{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2021-04-29-wagner-rl-counterexamples/","md":"https://postcutoff.com/e/2021-04-29-wagner-rl-counterexamples/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2021-04-29-wagner-rl-counterexamples","date":"2021-04-29","date_precision":"day","short_title":"Adam Zsolt Wagner uses reinforcement learning to find counterexamples to open graph-theory conjectures","deck":null,"takeaway":"Wagner's 'Constructions in combinatorics via neural networks' (arXiv 2104.14516) used a simple cross-entropy RL method to find explicit counterexamples to several published conjectures in extremal combinatorics and spectral graph theory.","category":"science","category_label":"Science & math","importance":2,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Constructions in combinatorics via neural networks (arXiv 2104.14516)","url":"https://arxiv.org/abs/2104.14516","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"Reimplementation and extension (arXiv 2403.18429)","url":"https://arxiv.org/abs/2403.18429","type":"paper","group":"primary","domain":"arxiv.org"}],"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Adam Zsolt Wagner"],"title":"Adam Zsolt Wagner uses reinforcement learning to find counterexamples to open graph-theory conjectures","summary":"Wagner's 'Constructions in combinatorics via neural networks' (arXiv 2104.14516) used a simple cross-entropy RL method to find explicit counterexamples to several published conjectures in extremal combinatorics and spectral graph theory.","key_facts":["arXiv 2104.14516 (29 Apr 2021)","Refuted several conjectures about graph eigenvalues and a Brualdi–Cao question on permanents of pattern-avoiding matrices","Small neural network plus deep cross-entropy method; no LLM","Wagner later joined Google DeepMind and co-authored the 2025 AlphaEvolve maths paper with Tao"],"key_numbers":[],"tags":["math","combinatorics","reinforcement-learning","counterexamples"],"science":{"field":"mathematics","subfield":"extremal combinatorics / spectral graph theory","problem":"Several published conjectures on graph invariants","result":"Explicit counterexamples found by an RL agent that treats building a graph as a game, rewarded by how badly the conjecture fails.","open_since":"","ai_system":["deep cross-entropy RL"],"human_role":"Human chose conjectures and reward functions; search autonomous; counterexamples trivially checkable","verification":{"key":"preprint","label":"Preprint only","text":"Counterexamples checkable by direct computation; reimplemented by others (arXiv 2403.18429)"},"status":"confirmed","shock":""},"body_md":"## What happened\n\nA lone mathematician showed that off-the-shelf RL could disprove conjectures by searching for graphs that violate them.\n\n## Why it matters\n\nIt was the template for the 2023–2026 wave of AI counterexample finding (FunSearch, AlphaEvolve, PatternBoost, LLM counterexamples).","disputed":[],"related":[{"id":"2025-11-05-alphaevolve-tao-67-problems","url":"https://postcutoff.com/e/2025-11-05-alphaevolve-tao-67-problems/","date":"2025-11-05","date_precision":"day","short_title":"Tao, Gómez-Serrano, Georgiev and Wagner test AlphaEvolve on 67 maths problems","deck":null,"takeaway":"Coming from Tao, it gave the maths community a credible, balanced picture of what AI search could do, just before the 2026 surge.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":3,"official":2,"filed":"2026-09-29","updated":"2026-10-19","orgs":["Google DeepMind","UCLA","Brown University"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":null}