database (MAP-elites plus island populations, balancing quality with diversity) feeds a prompt sampler (parent program, high-scoring “inspirations”, optional context up to PDFs, and self-evolved meta prompts); an LLM ensemble proposes SEARCH/REPLACE diffs to code marked with EVOLVE-BLOCK comments; an evaluator cascade scores survivors, with multi-metric scoring used deliberately as a diversity mechanism even when one metric is the target. Against FunSearch, its predecessor: whole files instead of one Python function, any language, hours-long parallel evaluations, thousands rather than millions of samples, and — per the ablations — real benefit from stronger base models. Every component ablates positive (evolution, prompt context, meta-prompts, full-file scope, model strength).

Results across three registers

• Algorithm discovery. 14 matrix-multiplication SOTA improvements, headlined by 4×4 complex matrices in 48 multiplications — the first improvement over Strassen’s recursive 49 in characteristic 0 in 56 years (AlphaTensor’s 47 was mod-2 only). Found by evolving a tensor-decomposition search program (loss shaping, hallucination noise, discretization annealing — Fig. 4’s 15-mutation diff), not the algorithm directly.
• Open mathematics. 50+ construction problems curated with external mathematicians (Gómez-Serrano, Tao): best-known matched on ~75%, improved on ~20% — including Erdős’s minimum overlap problem and the kissing number in 11 dimensions (593, from 592). The method insight: evolve search heuristics rather than constructions, chaining specialized heuristics (coarse gains early, fine-tuning late) each seeded with the predecessor’s best construction.
• Production infrastructure. A Borg scheduling heuristic recovering 0.7% of fleet compute (deployed; chosen over deep RL explicitly for interpretability and debuggability), Gemini kernel tiling heuristics (23% kernel speedup, 1% training-time reduction, months of tuning → days), a TPU Verilog simplification, and 32% FlashAttention IR speedup. The deployed-in-production register is what separates this from demo papers — and includes the reflexive loop of Gemini optimizing its own training stack, which the discussion is careful to size honestly: gains moderate, iteration cycle months.

Assessment

• Durable: evolution as the harness that converts test-time compute into discovery, with the evaluator sidestepping hallucination entirely (only executed, scored code persists — verification-before-persistence at population scale, wang2023‘s rule with the critic replaced by ground truth); the evolve-the-searcher abstraction choice; multi-metric scoring as diversity pressure; the solution-vs-constructor-vs-searcher abstraction menu.
• Era-bound: model roster, every specific record (the math details were deferred to a follow-up paper), and the white-paper genre — no peer review, self-reported infra numbers.
• Boundary: stated by the authors (automated evaluators only) and sharpened by jiang2026 — score-function-driven exploration is bound to predefined objectives, transfers no structure across problems, and invents no concepts; it widens search, not understanding. That critique coexists with this shelf’s strongest counterpoint to it: within evaluator reach, the system produced provably correct, humanly-verified new mathematics.
• In this library: in liu2026‘s taxonomy this is the canonical artifact-locus system, and its complement is hubert2025: AlphaProof searches proof space under a fixed verifier, AlphaEvolve searches object space under a fixed scorer — proofs of statements versus witnesses for bounds, the two halves of what openai2026-style claims must eventually integrate.