#Reasoning

AIMike Knoop says AI reasoning models, including swarms, are now useful for conceptual search. He argues this lets researchers empirically rule out whether they simply have not looked hard enough, and shift effort toward developing new prerequisite ideas.

AIAlberto Romero argues that AI solving Millennium Prize problems in 2026 threatens mathematics through success, not failure. He draws on Terence Tao's view that struggle shapes mathematicians, and that proof abundance without hard problems could leave fields depleted, like overplanted farmland.

AIJohn Schulman thanked Dwarkesh Patel, Beren Millidge, and Charlie O'Neill for a conversation about the AI frontier. The episode covers topics including the case against recursive self-improvement, the drivers of Chinese labs' progress, and whether long-horizon RL could elicit AGI.

AIMira Murati highlighted a conversation about where AI is heading and the work humans still need to do. Quoted context from Thinking Machines says John Schulman, in a talk with Dwarkesh, argues human judgment still matters for teaching models messy real-world tasks, applying taste, and specifying what people actually want.

AIThinking Machines shared a Dwarkesh Patel podcast episode with John Schulman discussing where human judgment remains essential as models improve and self-improve. Schulman highlights teaching models to handle messy real-world tasks, applying taste to what works in the long run, and specifying what people actually want. The episode also covers recursive self-improvement, long-horizon RL, and the sim-to-real gap.

AIRedwood Research reports that better prompt templates raise chain-of-thought controllability scores on the CoTControl eval for open-source reasoning models by roughly 2-3x or more. For example, GPT-OSS-120B rose from 5.5% to 15% in the zero-shot setting. The author concludes that current CoT controllability numbers may underestimate what models can do, though the finding does not significantly undermine the view that current models probably cannot consistently evade CoT monitoring.

AIJohn Schulman, Beren Millidge, and Charlie O'Neill discuss whether current training methods could produce recursive self-improvement. They argue that progress depends on whether models can learn their own objectives and on sample efficiency, and that distillation keeps frontier capabilities from centralizing quickly.

AIJunyang Lin warns that adding complexity to model architecture can cause unknown issues that existing evals, even internal ones, cannot detect. He notes that teams may still accept these small unknown costs for large efficiency benefits as foundation models increasingly target agentic tasks.

AIOpenAI announced that a swarm of 10,000 agents produced a solution to the Navier-Stokes Millennium Problem, a result that angered mathematicians. NYU mathematician Tristan Buckmaster and Anthropic-employed collaborator Levent Alpöge had been working on related problems and released three draft papers of about 245 pages. Buckmaster said OpenAI's offer to merge efforts required acknowledging an OpenAI model and excluded Alpöge as co-author.

Why it matters: The piece separates the mathematical result from the collaboration dispute, showing how AI labs' compute spending is straining academic norms around credit and openness.

AIRedwood Research defines NLS depth, a measure of how much unverbalized serial computation an AI system can perform, building on Brown-Cohen et al.'s opaque serial depth. The proposal counts only nodes that output natural language initialized from a pre-training prior as interpretable bottlenecks. Standard transformers scale with their layer count, while latent reasoning architectures would raise NLS depth sharply.

AICognition introduces SWE-2, a coding model post-trained from Kimi K3 that scores 50.0% on FrontierCode 1.1 Main, within one point of Fable 5.1 while costing 64% less. The post attributes the gains to an RL algorithm that trains all reasoning-effort levels in one run, with cost penalties tuned to the base model's Pareto frontier. SWE-2 is available starting today in Devin Desktop and CLI, with rollout to Devin Web and Fusion.

Why it matters: The post explains how the cost penalty and length-weighted baseline are derived, which helps readers judge the tradeoffs in coding model post-training.

AIRadixArk says Miles brings day-0 RL support to DeepSeek-V4.1-Flash, with SGLang providing inference support. The post says quantization-aware training mirrors SGLang's FP4/FP8 rounding, and that colocated training and rollout fit full-parameter RL on 16 GPUs. In a DAPO run over steps 0–80, per-token trainer–rollout KL stayed at 0.0012–0.0017 while reward rose from 0.51 to 0.78.

AITinker says it and OpenResearch let agents test dozens of competing published post-training methods automatically, with compute cost forecast to within a dollar. The main post cites a grant-supported effort, while the quoted alphaXiv post says agents reproduced SDFT's continual learning benefits across Qwen3-8B and Qwen3-30B-A3B over multiple seeds.

AIOpenAI's GPT-6 Astra scores 99.9% on ARC-AGI-3, versus 7.8% for GPT-5.6 Sol, and leads Raschka's coding and math tests. Its strongest showing is in graphics and computer-use tasks, such as redrawing an image in a browser-based Paint app. The author notes that Artificial Analysis shows Astra at the frontier but not pulling far ahead on its Coding Agent Index.

AIOpenAI says a group of agents using an unreleased next-generation model produced a solution to the Navier-Stokes Millennium Prize Problem. The problem asks whether smooth three-dimensional fluid motion described by the Navier-Stokes equations can break down, and it has remained unresolved for roughly 90 years. The author, Mckay Wrigley, reposted the claim with his own remark about roughly 10k agents working in a datacenter.

Why it matters: The quoted OpenAI post makes a major mathematical claim about the Navier-Stokes problem, so readers should weigh it against the proof's verification status.

AIMagic says its new pretraining recipe matches DeepSeek V4 Pro's pretraining while using 50x less compute, roughly half the FLOPs used for GPT-3, or about $0.5M on GB200. The post, which congratulates the team, suggests that during recursive self-improvement, automated AI researchers may be less bottlenecked by compute than expected.

AIMark Chen announced that a group of agents produced a solution to the Navier-Stokes Millennium Prize Problem, using an unnamed OpenAI next-generation model. The post says the problem concerns whether smooth three-dimensional fluid motion described by the Navier-Stokes equations can break down, and that it had been open for roughly 90 years. The quoted OpenAI post and the attached illustration of inward spiral and axial stretching are cited as context, but the source provides no proof details.

Why it matters: The post claims an AI-produced proof of a famous open problem, but the source gives no proof details or independent verification, so the claim itself is the main point.

AIOpenAI says a group of agents using an unreleased next-generation model produced a solution to the Navier-Stokes Millennium Prize Problem, a question about whether smooth 3D fluid motion can break down that has stayed open for about 90 years. Noam Brown says the result cost millions of dollars, but argues that Astra now scores higher on ARC-AGI for about $20, versus roughly $500,000 for o3 on ARC-AGI 1.

Why it matters: The post quotes OpenAI's claim about an AI-produced Navier-Stokes solution and adds cost comparisons that show how quickly test-time compute costs are falling.

AINoam Brown reposted an OpenAI statement that an internal model group reached a Navier–Stokes solution in 88 hours using about 10,000 coordinating AI agents. OpenAI said the model shows a step-function improvement on many benchmarks and that its training is ongoing, with monitoring and isolation safeguards applied throughout. The attached chart compares GPT-6 Astra and the internal model on a curated set of open math problems across test-time compute levels, with the internal model scoring higher at each point.

Why it matters: The quoted OpenAI post gives concrete figures on an internal model's Navier–Stokes result and on a benchmark comparison, showing how the model performs on open problems.

AITencent Hunyuan says its Hy4 preview has been upgraded to reduce long thinking and over-verification on complex tasks, which users had flagged. The company reports the same task quality with fewer turns and lower input and output tokens, confirmed by benchmark and human evaluation. The upgrade is live for all users, and Tencent says it will keep iterating based on feedback.

AIOpenBMB released JustRL-II-base-model, the pre-RL starting checkpoint for the JustRL II math-reasoning case study, scoring about 61% on AIME 2025 before reinforcement learning. The full JustRL II recipe reaches 81% on AIME 2025 in about 300 RL steps from this checkpoint, versus about 74% for a standard GRPO baseline. The Llama-architecture weights are available on Hugging Face and are intended for reproducing the recipe and research on long-CoT RL, not general assistant use.

AIJohn Schulman says a metric for explanation quality, centered on counterfactual simulatability, enables hillclimbing, and praises Adam et al. for a more diverse and realistic dataset and pipeline. He notes that models can be trained to write better post-hoc explanations of their own behavior, as described in a linked thread by @a_karvonen. That thread reports training on thousands of self-explanations of in-the-wild behaviors, with generalization to held-out evals.

AITinker, the platform from @tinkerapi, supported two recent papers testing counterfactual simulatability as a way to interpret LLM behavior. The core idea is that understanding a model means predicting how its output changes when the prompt changes, with causes ranging from specific words to abstract properties such as a user's angry tone.

AINoam Brown, speaking for OpenAI, says he is most excited about GPT-6 Astra's potential for scientific discovery and says OpenAI has not yet pushed the model to its limits on math and science. He looks forward to seeing new scientific breakthroughs built with the model. Background context from a quoted post notes a new OpenAI repo containing a Lean formalization by GPT-6-Astra that proves infinitely many pairs of consecutive primes are at most 186 apart.

AILightning Rod, working with Philip Tetlock and Ville Satopää, post-trained five versions of the same LLM that differed only in the scoring rule used as the RL reward. The versions reached similar aggregate scores but had very different bias, information, and noise (BIN) profiles, so a good Brier score alone does not show whether a forecaster can distinguish likely from unlikely events.

AIOpenAI's GPT-6 Astra (max) scores 62.7% on ARC-AGI-3 Semi-Private for $26K under the Standard harness, and 99.9% for $19K under the Provider Adapter harness. The authors say Astra used fewer actions than the human baseline on 96.0% of levels, and they note it is not claimed to be AGI.

Why it matters: The report pairs benchmark scores with replays of the model's notation and tool use, showing how it solved unfamiliar environments rather than only that it did.

AINVIDIA has published Nemotron-3-Labs-Ultra-Math-RL on Hugging Face, a 550B total, 55B active parameter model for solving difficult math problems and identifying proof mistakes. The model is part of an ensemble that reached gold-medal level at the International Mathematical Olympiad 2026, and it is available for commercial and non-commercial use under the OpenMDW-1.1 license. Deployment is designed for NVIDIA Blackwell or Hopper GPUs, with a recommended minimum of 8× B200 on a single node and a context length of up to 1M tokens.

Why it matters: The release details the model's math-proof role, its 550B total and 55B active parameters, and its vLLM deployment requirements for teams weighing adoption.

AIGoogle introduces Gemini 3.8 Flash for coding, agentic tasks, and multi-step reasoning, priced at $0.75 per million input tokens and $3.75 per million output tokens during the introductory period. Gemini 3.8 Flash Cyber targets vulnerability detection and automated patching and is available only to trusted defenders through the new Fairwind Program. The introductory price expires December 31, 2026, after which $1.50 and $7.50 per million tokens apply.

Why it matters: The post separates a general coding and agent model from a restricted cyber variant, showing how one shared core is deployed under different access and safety tiers.

AIGoogle's RT-2 model, announced in July 2023, trained a multimodal LLM to output robot actions directly, and the article argues this approach launched the current robotics boom. The author follows later work from Physical Intelligence, including action chunking with flow matching, reinforcement learning on real robots, and visual subgoal generation, and notes that the field is debating whether vision-language-action models will give way to world models.