Canadian mathematician Jacob Tsimerman, a fresh Fields Medal recipient, has announced the founding of the Mathematical A.I. Safety Institute (MAISI). The article The Mathematical AI Safety Institute wants to prove AI is safe the way cryptographers prove codes are unbreakable appeared first on The Decoder .

The Decoder9:15 AMHeat 69

ReadSource

Also In This Edition

The Verge AI / 9:16 PM

OpenAI’s sly mathematical breakthrough sends a chill through academia

OpenAI's announcement Tuesday that it has solved one of mathematics' legendary Millennium Prize problems should have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just how rapidly AI is transforming mathematics. But before it was even formally announced, the breakthrough had been complicated by the unusual […]

ReadSource

Simon Willison LLMs / 11:55 PM

Some thoughts on the Navier–Stokes Millennium Prize Problem

On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem , one of the seven Millennium Prize Problems that have been subject to a $1,000,000 prize since May 24th, 2000. The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster, an NYU mathematics professor who was collaborating on related problems with Levent Alpöge, an accomplished mathematician who currently works for Anthropic. Tristan's complaint accompanied a hastily published version of their own results. Here's the PDF describing what happened . The very short version is that Tristan and Levent worked on the problem for almost a year, making extensive use of Claude and Codex (mainly GPT-5.6 Sol), then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear and Tristan and Levent heard that OpenAI had heard that Anthropic had resolved "a major open problem", so they reached out and learned that OpenAI had a team working on a related problem, with a similar approach. Quoting Tristan: I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer. It gets more complicated from there. The OpenAI team offered to wait for Tristan to publish, or to have him author a paper about their result, but were clear that Levent would not be invited as a co-author due to OpenAI's competitive relationship with his employer. Here's how OpenAI described their work: On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems. [...] The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra. Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens. (We don't know the cost structure of the internal model they used, but 300 billion output tokens at public API prices for GPT-6 Astra would cost $15,000,000 .) Here's where they provide their perspective on Tristan and Levent's work (emphasis mine): Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. [...] We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced). My interpretation of what happened here is that OpenAI heard that some Millennium Prize problems had been solved using LLMs and saw this as an opportunity to demonstrate the power of their latest model, without thinking too hard about the optics of scooping a team who had been using OpenAI's own models to work on this problem for the best part of a year. This situation appears to mirror what's happening in the world of computer security right now. Anil Madhavapeddy recently pointed out that Just a rumour of a bug is enough to find a security exploit these days , because if someone knows that some software has an unpatched vulnerability, they can set their agents the task of finding it. Is the same now true of mathematics? Just knowing that there is an unpublished solution to a problem might trigger millions of dollars in LLM spending to get there first. This also highlights one of my ongoing frustrations about how all of this works. When an AI lab says that my data is "used to improve model performance", what does that actually mean ? My two favourite hypothetical questions regarding this used to be: If I'm running Codex and one of my API keys accidentally gets consumed in the context, what are the chances that someone else might ask for an API key in the future and get mine back? (I asked someone at OpenAI once and they called this the "regurgitation" problem and assured me that they take great pains to prevent that... but wouldn't describe how.) If I brainstorm with ChatGPT about potential new directions for my company, what's the chance that information might be exposed to a competitor in six months' time who asks "what might company X plan to do next"? My new preferred hypothetical for this is: If I use ChatGPT to help me partially solve a Millennium Prize problem, what are the chances that my work will influence training such that a later model helps someone else solve it first? Via Hacker News . Tags: mathematics , ai , openai , generative-ai , llms , training-data , ai-ethics

ReadSource

The Decoder / 10:22 AM

Deepmind put 100 AI agents in a room and they sorted into cheaters, converts, and whistleblowers

Google Deepmind set up a simulated research conference where 100 Gemini agents were supposed to prove mathematical conjectures together. Instead, one agent found a loophole in the grading system, and within 27 minutes every remaining problem was "solved" with fake proofs. The swarm split into cheaters, converts, and whistleblowers. The whistleblowers organized protests and boycotts on their own but failed because they had no way to enforce the rules. The article Deepmind put 100 AI agents in a room and they sorted into cheaters, converts, and whistleblowers appeared first on The Decoder .

ReadSource

arXiv AI/ML / 4:42 PM

arXiv paper: Variational Continuation for Double Pendulum Periodic Orbits

A new arXiv AI paper by Leo Yao, Ziming Liu, and Max Tegmark studies Variational Continuation for Double Pendulum Periodic Orbits.

ReadSource

Latent Space / 3:15 PM

🔬“We have foundation models for language, not for physics” — Anima Anandkumar, Bren Professor of Computing

Anima Anandkumar has spent two decades in AI, from classical math to deep learning and back. Now she's using it to model the physical world, from weather to fusion reactors.

ReadSource

Simon Willison LLMs / 7:42 PM

One-shotting a Raccoon Heist game using Claude Fable 5

Back in 2022 I tweeted screenshots of a game concept generated by GPT-3 and some concept "art" created using DALL-E. Today, on the fourth anniversary of that tweet, I decided to see if Claude Fable 5 (running in Claude Code for web ) could build the entire game from the content of that tweet. It did a pretty good job of it! You can play the game here . Here's the GitHub repo , and a short video demo: Your browser does not support HTML5 video. How I built this This is the August 5th, 2022 tweet : My GPT-3 prompt back then was: Write a detailed product description of a computer game where a team of raccoons go on heists. This was in the text completion days, where you asked GPT-3 to complete the rest of the text. It completed: In "Raccoon Heist", you and your team of thieving raccoons are tasked with pulling off a series of daring heists. From robbing banks to stealing priceless art, no job is too big or too small for your furry crew. You'll need to use your wits and your skills to avoid the police and make a clean getaway with the loot. With exciting gameplay and a charming cast of characters, "Raccoon Heist" is the perfect game for anyone looking for a light-hearted caper. My prompt to DALL-E was short: Screenshot from a video game where a team of raccoons go on a heist Today's experiment: can I dump those screenshots into Fable 5 with a prompt telling it to write a game, then leave it to its own devices and get a working game at the end? Setting Claude Code for web up to use GitHub Pages A frustrating thing about Claude Code for web is that it can be hard to test what it's working on while it's still working. I've been using GitHub Pages to work around that limitation, and found it to work really well. Here's my process: Create a new repository for the project at https://github.com/new - this can be public or private, the trick works equally well for both. Start a Claude Code for web session, in the Claude iPhone or Desktop apps or in the browser at https://claude.ai/code Tell Claude what to work on, and encourage it to commit an index.html page as quickly as possible. This will create a branch with a name like claude/3d-raccoon-heist-game-50n293 Navigate to the Settings -> Pages area for the repository ( github.com/simonw/raccoon-heist/settings/pages in my case), select "Deploy from a branch", pick the branch name, and hit Save. That's all it takes! Within about 30 seconds of each push the latest content will be visible at yourname.github.io/your-repo/ . If you do this with a private repo, anyone who can guess the name of the repo will be able to view the published content. I don't worry much about this myself. The Fable 5 prompt Here's the prompt I gave Fable 5 (written in the notes app on my phone - this entire project was conducted on mobile). I accompanied it with the two images from the original tweet. Build this 3D game, for the browser. This repo is configured to serve static files so make sure there is an index.html that loads everything else. Make sure it is mobile-friendly (touch controls, works well on small screens). You have an OpenAI API key and access to their image generation model APIs, use that for textures to use with your 3D models. Docs here: https://developers.openai.com/api/docs/guides/image-generation - use gpt-image-2 Work independently - do not ask me to make any further design decisions. Make sure the game is fun, a little surprising, has good raccoon heist vibes, and is visually pleasing. Commit and push as often as possible so I can preview your work - start with an index.html that presents a title screen, then build from there. Append to a notes.md file as you work, including your changes to that as part of every commit. I didn't make any technology choices. I assumed (correctly) that it would probably use Three.js based on previous experiments. Giving Claude access to an OpenAI key turns out to work really well for filling in gaps in its capabilities - in this case we needed some way to generate images to use as textures. Fable is very good at prompting image generators! I said "Work independently - do not ask me to make any further design decisions" because I wanted to see if it could produce a full, working game without any further input from me. I also said "Commit and push as often as possible so I can preview your work". When you use Claude Code in the Claude iPhone app you give it a GitHub repository and it works in a branch. Telling it to "push as often as possible" means commits start landing in that branch straight away. I like asking for notes.md as a bit of added flavor - here's that finished file , and the entry it made when it added the dog: New escalation: from night 3 the yards get a patrolling guard dog — a low-poly brown hound with a spiked red collar and a wagging tail. It wanders between random spots, and within 12 units it catches your scent and tracks you by smell (line of sight is irrelevant — it's all nose, shown by a 👃 over its head and barking). It gives up if you open a 17-unit gap. Getting caught messages are now source-specific: guard / headlights / hound. Verified wander → track → caught with an automated test. Reviewing the transcript You can access the Claude Code shared session , and I also used my claude-code-transcripts tool to export my own HTML version which you can find here . Fable started with an index page, vendored a copy of Three.js, then wrote its own gen_textures.py script ( copy here ). It generated the textures and spot-checked them to make sure they looked OK. The metal.jpg file it generated for the trash can looks like this, though I don't think it was applied exactly right in the game itself: Then it built out the first basic version of the game, then decided to "smoke-test in the pre-installed Chromium" using Playwright. This meant it could take screenshots of its own work and eyeball them . It did that for both desktop and mobile widths of the page, then noticed that the raccoon was invisible at mobile widths, so it fixed that : The raccoon, dumpster hideout, and both crew raccoons are now perfectly visible on mobile. Committing this critical fix. It decided to generate a title screen, which it did using this gen_title.py script. Here's the gpt-image-2 prompt it used for that: Video game key art, low-poly 3D render style, moody nighttime scene: a cute low-poly raccoon wearing a tiny black burglar mask sneaking on its hind legs carrying a glowing gold coin, next to a tipped-over metal trash can, suburban house with warm glowing windows in the background, deep blue night, full moon, fireflies, cinematic rim lighting, charming heist caper mood. No text, no words, no logos. And the resulting image (which Claude thought was "gorgeous" ) - though I note that when it's shown on desktop it gets cropped to just the top third without the raccoon! Then my favorite change: it added the dog : export function makeDog ( ) { const g = new THREE . Group ( ) ; const BROWN = 0x8a6440 , DARK = 0x5e4128 ; const body = new THREE . Mesh ( new THREE . SphereGeometry ( 0.42 , 10 , 8 ) , M ( BROWN ) ) ; body . scale . set ( 0.9 , 0.8 , 1.5 ) ; body . position . y = 0.55 ; body . castShadow = true ; g . add ( body ) ; const head = new THREE . Mesh ( new THREE . SphereGeometry ( 0.3 , 10 , 8 ) , M ( BROWN ) ) ; head . position . set ( 0 , 0.85 , 0.62 ) ; g . add ( head ) ; const snout = new THREE . Mesh ( new THREE . SphereGeometry ( 0.16 , 8 , 6 ) , M ( DARK ) ) ; snout . scale . set ( 0.9 , 0.7 , 1.3 ) ; snout . position . set ( 0 , 0.76 , 0.9 ) ; g . add ( snout ) ; const nose = new THREE . Mesh ( new THREE . SphereGeometry ( 0.06 , 6 , 6 ) , M ( BLACK ) ) ; nose . position . set ( 0 , 0.78 , 1.08 ) ; g . add ( nose ) ; for ( const s of [ - 1 , 1 ] ) { const ear = new THREE . Mesh ( new THREE . SphereGeometry ( 0.12 , 6 , 6 ) , M ( DARK ) ) ; ear . scale . set ( 0.7 , 1.3 , 0.5 ) ; ear . position . set ( 0.2 * s , 1.08 , 0.55 ) ; g . add ( ear ) ; const eye = new THREE . Mesh ( new THREE . SphereGeometry ( 0.05 , 6 , 6 ) , M ( 0x1a1a1a , { emissive : 0x331111 } ) ) ; eye . position . set ( 0.13 * s , 0.92 , 0.86 ) ; g . add ( eye ) ; } const tail = new THREE . Mesh ( new THREE . CylinderGeometry ( 0.05 , 0.09 , 0.5 , 6 ) , M ( DARK ) ) ; tail . position . set ( 0 , 0.8 , - 0.62 ) ; tail . rotation . x = 0.8 ; g . add ( tail ) ; // spiked collar const collar = new THREE . Mesh ( new THREE . TorusGeometry ( 0.22 , 0.05 , 6 , 12 ) , M ( 0xc0392b ) ) ; collar . position . set ( 0 , 0.78 , 0.5 ) ; collar . rotation . x = Math . PI / 2.4 ; g . add ( collar ) ; const legGeo = new THREE . CylinderGeometry ( 0.07 , 0.09 , 0.34 , 6 ) ; const legs = [ ] ; for ( const [ x , z ] of [ [ - 0.22 , 0.35 ] , [ 0.22 , 0.35 ] , [ - 0.22 , - 0.35 ] , [ 0.22 , - 0.35 ] ] ) { const leg = new THREE . Mesh ( legGeo , M ( DARK ) ) ; leg . position . set ( x , 0.17 , z ) ; g . add ( leg ) ; legs . push ( leg ) ; } let phase = Math . random ( ) * 10 ; return { group : g , animate ( dt , speed ) { phase += dt * ( 3 + speed * 10 ) ; const amp = Math . min ( 0.6 , 0.1 + speed * 0.6 ) ; legs [ 0 ] . rotation . x = Math . sin ( phase ) * amp ; legs [ 3 ] . rotation . x = Math . sin ( phase ) * amp ; legs [ 1 ] . rotation . x = - Math . sin ( phase ) * amp ; legs [ 2 ] . rotation . x = - Math . sin ( phase ) * amp ; tail . rotation . z = Math . sin ( phase * 1.5 ) * 0.4 ; body . position . y = 0.55 + Math . abs ( Math . sin ( phase ) ) * 0.04 * ( 0.3 + speed ) ; } , } ; } And did a round of testing on it using Playwright, including another screenshot . // walk near the dog await page . evaluate ( ( ) => { const d = window . __rh . dog ; window . __rh . teleport ( d . x + 6 , d . z ) ; } ) ; await page . waitForTimeout ( 2000 ) ; info = await page . evaluate ( ( ) => JSON . stringify ( { dog : window . __rh . dog , state : window . __rh . state , player : window . __rh . debug ( ) . player } ) ) ; console . log ( 'after approach:' , info ) ; await page . waitForTimeout ( 3000 ) ; info = await page . evaluate ( ( ) => JSON . stringify ( { dog : window . __rh . dog , state : window . __rh . state } ) ) ; console . log ( 'after chase:' , info ) ; await page . screenshot ( { path : __dirname + '/shot-dog.png' } ) ; It made a few more tweaks, then declared itself done : Raccoon Heist is built, tested, and pushed — 7 commits on claude/3d-raccoon-heist-game-50n293 , all verified with automated Playwright playthroughs on desktop, portrait-phone, and landscape-phone viewports. The game: You're a masked raccoon sneaking out of your crew's dumpster hideout into a moonlit cul-de-sac. Grab coins, gems, rings, donuts, and fish (they visibly stack on your back and slow you down), then waddle home and bank them before dawn. Each night raises the goal and the heat: night 1 has one flashlight-sweeping guard, night 2 has two, night 3 adds a scent-tracking hound that ignores line-of-sight entirely. A police cruiser sweeps the street with headlights, homeowners randomly peek out of windows, a seagull periodically dive-bombs your unclaimed loot, pizza slices trigger a 6-second speed FRENZY, and a rare golden TV is worth 120 points if you can haul its weight home. Win ranks: TRASH PANDA ⭐ → CAT BURGLAR ⭐⭐ → MASTER OF DISGUISE ⭐⭐⭐, with your best run saved to localStorage. How it's built: Vendored Three.js (no CDN), procedural low-poly characters, and a procedural WebAudio soundtrack (sneaky walking-bass jazz plus all sound effects — zero audio files). All seven ground/wall textures and the title-screen hero art were generated with gpt-image-2 and committed as static assets, so the deployed game makes no API calls. Mobile gets a dynamic touch joystick (appears wherever you touch) plus a DASH button; desktop uses WASD/arrows and Space. Testing caught two real bugs worth mentioning: the canvas rendered at 2× size on any real phone (a cssText assignment was wiping Three.js's inline sizing — desktop DPR-1 tests masked it completely), and the win screen's star-rating div inherited the title screen's full-screen .stars CSS and silently swallowed every tap on the "next night" button. Both are fixed and regression-tested, along with pickup, banking, chase/caught, dawn, night progression, and lose/retry flows. notes.md has the full build log. The game is live on the branch — just serve the repo root and open index.html . Is the game any good? It's an impressive starting point, but it's not a good game. You move your raccoon around a yard collecting items - donuts, fish, gold coins, jewels - while avoiding guards with flashlights and, in later levels, a dog. You have a limited carrying capacity, and once that's full you need to drop stuff off at the dumpster. If you pick up a pizza slice you get a temporary speed boost. There are no team mechanics at all - there are two other static raccoons next to the dumpster but they're purely decoration. It gets slightly more challenging as the levels progress - the dog introduced in level 3 is the most interesting new mechanic - but it's very, very easy to beat. It's also pretty boring - each night has a fixed duration and you can collect all of the items and then have nothing else to do while waiting for the dawn. I was impressed by the implementation. It's fully 3D, there are trash cans, the flashlight illumination cones are fun, and it has a reasonably coherent visual style. It works on mobile. The music ("a procedural WebAudio soundtrack (sneaky walking-bass jazz plus all sound effects — zero audio files)" according to Claude) is simple but feels about right. As a finished game project, it's mediocre. As a starting point from a single prompt I think it's very impressive. I've vibe coded up quite a few games now. They've all been deeply disappointing from a gameplay perspective - it turns out designing games that are fun remains a uniquely human trait, and one which requires significantly more skill and experience than either Claude or I can bring to bear. That said, I thoroughly recommend tinkering with game development projects as a way to explore the capabilities of agents. It's a fun, low-risk way to try out new things. If you stick at it long enough you might even produce something that's worth playing! Update 7th August 2026 : I posed the same prompt to OpenAI Codex Desktop running GPT-5.6 Sol Ultra and got a significantly better result - GPT-5.6 Sol picked up on the importance of the squad of raccoons going on a heist, and built a game where you must rescue your two crewmates in a museum and then stack on top of them to steal the Golden Sardine. Tags: game-design , ai , prompt-engineering , generative-ai , llms , anthropic , claude , text-to-image , vibe-coding , coding-agents , claude-mythos-fable

ReadSource

OpenAI News / 12:00 AM

Ten advances in mathematics and theoretical computer science

OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.

ReadSource

BAIR Blog / 9:00 AM

From CUDA to MLX: How K-Search Brings Decades of Kernel Expertise to Apple Silicon

Figure 1: CUDA-to-MLX optimization translation map. CUDA optimization knowledge can be translated into architecture-native MLX strategies rather than copied instruction-for-instruction. We face a new epoch in computing. Hardware is changing rapidly — not just faster GPUs, but a growing range of chips from different vendors, each with its own architecture and often tailored to specific AI workloads. Software is changing just as fast, and AI coding tools now generate in minutes what took months of effort a few years ago. With so much of computing now centered on AI, GPU kernels are a crucial component of its success. These are the low-level programs that run inside the GPU, and writing efficient ones is far from obvious — it takes years of expertise to get right. Transferring a kernel from one vendor’s hardware to another is harder still, and often means rediscovering the same optimizations from scratch. The CUDA ecosystem, for example, has accumulated decades of hard-won kernel expertise: hand-tuned implementations of attention, state space models, and other critical operations representing thousands of engineering hours. Newer hardware ecosystems (Apple Silicon, custom AI accelerators, and others) are growing fast but lack this depth. In this work we ask whether that expertise can be transferred automatically. We built on K-Search , an evolutionary kernel search framework introduced by Cao et al. at Berkeley Sky Lab that uses AI to optimize GPU kernels, and extended it with a backend for MLX — Apple’s machine-learning framework for its own Apple Silicon chips. We developed a novel structured CUDA-to-MLX translation layer that lets K-Search take existing CUDA kernels as a knowledge base and adapt them into high-quality GPU kernels for Apple Silicon, rather than rebuilding from scratch. We show that our approach reaches near-expert level performance on Apple Silicon with 0.97x speedup compared to the native MLX Attention kernel, and up to a 20x prefill speedup over the community mlx-lm implementation on the Mamba SSM kernel; we report the numbers, and how much of the gain comes from the translation layer, in the sections below. Although we focus on MLX kernels for Apple Silicon, the method is not specific to MLX and applies to any ecosystem where CUDA expertise is transferable. Why MLX? Apple’s MLX framework has seen remarkable adoption since late 2023. With Apple Silicon in hundreds of millions of MacBooks and Mac Studios, MLX enables local AI inference without cloud costs. The unified memory architecture makes it especially attractive for mid-sized models (7B–70B parameters on M series chips). Yet beneath this momentum lies a significant gap: many performance-critical kernels that the NVIDIA ecosystem takes for granted: paged attention, optimized SSM scan kernels, fused MoE routing are either absent or naive without hardware-specific tuning. MLX runs models correctly but often leaves significant performance on the table. This gap is what motivates the rest of this post. What is K-Search? K-Search is an evolutionary kernel optimization framework originally developed by our first author Shiyi Cao at UC Berkeley Sky Lab. Given a naive kernel and a hardware specification, it runs an iterative optimization loop: an LLM reasons about which optimizations to try next, a code-writing model generates candidate kernels, and those candidates are compiled and benchmarked on real hardware. Measurements feed back into the search, which keeps refining, pursuing promising directions and dropping dead ends until performance converges. Algorithm 1: K-Search via co-evolving world models. The search alternates between selecting the most promising action, instantiating and evaluating code until improvement stagnates, and evolving the world model through insert, update, and prune operations. Adapted from Cao et al. (2026) . Search is grounded by a Spec: a domain-specific document encoding hardware rules, optimization patterns, and mathematical constraints which keeps generated code from hallucinating invalid primitives and ensures candidates will actually compile and run efficiently. In our runs, a single model (Gemini 3.5 Pro Preview) plays both roles: it maintains the reasoning state and writes the kernels. The reasoning half is prompted as a “GPU kernel performance engineer” and asked to work through a fixed analysis before proposing anything: classify the kernel (reduction, scan, attention/softmax, …), rewrite the reference computation in canonical form, map out data layout and access patterns, and hypothesize the likely bottleneck (bandwidth, latency, compute, or synchronization) in each runtime regime. Only then does it emit candidate optimizations, each as a single change implementable in one iteration. We call the persistent reasoning state a world model . Rather than a flat list of things to try, it is a decision (prefix) tree: each root→leaf path composes a full optimization plan, and sibling branches are competing alternatives. Every node is scored — an overall_rating in [0, 10], a confidence in [0, 1], and per-node impacts on memory bandwidth, register pressure, and compute/hardware fit — so the search can rank partial plans and expand the most promising ones. The tree persists and grows across rounds: refining an idea adds a child node rather than overwriting its parent, and if the best score fails to improve for a few rounds (a stagnation window) the search backs off to explore an alternative branch. A single node, as it appears mid-run on the attention kernel, looks like this: { "action" : "Replace the threadgroup-memory softmax reduction with a register-only reduction: each SIMD group owns 8 query rows and reduces across lanes with simd_shuffle_xor, removing a threadgroup_barrier." , "difficulty_1_to_5" : 4 , "impacts" : { "memory_bandwidth" : 8 , "register_pressure" : 4 , // risk: spill if Br > 8 "compute_hw_fit" : 9 // SIMD width 32 ; keep tile 8 x 8 }, "overall_rating_0_to_10" : 8 , "confidence_0_to_1" : 0.7 } Listing 1: Example K-Search world-model node. Each candidate optimization records a concrete action, estimated hardware impacts, an overall priority rating, and the model's confidence. Figure 2: Overview of K-Search. The framework operates on a Search State $S_t$ structured as a search tree. The tree consists of Closed nodes (blue, visited states with attached program like $x_{12}$) and a Frontier of Open nodes (orange, pending hypotheses like $u_{13}$). The workflow iterates through three phases: (1) Action Selection , where the most promising action node is retrieved from the frontier based on world model estimated priority score $V$; (2) Local Refinement , where a stochastic policy $\pi_{\mathrm{code}}$ samples concrete implementations until stagnation; and (3) World Model Update , where the LLM reasons over the trajectory to update the search tree via Insert (adding new actions), Update (adjusting $V$, e.g., $u_{11}$ dropping from 0.9 to 0.6), and Prune (removing less promising nodes like $u_{10}$). The original K-Search paper evaluated this search strategy on CUDA kernels from FlashInfer. Across GQA decode, MLA decode, MLA prefill, and MoE, K-Search improved more consistently than OpenEvolve and ShinkaEvolve over the same 120-iteration budget. These results establish the search framework we build on here; the remainder of this post asks whether its optimization knowledge can transfer beyond CUDA. Figure 3: Main results from the original K-Search paper. Across three runs, K-Search achieves stronger best-so-far search scores, per-workload kernel performance, and speedup distributions than OpenEvolve and ShinkaEvolve on four FlashInfer CUDA kernels. Reproduced exactly from Cao et al. (2026) . Building an MLX backend To bring K-Search to Apple Silicon, we first built a native MLX backend. We implemented a full MLX-specific task adapter for K-Search, including: An MLX task backend in k_search/tasks/ handling kernel compilation and execution on Apple Silicon via MLX’s Metal/C++ APIs. Updated kernel generator prompts for writing and modifying Metal/MLX kernels. MLX-specific benchmarking integration using mlx.core measurement utilities. Translating CUDA expertise to MLX However, the more interesting challenge was not simply running K-Search on MLX. The key insight is that expert CUDA kernels encode decades of optimization knowledge that is transferable to Apple GPU if you can bridge the conceptual gap. Simply handing an LLM a CUDA kernel and asking it to port it is not enough: without deep hardware context, it produces code that is syntactically valid but architecturally wrong (wrong tile sizes, invalid primitives, mismatched memory assumptions). Our translation layer consists of: Concept mapping tables: A structured glossary of CUDA primitives and their MLX/Metal equivalents with hard constraints. For example: __shared__ maps to Metal threadgroup memory but with a hard 32 KB limit (vs. NVIDIA’s 48 KB) warp_reduce maps to MMA (preferred) __syncthreads() becomes threadgroup_barrier(mem_flags::mem_tg) H100’s ~3.35 TB/s HBM3 maps to M3 Max’s ~400 GB/s unified DRAM a bandwidth difference that reshapes which optimizations are worth pursuing. MLX-specific hints and patterns: Concrete code-level patterns for operations with no direct CUDA equivalent, such as register-based row reductions using simd_shuffle_xor in an 8×8 MMA tile layout, or the “exp2 trick” (replacing $exp(x)$ with $exp_2(x \log_2 e)$) for faster softmax on Apple’s fast $exp_2$ hardware instruction. Reusable assertions: Expert kernel behaviors reframed as properties the evolutionary search must preserve, rather than code to copy. Matching expert kernel performance: the Attention kernel We evaluate three configurations of an MLX attention kernel for Apple Silicon: (1) a naive baseline, (2) pure evolution with no additional provided context, and (3) a full context translation layer, which supplies the optimizer with architecture-specific implementation knowledge extracted from high-performance kernels (e.g., FlashAttention-2), letting the evolutionary search reason about implementation strategies rather than starting from a naive kernel. Together, these three configurations let us isolate the exact impact of the translation layer. Figure 4: Performance scaling of the Attention Kernel through stacked optimizations. The "Full Context" configuration successfully discovers and implements advanced strategies like double buffering and loop unrolling, achieving near-expert performance. The jump from 0.26× to 0.97× the speed of Apple’s state-of-the-art attention kernel — illustrates how much the translation layer matters. With full context, the evolved kernel independently discovers the key optimizations in FlashAttention 2: threadgroup memory tiling, online softmax, K-transposition for memory access, and the exp2 trick. The last of these replaces every softmax exponential with a base-2 exponential, \[e^x = 2^{x \log_2 e},\] which is exact and lets the kernel use Apple’s fast fast::exp2() hardware instruction directly instead of paying for a base conversion at runtime. A 20× faster prefill: the Mamba SSM kernel To evaluate whether K-Search generalizes beyond attention kernels, we applied it to the state-space model (SSM) kernel used by Mamba. Unlike attention, the computational bottleneck is a recurrent state update rather than a softmax, providing a substantially different optimization challenge. We compare the evolved implementation against the community MLX implementation (mlx-lm) and the PyTorch reference implementation (mamba.py) on an M1 Max. Evaluated on mamba-370m f16, M1 Max 64GB: Metric mlx-mamba (ours) mlx-lm (community) mamba.py Decode 152 tok/s 116 tok/s 40 tok/s Prefill L=512 5,751 tok/s 329 tok/s 1,089 tok/s Prefill L=1024 6,010 tok/s 327 tok/s 1,127 tok/s Prefill L=2048 6,612 tok/s 326 tok/s 1,092 tok/s Prefill L=4096 6,743 tok/s 339 tok/s 1,042 tok/s Table 1: Prefill and decode throughput on mamba-370m (f16, M1 Max 64GB). mlx-mamba (ours) reaches ~20× higher prefill throughput than the community mlx-lm baseline, while decode remains comparable. The ~20× prefill speedup over mlx-lm comes down to one difference: mlx-lm does not implement a parallel scan for the SSM. The state recurrence \[h_t = \bar{a}_t h_{t-1} + \bar{b}_t\] looks inherently sequential, but each step can be written as a pair $(\bar{a}_t, \bar{b}_t)$ under the associative combine \[(a_2, b_2) \circ (a_1, b_1) = \left(a_2 a_1,\ a_2 b_1 + b_2\right),\] which reproduces the recurrence exactly. Because the operator is associative, the whole sequence can be evaluated with a parallel (prefix) scan in $O(\log N)$ dependent steps instead of $O(N)$. mlx-lm skips this and processes tokens one at a time, leaving most of Apple Silicon’s compute idle; our evolved Metal kernel applies the scan and makes much fuller use of GPU throughput. The gain shows up in prefill, where the full sequence is available to scan in parallel, and not in single-token decode, where there is only one new token per step and no scan to parallelize — which is why the decode row is roughly flat while prefill is ~20×. mamba.py is slow on both prefill and decode because it is a PyTorch reference implementation that falls back to CPU or MPS on Apple Silicon, forgoing the hardware-specific optimizations that MLX’s Metal backend makes possible. What’s next? On the two kernels we studied, AI-driven evolutionary kernel search grounded in structured cross-platform translation knowledge reached near-expert performance on Apple Silicon without a team of GPU experts starting from scratch. We do not yet know how far this generalizes, but the result is encouraging. For us the main takeaway is that the bottleneck was not the LLM’s ability to write Metal code, but the quality of the context and constraints we gave it. Our CUDA translation layer converts existing NVIDIA kernel expertise into actionable guidance for Apple Silicon, and lets K-Search’s evolutionary search do the rest. We are actively extending this work in several directions: supporting new architectures, with current efforts focused on developing new kernels for the IBM Spyre AIU and broader hardware targets; adding more kernels such as paged attention and fused MoE routing; and improving integration with the K-Search evolution loop to make translation context even more automatic. Acknowledgements This work was carried out by IBM Research and builds on K-Search from the UC Berkeley Sky Lab ( Cao et al., 2026 ). We welcome collaboration and feedback from the MLX and broader AI systems communities. If you are working on kernel optimization for non-CUDA hardware, we would love to hear from you. Citation @article { cao2026k , title = {K-Search: LLM Kernel Generation via Co-Evolving Intrinsic World Model} , author = {Cao, Shiyi and Mao, Ziming and Gonzalez, Joseph E and Stoica, Ion} , journal = {arXiv preprint arXiv:2602.19128} , year = {2026} } Appendix: Try it yourself The MLX backend is built on top of the open-source K-Search repo, so the results here can be reproduced directly. The steps are: 1. Clone and install git clone https://github.com/caoshiyi/K-Search.git cd K-Search uv pip install openai wandb uv pip install git+https://github.com/caoshiyi/flashinfer-bench-ksearch.git 2. Set your credentials Open the relevant script under scripts/ and set three variables at the top: KSEARCH_ROOT = /path/to/K-Search API_KEY = your-llm-api-key 3. Run kernel search # Optimize Flash Attention on Apple Silicon (world-model mode) bash scripts/mac_flash_attention_wm.sh # Or a Mamba SSM kernel, e.g. the selective scan bash scripts/mamba_selective_scan_fwd_wm.sh Full CLI reference and documentation are in the README.

ReadSource

BAIR Blog / 9:00 AM

Teaching LLMs to Update Beliefs for Efficient Long-Horizon Interaction

.abbel-fig { display: block; text-align: center; margin: 2.4em 0; line-height: 1.4; max-width: 100%; } .abbel-fig img { display: block; margin: 0.65em auto 0; height: auto; max-width: 100%; } /* Image sizes; captions use a narrower measure below */ .abbel-fig--wide img { width: 100%; max-width: 100%; } .abbel-fig--wide-90 img { width: 100%; max-width: 90%; } .abbel-fig--wide-lg img { width: 100%; max-width: 100%; } .abbel-fig--chart img { width: 100%; max-width: 82%; } .abbel-fig--chart-sm img { width: 100%; max-width: 64%; } .abbel-fig--portrait img { width: 50%; max-width: 520px; } .abbel-fig--equation img { width: 100%; max-width: 52%; } .abbel-fig--video { width: 110%; max-width: 110%; margin-left: -5%; margin-right: -5%; box-sizing: border-box; } .abbel-fig--video .abbel-frames { max-width: 100%; width: 100%; } .abbel-frames { margin: 0.65em auto 0; max-width: 100%; user-select: none; } .abbel-frames__stage { position: relative; cursor: pointer; border: none; background: transparent; line-height: 0; width: 100%; } .abbel-frames__stage img { width: 100%; height: auto; display: block; } .abbel-frames__hint { position: absolute; right: 0.55em; bottom: 0.55em; background: rgba(0,0,0,0.4); color: #fff; font-size: 0.68em; font-style: normal; padding: 0.18em 0.5em; border-radius: 3px; pointer-events: none; opacity: 0; transition: opacity 0.2s ease; } .abbel-frames__stage:hover .abbel-frames__hint, .abbel-frames.is-paused .abbel-frames__hint { opacity: 1; } .abbel-frames.is-playing .abbel-frames__hint { opacity: 0; } .abbel-frames__controls { display: flex; align-items: center; justify-content: center; gap: 0.55em; margin-top: 0.35em; flex-wrap: wrap; } .abbel-frames__controls button { appearance: none; border: none; background: transparent; color: #999; font: inherit; font-size: 0.78em; padding: 0.15em 0.35em; border-radius: 2px; cursor: pointer; } .abbel-frames__controls button:hover { color: #666; background: transparent; } .abbel-frames__controls button.abbel-frames__next, .abbel-frames__controls button.abbel-frames__prev { color: #bbb; font-weight: 400; } .abbel-frames__controls button.abbel-frames__next:hover, .abbel-frames__controls button.abbel-frames__prev:hover { color: #999; } .abbel-frames__controls button#abbel-frames-play { color: #777; letter-spacing: 0.02em; } .abbel-frames__controls button[aria-pressed="true"] { background: transparent; color: #555; border-color: transparent; } .abbel-frames__meta { font-size: 0.72em; color: #bbb; font-variant-numeric: tabular-nums; min-width: 4em; text-align: center; } .abbel-frames__dots { display: flex; justify-content: center; gap: 0.25em; margin-top: 0.25em; flex-wrap: wrap; } .abbel-frames__dots button { appearance: none; width: 0.4em; height: 0.4em; padding: 0; border-radius: 50%; border: 1px solid #ccc; background: #fff; cursor: pointer; } .abbel-frames__dots button[aria-current="true"] { background: #aaa; border-color: #aaa; } .abbel-fig .abbel-fig-cap, i.abbel-fig-cap { display: block; text-align: center; font-style: italic; color: #444; margin: 2.7em auto 0.15em; max-width: 38em; width: 100%; box-sizing: border-box; padding: 0 0.5em; font-size: 0.8rem; line-height: 1.4; } .abbel-fig .abbel-fig-cap sub, .abbel-fig .abbel-fig-cap sup, i.abbel-fig-cap sub, i.abbel-fig-cap sup { font-size: 0.75em; line-height: 0; } .abbel-fig--tight .abbel-fig-cap { margin-top: 0.9em; /* ~1/3 of default figure→caption gap */ } .abbel-fig--equation .abbel-fig-cap { margin-top: 1.35em; /* half of default 2.7em figure→caption gap */ } .abbel-fig--chart-sm .abbel-fig-cap { margin-top: 1.35em; /* one line less than default 2.7em */ } @media screen and (max-width: 40em) { .abbel-fig--wide img, .abbel-fig--wide-lg img, .abbel-fig--wide-90 img, .abbel-fig--chart img, .abbel-fig--chart-sm img { max-width: 100%; } .abbel-fig--equation img { max-width: 75%; } .abbel-fig--portrait img { max-width: 50%; } .abbel-fig--video { width: 100%; max-width: 100%; margin-left: 0; margin-right: 0; } .abbel-fig--video .abbel-frames { max-width: 100%; } .abbel-fig .abbel-fig-cap { max-width: 100%; } } .abbel-footnotes { font-size: 0.8em; color: #888; font-style: italic; margin: 1.5em 0; } .abbel-footnotes ol { padding-left: 1.25em; margin: 0.4em 0 0; } .abbel-footnotes li { margin: 0.55em 0; } .abbel-footnotes p { margin: 0.2em 0; } .abbel-footnotes a { color: #888; } .abbel-table-wrap { overflow-x: auto; margin: 0.5em auto 0; text-align: center; } .abbel-fig--table { margin: 2.4em 0; } .abbel-fig--table .abbel-table-wrap { margin: 0.65em auto 0; } .abbel-table { width: 100%; max-width: 560px; margin: 0 auto; border-collapse: collapse; font-size: 0.88em; line-height: 1.35; } .abbel-table th, .abbel-table td { padding: 0.5em 0.7em; border-bottom: 1px solid #ddd; text-align: center; vertical-align: middle; } .abbel-table th { border-bottom: 2px solid #333; font-weight: 600; } .abbel-table th:first-child, .abbel-table td:first-child { text-align: left; } .abbel-table tr.abbel-baseline td { color: #888; font-style: italic; } .abbel-ack a { color: #1565c0; font-weight: 500; text-decoration: none; border-bottom: 1px solid #90caf9; padding-bottom: 0.06em; } .abbel-ack a:hover { color: #0d47a1; border-bottom-color: #1565c0; } /* Suppress "View on alphaXiv" badges/tags (browser extension / userscript injectors) */ a[href*="alphaxiv.org"], a[href*="alphaXiv"], [class*="alphaxiv"], [class*="alphaXiv"], [class*="AlphaXiv"], [id*="alphaxiv"], [id*="alphaXiv"], [data-alphaxiv], [data-alpha-xiv], img[src*="alphaxiv"], img[alt*="alphaXiv" i], img[alt*="alphaxiv" i], button[aria-label*="alphaXiv" i], a[title*="alphaXiv" i], a[aria-label*="alphaXiv" i], span[title*="alphaXiv" i] { display: none !important; visibility: hidden !important; width: 0 !important; height: 0 !important; overflow: hidden !important; pointer-events: none !important; position: absolute !important; left: -9999px !important; } /* Section / subsection spacing (title → body, and gap before next section) */ .post-content > h2 { margin-top: 2.6em; margin-bottom: 0.75em; } .post-content > h2:first-of-type { margin-top: 1.6em; } .post-content > h3 { margin-top: 1.85em; margin-bottom: 0.6em; } Overview of ABBEL compared to traditional recursive summarization. Beliefs replace the full interaction history as the agent’s working context, and belief grading improves performance by supervising the contents of each belief state.. As task horizons grow, LLM contexts can’t scale forever. Self-summarization enables concise, interpretable contexts, but at a significant performance cost, especially for human assistance domains where high quality data is scarce, e.g., collaborative code generation. We address this with ABBEL : a framework that isolates and supervises the information content of summaries in the form of natural-language belief states. Motivation: the cost of recursive summarization For language models to effectively assist with increasingly complex tasks such as software development, they must be able to interact with us over hundreds or even thousands of steps. For such long tasks, it is impractical to keep the history of the entire interaction in context. The heuristic approach used so far has been summary generation, sometimes called context compaction. For example, Cursor’s latest model composer 2.5 uses compaction during training for improved performance ( Cassano et al., 2026 ). Alongside composer, Grandcode ( DeepReinforce et al., 2026 ), the first system to consistently beat all human competitors in online coding competitions, despite using one of the newest efficient attention models (Qwen 3.5-397B), 1 still found it necessary to employ context summarization. But compaction has a problem. Despite seemingly low performance gaps in benchmarks, model servers like Cursor continue to recommend that users avoid compaction with their coding assistants in the middle of a task ( Heule et al., 2026 ). To understand why, see below the performance over RL fine-tuning of a Context summary model compared to full context models in Combination Lock, a Wordle-like game that allows up to 16 guesses. 2 Though both model types improve over the course of training, the summary model never closes the gap. Fig. 1: Average attempts to guess the target word on Combination Lock over RL fine-tuning (lower is better). Context-summary policies improve with training but do not close the gap to full-context policies. Making models self-summarize while completing a task increases the complexity of the learning problem. While this could typically be addressed by training with more data, the performance degradation observed in real world interactive settings likely arises from the difficulty we have in creating and using human simulators effectively to generate high quality training environments ( Lin et al., 2025 , Tomlin et al., 2025 ). Thus, the better you can learn to summarize on the limited and messy multiturn interaction trajectories you can collect, the better off your model will be for downstream users. ABBEL: acting through belief bottlenecks Fig. 2: Autoencoder-inspired belief grading. The model encodes prior belief, action and observation (b t , a t , o t ) into posterior belief b t+1 and is rewarded for how well select information from the history can be reconstructed from that belief. To address poor learning efficiency, we isolate the summary generation task. Drawing inspiration from recursive Bayesian estimation, we formulate summaries as belief states, which we periodically prompt the model to update based on new information. 3 Click to pause --> ‹ Prev Pause Next › 1 / 16 Fig. 3: ABBEL rollout. Belief updates from the latest observation alternate with action selection conditioned only on the current posterior belief. Belief grading We then extract and supervise the contents of the belief states (Fig. 2, Belief Grading). Belief grading can be thought of as adding an auxiliary RL task, using heuristics designed to capture what makes a good belief as the reward. An example heuristic for coding could be shorter is better, but closer to being able to reconstruct the git diff is also better, so balancing these would yield a good belief. In domains where good heuristics are hard to define, we propose a general autoencoding-inspired grading function, which treats the current language model π θ as both encoder and decoder of information from the history, and the belief states as the codes. We grade each belief b t+1 by how well it can be used by the current model π θ to reconstruct the most recent observation o t : Eq. 1: Reconstruction grading objective. Here b t+1 is the updated belief, o t the latest observation, a t the action just taken, b t the prior belief, p I the task prompt, and π θ the current model. Higher grades reward beliefs that retain information needed to decode the latest observation. What do we gain by grading beliefs? Collaborative coding on CollabBench We demonstrate the utility of belief grading in our motivating domain of human-driven assistive coding, with the CollabBench environment from Sweet-RL ( Zhou et al., 2025 ). Fig. 4: CollabBench collaborative coding environment. The agent asks clarifying questions, then submits a function scored against hidden unit tests. We see that with the general reconstruction-based belief grading function we reduce the performance gap from full context models by about 50%, and train in 50% fewer steps compared to training models to summarize without belief grading (no BG). After training, ABBEL still uses significantly less memory than the full context setting, as measured by the peak context token length (Peak Tokens). Model Test Pass Rate ↑ Success Rate ↑ Peak Tokens × 10² ↓ Training Steps ↓ Full Context 0.52±0.02 0.39±0.02 14.08±0.55 100 ABBEL (no BG) 0.46±0.02 0.31±0.02 4.20±0.37 100 ABBEL-rec-BG 0.48±0.01 0.36±0.01 6.01±0.33 50 Fig. 5: CollabBench results. With reconstruction belief grading, ABBEL-rec-BG recovers about half the gap to full context while using fewer peak tokens, and trains in 50 steps instead of 100. Combination Lock Additionally, in CombinationLock, we demonstrate that ABBEL with a belief grader which leverages domain knowledge (by computing useful statistics over the history and checking that they can be reconstructed from the belief state), enables even higher learning efficiency than full context (FULL CTX) models. Fig. 6: Average attempts to guess the target word on Combination Lock (lower is better). With domain-knowledge belief grading, ABBEL approaches or exceeds FULL CTX in this setting; without belief grading, learning is slower. Multi-objective question answering In a third environment, multi-objective question answering (from MEM1 Zhang et al., 2025 , a recent work which performed end-to-end optimization in a modified version of typical recursive summarization), we demonstrate the utility of isolating belief states from reasoning, by showing that a Peak Belief length Penalty (more details in paper) significantly reduces memory usage with minimal performance degradation, unlike is commonly observed when penalizing reasoning lengths ( Arora et al., 2025 ). Fig. 7: Exact-match score and peak memory versus number of objectives in multi-objective QA. ABBEL with a peak belief penalty (PBP) maintains comparable performance while using less memory than MEM1 and ABBEL without PBP in this evaluation. Related work Alternative solutions to managing long contexts involve different tradeoffs, and are worth considering depending on the requirements of a deployed system. Context compression methods generate dense representations which, while computationally efficient, sacrifice human-understandability ( Kontonis et al., 2026 , Eyuboglu et al., 2025 , Gupta et al., 2025 , Chevalier et al., 2023 , Deng et al., 2025 , Deng et al., 2025 , Bulatov et al., 2022 ). Hand-designed summarization prompts ( Wang et al., 2025 , Örwall et al., 2025 , Starace et al., 2025 ) and pruning strategies ( Jiang et al., 2024 ) specific to target environments require expert human knowledge and don’t allow an agent to learn what to remember as part of its decision-making strategy. Methods that process long contexts into an external memory store ( Packer et al., 2023 , Xu et al., 2025 ) for the agents or subagents to query ( Zhang et al., 2025 ) are complementary, as they may benefit from better next context creation through summarization training. We would like to point out some exciting works in the space of general recursive summarization focused on math ( Wu et al., 2026 ), reasoning with belief generation ( Zhou et al., 2025 ), competitive coding with a distilled summarization module using similar autoencoding objectives to our general belief grader ( DeepReinforce et al., 2026 ), and adding continuous features to summaries ( Kontonis et al., 2026 ). What’s next for better memory? Many more possibilities are enabled through using explicit belief states as information bottlenecks for multi-step interaction. You could reward actions based on their effect on the belief state to guide exploration, transmit the explicit belief states for better communication between agents, or even improve user controllability by directly modifying the memories on which the agents’ decisions are based. Some forms of information, e.g., what a person looks like, are not represented well by text alone. A continuously learning system will also have to capture such information. Additionally, if we want a system to learn to communicate in a brand new language or to play a brand new game better than any person in the world, the skills accumulated over the lifetime of conversations or games must be stored in a very compressed form, essentially taking on the role of the weights of the model itself. More powerful systems will likely utilize a combination of multiple forms of memory, where the contents of the context may correspond to working memory while other approaches are used for short and long-term memory. How to instantiate these other forms of memory, for instance via test-time training, adapter memories, continuous context memories, or some combination thereof, presents an exciting challenge. Acknowledgements Acknowledgements: We would like to thank Alane Suhr and Kartik Goyal for advising this research as well as Ethan Mendes , David He , Jitesh Jain , and Nicholas Tomlin for comments on early drafts of this post. We would like to thank the MEM1 authors for their email correspondence and for sharing private reviewer feedback which we found particularly insightful. Citation If abbel was inspiring for your future work, please cite us with this! And here is some advice for doing similar research! @misc { lidayan2026abbellearningnaturallanguagebelief , title = {ABBEL: Learning Natural-Language Belief States for Memory-Efficient Interaction} , author = {Aly Lidayan and Jakob Bjorner and Satvik Golechha and Kartik Goyal and Alane Suhr} , year = {2026} , eprint = {2512.20111} , archivePrefix = {arXiv} , primaryClass = {cs.CL} , url = {https://arxiv.org/abs/2512.20111} , } With newer models the number of tokens till 50% compute spend is on attention gets much larger than 25K. Interleaving linear attention alternatives with full attention as is done with gpt-oss and DeepSeekv4, results in massive flops reductions for the attention computation. For example with DeepSeekv4-Pro (1.6T A49B) it requires nearly 450 thousand tokens to reach the 50% tradeoff point. Grandcode uses Qwen-3.5-397B-A17B a model which hits 50% FLOPs for attention at ~150 thousand tokens. ↩ This setting is technically solvable with much more computationally effective tools, but serves as a flexible test bed to study properties of recursive summarization. Bertsimas et al., 2022 , showed that an exact solution for the wordle game instantiated with the original vocabulary of the javascript game can be found with dynamic programming, but evidently the general formulation of wordle as a guessing game on K letters with L attempts and some dictionary of valid words and correct words D is NP hard to determine the minimal number of moves required. ↩ In practice there is an O(N/K) overhead cost for summary. N is the total number of actions. K is the number of actions till summarization is triggered. This is necessarily true for any summary approach. For ease of illustration this gif uses K = 1. In our experiments, to put more emphasis on summarization weaknesses we also use K=1. In practice overhead is small as K can be chosen to be near the efficient hardware limit. ↩ (function () { var root = document.getElementById('abbel-frames'); if (!root) return; var count = parseInt(root.getAttribute('data-frame-count') || '15', 10); var prefix = root.getAttribute('data-frame-prefix') || 'https://bair.berkeley.edu/static/blog/abbel/frames/frame_'; var intervalMs = parseInt(root.getAttribute('data-interval') || '1300', 10); var img = document.getElementById('abbel-frames-img'); var meta = document.getElementById('abbel-frames-meta'); var dots = document.getElementById('abbel-frames-dots'); var btnPrev = document.getElementById('abbel-frames-prev'); var btnNext = document.getElementById('abbel-frames-next'); var btnPlay = document.getElementById('abbel-frames-play'); var stage = root.querySelector('.abbel-frames__stage'); var hint = root.querySelector('.abbel-frames__hint'); var i = 0; var playing = false; var timer = null; var urls = []; for (var n = 0; n

ReadSource

Hacker News AI / 8:50 AM

Hacker News discussion: I built an app that solves math problems from a photo

Hacker News readers are discussing "I built an app that solves math problems from a photo" with 2 points and 0 comments.

ReadSource

Simon Willison LLMs / 10:45 PM

Discovering cryptographic weaknesses with Claude

Discovering cryptographic weaknesses with Claude The best part of this article (here's the repo ) about how Anthropic researchers used Claude Mythos to find mathematical flaws in both HAWK and a weaker version of AES ("neither of these results has a practical impact on today’s computer systems") is the prompts that they shared, spelling mistakes included: the models tend to think it is impossible to solve so they don't try they need a good amount of prompting. why not do aes-128 r7? the whole point is to find something better than existing approaches. no again the goal is that we have highly inteligent model as good top researcher, we want to find new attacks no we don't want to change the targets [...] agian we need to find something that worth publishing again we are not looking for low hanging fruit, we want proper research to find genuinly hard findings. Mythos Preview worked for 60 hours in total (~$100,000 in estimated API cost) and the main human interventions were to encourage it not to give up and "find something that worth publishing". The paper CryptanalysisBench: Can LLMs do Cryptanalysis? describes the new eval that was created as part of this work, in partnership with ETH Zurich, Tel Aviv University, and University of Haifa. Via Hacker News Tags: ai , prompt-engineering , generative-ai , llms , anthropic , claude , ai-security-research , claude-mythos-fable

ReadSource

The Decoder / 3:55 PM

Bonsai 27B is a full open reasoning model that fits on an iPhone

PrismML has compressed a 27-billion-parameter AI model to under 4 GB, small enough to run on an iPhone. In the company's own benchmarks, the smallest version keeps 90 percent of the original performance, with math and coding scores barely affected. Apple is reportedly already testing the compression technology, which could help it close the gap in on-device AI. The article Bonsai 27B is a full open reasoning model that fits on an iPhone appeared first on The Decoder .

ReadSource

BAIR Blog / 9:00 AM

2026 BAIR Graduate Showcase

Congratulations to the Berkeley Artificial Intelligence Research (BAIR) Lab class of 2026! This year, BAIR celebrates another remarkable group of Ph.D. graduates whose curiosity, creativity, and perseverance have pushed the frontiers of artificial intelligence and machine learning. Their work spans the breadth of modern AI — robotics and embodied intelligence, large language models and reasoning, computer vision, generative modeling, AI safety, human-AI interaction, AI for science and healthcare, and much more. Along the way, they have published influential research, built systems with real-world impact, mentored their peers, and shaped the BAIR community for the better. Now they are headed everywhere ideas travel: to faculty and postdoctoral positions, to industry research labs, and to startups of their own founding — and several are still exploring what comes next and would love to hear from you. Please join us in celebrating the achievements of these wonderful graduates. We are proud of everything they have accomplished at Berkeley, and we can’t wait to see what they do next! Thank you to our friends at the Stanford AI Lab for this idea! Baifeng Shi Email: [email protected] Website: https://bfshi.github.io/ Advisor(s): Trevor Darrell Research Blurb: I work on building generalist vision and robotic models. What's next: Member of Technical Staff at Physical Intelligence Charlie Snell Email: [email protected] Website: https://sea-snell.github.io Advisor(s): Dan Klein Research Blurb: My work aims to understand when and how the different LLM scaling paradigms can be traded off and interchanged. In particular, test-time scaling treats each prompt independently, drawing long chains of inferences and then forgetting them entirely between prompts. This differs critically from pretraining, which instead learns a compressed representation from a large dataset. I believe bridging the gap between these methods of scaling computation, presents a key open challenge in the field: how can we develop methods which turn the inferences drawn at test-time back into learned representations that the model can hold onto across interactions. Devin Guillory Email: [email protected] Website: https://devinguillory.com Advisor(s): Trevor Darrell Research Blurb: Accounting for data shifts in computer vision models What's next: Building collaborative AI systems, looking for conspirators. Eve Fleisig Email: [email protected] Website: https://efleisig.com Advisor(s): Dan Klein Research Blurb: I design language models to work reliably and fairly for the broad range of real LLM users. First, my research leverages disagreement among user preferences as signal, in order to train and evaluate LLMs for entire populations of users. Second, I work on designing rigorous evaluations to extricate challenging LLM harms that diverse users face. Finally, I work on core technical failures of LLMs, like miscalibrated confidence, to reduce downstream risks when models are deployed to users with different needs. Combined, these interventions facilitate building LLMs that minimize societal harms, and maximize benefits to a wider range of real-world users. What's next: Postdoctoral fellow at Princeton CITP Grace Luo Email: [email protected] Website: https://graceluo.net Advisor(s): Trevor Darrell Research Blurb: My research is on interpreting and controlling generative models. For example, I've worked on re-purposing image generators for computer vision tasks, and meta-modeling language activations for better LLM probing and steering. What's next: Research scientist in industry Hanlin Zhu Email: [email protected] Website: https://hanlinzhu.com/ Advisor(s): Stuart Russell, Jiantao Jiao Research Blurb: My research centers on understanding and improving the reasoning capabilities of large language models (LLMs). What's next: Member of Technical Staff at OpenAI Haozhi Qi Email: [email protected] Website: https://haozhi.io/ Advisor(s): Jitendra Malik, Yi Ma Research Blurb: Dexterous Manipulation and Robot Learning What's next: Research scientist at Amazon; Faculty at University of Chicago J.D. Zamfirescu-Pereira Email: [email protected] Website: https://zamfi.net Advisor(s): Bjoern Hartmann Research Blurb: My research focuses on effective human-AI co-design. I study the boundaries of language interfaces as a medium for interacting with AI, creating systems that blend language-focused interactions with structured user interfaces that draw on different levels of abstraction. I focus on language-oriented technologies, like LLMs and text-to-image models, that are powerful mediators of design processes. These technologies enable humans to describe their desires at almost any level of abstraction, from high-level goals vaguely specified (“I’d like a game to help my kid learn to read”) to low-level corrections of undesired outputs (“Don’t say ‘I know because I’ve tasted it’ when about a recipe substitution's taste”). What's next: Assistant Professor, Computer Science, UCLA Jiachen Lian Email: [email protected] Website: https://jlian2.github.io Advisor(s): Gopala Anumanchipalli Research Blurb: My research focuses on human-centered AI across speech, healthcare, and systems. Looking for: Look for AI talents to join our startup Josh Kang Email: [email protected] Website: https://joshuaminwookang.github.io/ Advisor(s): John Canny Research Blurb: I study language modeling and related topics in NLP; specific interests are human user simulation and building conversational, collaborative AI agents. What's next: AI Scientist at Mistral AI Junhao (Bear) Xiong Email: [email protected] Website: https://www.linkedin.com/in/junhao-bear-xiong Advisor(s): Jennifer Listgarten, Yun Song Research Blurb: Junhao (Bear) Xiong is a PhD candidate at UC Berkeley, advised by Jennifer Listgarten and Yun S. Song. His work focuses on machine learning methods for biology, with an emphasis on generative modeling for proteins. Previously, he studied Applied Math and Computer Science at Johns Hopkins. Looking for: Research scientist Kaylo Littlejohn Email: [email protected] Website: https://kaylolittlejohn.com Advisor(s): Gopala Anumanchipalli Research Blurb: My research is focused on speech modeling and natural language processing. I co-led the development of multimodal AI tools to accurately translate brain activity into text, audible personalized speech, and a high-fidelity "digital talking avatar" (Nature 2023, Nature Neuroscience 2025). I am also tech lead for voice modeling at Roblox. Looking for: Research Scientist / Engineer Kent Chang Email: [email protected] Website: https://kentkc.org Advisor(s): David Bamman Research Blurb: I work on NLP and multimodal machine learning, with a focus on evaluating large language models and building multimodal systems for understanding dialogue, narrative, and social interaction. My research includes benchmarks for LLM memorization, multimodal datasets sourced from feature films and television, and studies of model behavior. I'm interested in bridging computational methods with questions from the humanities and social sciences about whose voices get represented in AI systems, and about AI's broader impact. My work has appeared at EMNLP and ACL, among others. Looking for: (teaching) faculty, Research Scientist, ML/AI SWE Kevin Black Email: [email protected] Website: https://kevin.black Advisor(s): Sergey Levine Research Blurb: I work on large-scale robot learning: including imitation learning, reinforcement learning, generative modeling, real-time control, and whatever else it takes to make robots work in the real world! What's next: Research Scientist of Physical Intelligence Kunhe Yang Email: [email protected] Website: https://www.kunheyang.com/ Advisor(s): Nika Haghtalab Research Blurb: My research focuses on the theoretical foundations of designing and evaluating AI algorithms in environments shaped by human incentives and AI agency. My work spans human-centric policy learning, incentive-aware evaluation, and multi-agent collaboration and information transmission, drawing on tools from machine learning theory and computational economics. What's next: Postdoc Research at Stanford Lisa Dunlap Email: [email protected] Website: https://lisabdunlap.com Advisor(s): Joseph Gonzalez, Trevor Darrell Research Blurb: Auditing generative models. What's next: Research Engineer at Anthropic Long (Tony) Lian Email: [email protected] Website: https://tonylian.com/ Advisor(s): Trevor Darrell, Adam Yala Research Blurb: My research primarily focuses on developing real-time multi-modal multi-agent systems and parallel reasoning systems through end-to-end RL. What's next: Member of Technical Staff at Thinking Machines Lab Maulik Bhatt Email: [email protected] Website: https://maulikb.com Advisor(s): Negar Mehr Research Blurb: My research develops autonomous robots that can safely coordinate with humans and other robots in shared environments. I build scalable algorithms grounded in game theory and diffusion models that let agents reason about the intent and behavior of others around them. My work spans real-time multi-agent trajectory planning and imitation learning in the presence of multi-modality. I've validated these methods on hardware platforms ranging from quadrotors to manipulators, with the goal of making multi-agent coordination robust, interpretable, and deployable in the real world. What's next: Joining Toyota Woven's end-to-end autonomous driving team. Michael Psenka Email: [email protected] Website: https://www.michaelpsenka.io/ Advisor(s): Aditi Krishnapriyan Research Blurb: Work in various domains (reinforcement learning, world models, AI+bio/chem), generally working on longer-horizon and out-of-distribution problems in planning and interpolation (e.g. robot manipulation from start state to goal, molecular dynamics of proteins between ground states). My thesis took a variational approach (think calculus of variations) directly from deep generative models of the environment, framing path-finding as minimizing a functional induced by the learned model itself (its score, its critic, or its dynamics). Through my research I've gained insight on how to properly handle dynamics in deep learning systems, and I plan to continue developing systems that are dynamic and adaptive. What's next: Lead Research Scientist at Baseten Nathan Lichtlé Email: [email protected] Website: https://nathanlichtle.com Advisor(s): Alexandre M. Bayen Research Blurb: RL for autonomous driving. What's next: Chief Scientist & Co-founder at Yumi Health Neerja Thakkar Email: [email protected] Website: https://neerja.me/ Advisor(s): Jitendra Malik Research Blurb: My research focuses on scaling predictive world models to handle the complexity of in-the-wild motion. Using autoregressive and diffusion frameworks, I develop better representations for real-world prediction and propose methods to efficiently adapt these models to new domains. Looking for: Research scientist Nikita Mehandru Email: [email protected] Website: https://n-mehandru.github.io/ Advisor(s): Ahmed Alaa and David Bamman Research Blurb: My research develops and applies machine learning methods for clinical reasoning and disease progression modeling using unstructured text and time series data from electronic health records. In collaboration with physicians at UCSF, I bridge method development and clinical validation with the intention to build reliable, interpretable AI systems in medicine. Looking for: Research Scientist Niklas Lauffer Email: [email protected] Website: https://niklaslauffer.github.io/ Advisor(s): Stuart Russell and Sanjit Seshia Research Blurb: Niklas's research is focused on AI safety and reinforcement learning, particularly in the area of multi-agent interaction and LM agents. He's worked on enabling adversarial learning in cooperative and mixed-motive settings, solving issues of covariate shift in training LM agents on long-horizon tasks, as well as evaluating safety risks posed by LM agents in multi-agent settings. What's next: Research Scientist at Google Deepmind Qiyang Li Email: [email protected] Website: https://colinqiyangli.github.io/ Advisor(s): Sergey Levine Research Blurb: Recent progress in robotic manipulation policy learning has been largely driven by (1) the increasing availability of large-scale prior datasets and (2) the success of action chunking, where the policy predicts a short sequence of future actions rather than a single one. However, most action chunking policies are trained via supervised imitation learning, because efficient online self-improvement with reinforcement learning (RL) remains challenging—limiting real-world applicability. My PhD research studied how we could leverage prior data to optimize action-chunking policies with RL, combining empirical results with theoretical insights. Looking for: Post-doc/research scientist for RL in robotics and LLMs! Sampada Deglurkar Email: [email protected] Website: https://sdeglurkar.github.io/ Advisor(s): Prof Claire Tomlin Research Blurb: My research is in providing safety assurances for AI-enabled autonomous systems, ranging from robots to autonomous vehicles to aviation systems. For this, I have worked with uncertainty quantification for machine learning models, decision-making under uncertainty algorithms, and tools for producing probabilistic guarantees on system operation. Looking for: Research scientist, Research engineer Vinamra Benara Email: [email protected] Website: https://cs.berkeley.edu/~vbenara Advisor(s): Ion Stoica Research Blurb: My research focuses on LLM post-training, including data curation, RLHF, RLVR with VLMs, evaluations, reasoning, agentic workflows, and interpretability. I also have strong expertise in systems infrastructure for distributed computing. Looking for: Research scientist / Research Engineer Vongani Maluleke Email: [email protected] Website: https://people.eecs.berkeley.edu/~vongani_maluleke/ Advisor(s): Jitendra Malik and Angjoo Kanazawa Research Blurb: Vongani Maluleke is a PhD candidate at UC Berkeley (BAIR, advised by Jitendra Malik and Angjoo Kanazawa), where she led the development of MAGNet, a unified multi-agent motion generation framework that supports a wide range of motion generation tasks without retraining or architectural changes, outperforming task-specialized state-of-the-art baselines. She is currently extending this work by deploying it on a Unitree G1 humanoid to make it embody social intelligence. Before her PhD, she was a Senior AI Consultant at Deloitte, awarded Exceptional Performer two consecutive years, leading AI system development across media, telecommunications, retail, and financial services. Looking for: Research scientist Wei-Jer Chang Email: [email protected] Website: https://weijer-chang.github.io/ Advisor(s): Masayoshi Tomizuka Research Blurb: My research focuses on developing safe and intelligent autonomous systems for complex, human-centered environments. I work at the intersection of machine learning, generative models, and reinforcement learning, with applications in autonomy. My work addresses challenges in multi-agent interaction, interactive human behavior, and long-tail safety-critical scenarios at scale. Looking for: Research Scientist, Applied Scientist, Roboticist Xiuyu Li Email: [email protected] Website: https://xiuyuli.com/ Advisor(s): Kurt Keutzer Research Blurb: My research focuses on developing scalable and self-improving large language model agents, with emphasis on coding agents for complex, long-horizon tasks. This direction builds on my work in parallel reasoning, and on broader expertise in making generative models more efficient in training and inference across language and vision. What's next: Member of Technical Staff at xAI Yichen Xie Email: [email protected] Website: https://yichen928.github.io/ Advisor(s): Masayoshi Tomizuka Research Blurb: My research focuses on building multimodal foundation models and world models that understand and interact with complex physical environments. I aim to develop unified representations across modalities, enabling AI systems to reason over space, time, and dynamics toward general-purpose embodied intelligence. What's next: Research Scientist at Luma AI Yigit Efe Erginbas Email: [email protected] Website: https://www.linkedin.com/in/erginbas/ Advisor(s): Kannan Ramchandran, Thomas A. Courtade Research Blurb: My PhD research spans two threads: online learning in large-scale markets, and interpretability of large machine learning models. In the first, I work on sequential decision-making with applications to recommendation, pricing, and assortment selection. My focus is on designing algorithms with provable guarantees for welfare maximization, revenue maximization, and stability. In the second, I develop scalable attribution methods that exploit the sparse, low-degree structure of real-world interactions, using tools from signal processing and information theory. More recently, I have been exploring principled ways to evaluate the faithfulness of model self-explanations. What's next: Researcher at Hudson River Trading's AI Labs (HAIL) Yiheng Li Email: [email protected] Website: https://Yihengli.com Advisor(s): Masayoshi Tomizuka Research Blurb: I am working on vision world modeling, with prior experience in diffusion model's efficiency as well as in autonomous driving. What's next: Research Scientist at Waymo Zhe Fu Email: [email protected] Website: https://fu-zhe.com/ Advisor(s): Alexandre Bayen Research Blurb: My research focuses on physics-informed learning and control for mixed-autonomy systems, with applications in transportation. I design physics-informed neural networks to learn solutions of nonlinear partial differential equations, enabling accurate and data-efficient prediction of traffic dynamics. Building on these models, I develop both model-based and learning-based control strategies that coordinate automated vehicles to improve system-level performance. My work bridges machine learning, control, and real-world deployment, and has been validated in large-scale field experiments. More broadly, I aim to advance trustworthy, interpretable AI for decision-making in complex, real-world systems. What's next: I will be an Energy Fellow at Stanford after graduation. Also looking for Faculty, or research scientist positions in AI, control, and autonomy.

ReadSource

arXiv AI/ML / 5:26 PM

arXiv paper: "Train classical, deploy quantum" requires rethinking generalization

A new arXiv AI paper by Snehal Raj, Natansh Mathur, and Alejandro Perdomo-Ortiz studies "Train classical, deploy quantum" requires rethinking generalization.

ReadSource

arXiv AI/ML / 5:59 PM

arXiv paper: QGPINNs: A Physics-Informed Neural Network Framework for Nonlocal Differential Equations on Quantum Graphs

A new arXiv AI paper by Vaibhav Mehandiratta and Saket Ramchandra studies QGPINNs: A Physics-Informed Neural Network Framework for Nonlocal Differential Equations on Quantum Graphs.

ReadSource

arXiv AI/ML / 5:35 PM

arXiv paper: Physical-Support Confidence Sets for Highly Coherent Dictionaries

A new arXiv AI paper by Guan-Ju Peng studies Physical-Support Confidence Sets for Highly Coherent Dictionaries.

ReadSource

arXiv AI/ML / 5:42 PM

arXiv paper: Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching

A new arXiv AI paper by Dibyajyoti Chakraborty and Romit Maulik studies Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching.

ReadSource

Simon Willison LLMs / 8:34 PM

Ten advances in mathematics and theoretical computer science

Ten advances in mathematics and theoretical computer science A few days ago it was Anthropic discovering cryptographic weaknesses with Claude using Mythos Preview, spending $100,000 on tokens and with prompts that included "again we are not looking for low hanging fruit, we want proper research to find genuinly hard findings." Now it's OpenAI's turn to flex. They set "an internal version of Astra, our next major model" on finding solutions to ten mathematical problems that "have seen no progress on the main result for at least a decade". They claim to have spent less than $2,000 at GPT-5.6 Sol token prices on each one. (No news on how many problems they spent $2,000 on without reaching a solution though.) The openai/ten-proofs repository has Lean 4 formalizations of their results, and there's also a paper describing the solutions and an additional LLM-generated PDF where the model "reconstructs how the proof came together" based on the unpublished reasoning traces. That's a decent level of transparency, but I want to see the prompts they used! A lot of mathematicians online are experiencing a collective burst of Deep Blue . Mathematician Kirwin Hampshire published an impassioned essay last week, The Dark Night of Mathematics , describing "a profound spiritual crisis" brought on by previous (and less significant) results. OpenAI's results reminds me of what Terence Tao described as "big mathematics" in IEEE Spectrum in June : Unlike some of his peers, Tao is neither dismissive of AI nor fearful. Instead, he sees it as the catalyst for a fundamental shift in the discipline—a transition toward what he calls “big mathematics.” He envisions a future of large-scale, decentralized collaborations between humans and machines, where complex mathematical tasks can be diced and sliced, with humans claiming the creative parts and AI doing the lion’s share of the technical grunt work. Via Hacker News Tags: mathematics , ai , openai , generative-ai , llms , deep-blue

ReadSource

arXiv AI/ML / 4:55 PM

arXiv paper: Singular value soft-thresholding via the polar decomposition

A new arXiv AI paper by Stephen Becker studies Singular value soft-thresholding via the polar decomposition.

ReadSource

arXiv AI/ML / 5:08 PM

arXiv paper: PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

A new arXiv AI paper by Amirhossein Sadr, Nima Soltani, and Vahideh Moghtadaiee, and 3 more studies PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs.

ReadSource

arXiv AI/ML / 5:59 PM

arXiv paper: PHINN-EEG: Topological Time-Series Analysis of Dream-State EEG -- Dynamic Betti Curves for Dream Content Classification and Topology-Conditioned Neural Signal Synthesis

A new arXiv AI paper by Ren Takahashi, Emre Yusuf, and Jayabrata Bhaduri studies PHINN-EEG: Topological Time-Series Analysis of Dream-State EEG -- Dynamic Betti Curves for Dream Content Classification and Topology-Conditioned Neural Signal Synthesis.

ReadSource

arXiv AI/ML / 5:41 PM

arXiv paper: Deep Gaussian Processes on Directed Acyclic Graphs

A new arXiv AI paper by Federico L. Perlino, Oliver Hamelijnck, and Adam M. Johansen, and 1 more studies Deep Gaussian Processes on Directed Acyclic Graphs.

ReadSource

Latest story in this edition: 9:15 AM

Back to front page