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Reasoning Models

6 items across 3 editions. First seen Sat 12 Sep, last seen Tue 15 Sep. Traced across 1 weekly review.

How this story has evolved

From the week in review: the connections, developments and open questions filed under Reasoning Models, newest week first.

Week of 7–13 September 2026

Development · Tue 8 Sep, Fri 11 Sep
OpenAI says an internal model with 10,000 sub-agents solved Navier-Stokes; an NYU mathematician says he was pressed to drop an Anthropic-affiliated co-author

On 8 September OpenAI announced "that a multi-agent system, powered and coordinated by an unreleased internal model—that at one point had 10,000 different sub-agents working different parts and variations of the problem—has solved Navier-Stokes", one of the Clay Mathematics Institute's Millennium Prize problems. CNN reports OpenAI said "its model took 88 hours to solve the problem". Fortune puts the compute cost at "about $2 million" on one estimate, with "other reports put the number at 10 times greater still, at $22.5 million".

Open question
Will OpenAI's Navier-Stokes claim be verified, and what happened in the exchange Buckmaster describes?

The Clay Mathematics Institute has issued no determination; CNN reports that "Only one Millenium Prize problem has been officially solved so far". The model is unreleased and OpenAI's announcement page returned HTTP 403, so it was not read for this edition. Fortune derives the roughly $2 million from OpenAI's own briefing statement about compute "at least 1,000 times greater" than a prior about $2,000; the $22.5 million is an outside figure. Buckmaster's account of his exchange with Sebastien Bubeck is his own; Bubeck calls the circulating allegations "false and inflammatory" but his published replies do not address the specific allegation about removing a co-author's name. OpenAI says "we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Tuesday, 15 September 2026

Plan injection evades chain-of-thought monitors 25–33% of the time, Stanford and CMU researchers report Preprint

arXiv
  • arXiv:2609.15989, "Corrupt Plans, Clean Traces: Evading Chain-of-Thought Monitoring with Plan Injection" by Keertana Chidambaram, Andrew Ilyas and Vasilis Syrgkanis, submitted 14 September 2026, reports that planting harmful but benign-sounding reasoning in a model's context steers it to adversarial actions while evading monitors, "achieving 25-33% monitor evasion rates across different monitorability benchmarks" and scaling to larger models such as DeepSeek-R1.
  • The paper reports that actor models "not only follow injected plans but also paraphrase them as their own reasoning, without explicit attribution to the injections" — the property that defeats a monitor reading the trace.
  • The authors report that extra monitor resources can hurt: "giving the monitor access to the injected plan drops detection by as much as 50% in the Bio-Math task", and in a case study on monitor reasoning budget they find transcripts where additional thinking tokens "are spent rationalizing the injected plan rather than flagging it".
  • The paper is a preprint and has not been peer reviewed. It reports no results against monitoring as deployed in production by any frontier lab.
AlignmentEvalsAgent SecurityReasoning Models

Google Research and CMU harness scores 71.0% on research-level TCS-Bench, solves 218 of 222 Codeforces problems PreprintCompany claim

arXiv
  • arXiv:2609.15983, "Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science" by Honghao Lin, David P. Woodruff, Yuan Deng, Jieming Mao, Song Zuo and Vahab Mirrokni, submitted 14 September 2026, reports: "On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash."
  • The paper reports that in a separate Codeforces evaluation using Gemini 3.1 Pro, "the proof-oriented pipeline with execution feedback solves 218 of 222 problems", and that with Gemini 3.1 Pro the authors "obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR".
  • The authors state the workflow "has also been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern", so the harness is already shipping inside a Google product.
  • The paper is a preprint by authors at the company whose models it evaluates, the abstract does not name the open problems said to be resolved, and the claimed new results have not been independently checked.
Mathematicians vs the labsGoogle DeepMindEvalsAgentsReasoning Models

Sunday, 13 September 2026

Analysis finds no sign of backtracking in latent reasoning models; Huginn answer flips are indistinguishable from noise PreprintSingle source

LessWrong
  • The post tests the claim that latent-reasoning models backtrack, taking the published definition that backtracking counts when the top answer changes. On Huginn, a 3.5B latent reasoning model, the author reports finding answer changes on 66% of ARC-Challenge questions against the 32% originally claimed, a median logit gap at the swap of 0.12, and only 1 of 176 top-answer swaps exceeding a 95th-percentile noise threshold.
  • On a Coconut-style two-layer model trained from scratch on graph reachability at 95% test accuracy, the candidate pair's winner swaps in 29 to 38% of transitions, but a random node pair's winner flips in 32 to 42% of cases. Two training runs agreed on which questions flipped only 31% of the time.
  • As a comparison, a text-based 1.5B distilled reasoning model produced naturally occurring answer changes in 198 of 193,767 transcripts, about 0.1%.
  • This is a blog post, not a peer-reviewed paper, and the author is pseudonymous with no stated institutional affiliation. It has not been independently replicated.
InterpretabilityReasoning ModelsEvals

Saturday, 12 September 2026

Twenty-five Fields Medallists sign declaration that AI labs' benchmark chasing is "severely misaligned" with mathematics

Terence Tao·TechCrunch
  • Terence Tao published the declaration on his blog on 11 September; it is signed by 25 Fields Medallists and argues that "solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight".
  • The signatories write that AI solutions are "announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others", and warn that without that step "AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost".
  • TechCrunch reports that New York University mathematician Tristan Buckmaster alleged OpenAI pressed him to exclude an Anthropic collaborator from credit on a mathematics problem, and questioned whether OpenAI had drawn on earlier Codex work to produce its own proof.
  • The full text of the declaration is hosted at mathandai.org, which blocked our fetcher, so the quotations above are taken from Tao's own post and TechCrunch. Neither source gives a count of signatories who are also AI-lab collaborators.
Mathematicians vs the labsOpenAIEvalsReasoning ModelsAI For Science

NVIDIA team reports an open Nemotron pipeline scoring 30 of 42 at IMO 2026 with no formal prover or tools PreprintCompany claim

arXiv
  • The paper, posted to arXiv on 9 September 2026 and announced in the 11 September listing, reports that the system "scored 30 out of 42 points at IMO 2026, reaching the gold-medal threshold".
  • The abstract states the pipeline "operates entirely in natural language, with no formal prover, external tools, or internet access", using three Nemotron 3 Ultra checkpoints — the general-availability model and two post-trained specialists — in "an iterative search that generates, verifies, and refines candidate proofs", with a separate high-compute stage selecting each submission.
  • The authors say they release both post-trained checkpoints plus the training data, training and inference code, the submitted solutions, and "Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems".
  • The arXiv abstract page carries no affiliation block; Hugging Face lists the institution as NVIDIA. The IMO score is the authors' own report of their own submission and is not peer reviewed.
Mathematicians vs the labsNVIDIAReasoning ModelsEvalsOpen Weights

Magenta pipeline reports 100% on AIME 2025, AIME 2026 and HMMT February 2026 with Lean-checked proofs Preprint

arXiv
  • The paper, posted to arXiv on 10 September 2026, describes "a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof", and reports "100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026".
  • The abstract states that when paired with the open-weight K2-Horizon-7B reasoner "it solves all six IMO 2026 problems".
  • The design puts a statement judge in front of the prover to check that the Lean formalisation preserves the original problem, and an error-attribution judge that routes failures either to mathematical re-derivation or to local Lean repair — the guard against a proof that is machine-checked but of the wrong statement.
  • This is a preprint with no peer review, and the benchmark figures are the authors' own runs. The abstract does not report compute cost or the number of attempts per problem.
Mathematicians vs the labsReasoning ModelsEvalsAgents