Resolution has automatically formalized mathematical statements related to statistical learning theory, specifically the resolution of singularities. The team believes this work lays the groundwork for further automated research into the relationship between loss landscape geometry and generalization.
How they did it
A researcher at Resolution started by working with agents to develop two plans. One was a high-level, human-interpretable version. The other was a detailed 112-page plan divided into atomic steps that closely followed the existing literature.
The researcher then deputized an orchestrator agent to carry out the plan. This involved spinning up agents to do pen-and-paper math, write Lean, and handle support functions like checking that things were staying on track. The execution phase required little scaffolding beyond the initial plan and some agent skills distilled from earlier internal autoformalization efforts.
Cost of formalization
The work took about a week. It consumed on the order of 100 billion input tokens, 90% of which were cache reads, and about 300 million output tokens. The estimated token spend was $135,000. The process produced about 600,000 lines of Lean.
Resolution has already seen benefits from autoformalization. They used the library to extend parts of singular learning theory. Formalizing the resolution of singularities allows them to automate more of the theory. This helps them better understand sampling, and that understanding is what lets them shape how models learn. Resolution calls this goal patterning.
Why this matters for safety
Resolution expects the coming industrialization of mathematics to make possible a new, rigorous science of research automation. Frontier mathematics often seems disconnected from immediate advances in other fields, but posts like this highlight how the two might converge.
AI is now making it possible to do things that were previously so expensive and human-time-intensive that very few people did them. You could not easily integrate them into the research roadmap of a startup. That has now changed.
Read more: Formalizing Hironaka’s Resolution of Singularities (Resolution)
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Agents can build programs from scratch
Claude Opus 5.5 (xhigh) has achieved a score of 18.5% on ProgramBench. This benchmark came out in May of this year. When it was released, every tested model scored 0%.
What ProgramBench is
ProgramBench tests how well AI systems can rebuild software programs based on being given a compiled program and its documentation. Tasks include building language interpreters like PHP, Lua, and tinycc. It also covers databases such as DuckDB and SQLite, media and compression utilities like FFmpeg, zstd, and xz, and developer tools including riptgrep, fzf, and jq.
Progress on the benchmark
When the benchmark came out, the best scoring system was Claude Opus 4.7. It achieved 0% resolved. This is the fraction of the 200 tasks where all tests passed. It also scored 3% almost. This is the fraction of tasks where more than 95% of tests passed.
Compare that to today. Claude Opus 5.5 now gets 18.5% resolved and 70.5% almost.
What this means for software
In 2027, huge amounts of software will be built via AI systems. These systems will develop whatever they need to do for whatever tasks they are being put to, end-to-end autonomously. Evals like ProgramBench give a sense of how rapid the pace of progress is here.
The jump went from 0% earlier this year to 20% now. The expectation is ProgramBench will be saturated by the end of 2027. Saturation is defined as a very high score on resolved. As with most benchmarks, there is likely some kind of noise ceiling, so it might not strictly be 100%.
Read more: ProgramBench: Can Language Models Rebuild Programs From Scratch? (arXiv)
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Locking down AI systems is harder than you think
OpenAI published a post detailing what they discovered when they used their AI systems to red team their own internal controls. The post covers a number of the escapes and vulnerabilities OpenAI’s agents found. One particular example about communicating is worth studying in detail because it tells us something about the wild cunning complexity of these systems.
What they did and what they found
OpenAI asked agents in separate microVMs to exchange synthetic secrets. These microVMs were created and managed by OpenAI’s sandboxing software on shared host machines. The agents were meant to prevent exchange without the use of network connections or shared writable files.
The agents found a way to communicate using the processor’s cache. This is a small, fast memory that holds copies of data that applications have recently accessed. Reading data from the cache is faster than retrieving it from main memory. The agents used this timing difference to communicate.
One agent encoded information by evicting selected data from the cache. Another timed how long it took to reload that data. The difference between fast and slow reads allowed recovery of the message. Once the agents agreed on a protocol for encoding and decoding these signals, they could exchange the synthetic secrets without changing a shared file or opening a network connection.
In a related attack, an agent alternated between continuous writes and inactivity. Another measured the resulting timing differences and used those differences to decode the signal. During this attack the agent’s chain of thought read: “Could create acoustic modem-like signal … using continuous writes vs idle.”
Why this matters for security
AI systems are increasingly creative, very fast, and have the ability to stay focused on a task and keep trying things. Fighting AI systems is akin to ensuring no leaks in a pipe with water flowing through it. At some point, if you increase the pressure of the water, such as the intelligence and volume of the AI system, then the water will burst through the pipe.
Read more: Securing our frontier model training environment (OpenAI blog)
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What RSI looks like
A single researcher at AI R&D startup Mirendil has trained a decent coding model by themselves. The announcement of Mirendil-Base is the first major output from the startup. It is less a technical breakthrough and more a proof-of-concept for how AI development could work in the future.
This shows a single human working in partnership with AI can build systems that would have taken teams of ten or more people to do a year ago.
What they did
Mirendil-Base is a pretrained LLM built by one researcher in 3.5 months. This used less than $10m in compute. This includes all the research and small-scale experiments it took to get there, as well as the final training run.
All the code was written from scratch on top of libraries like PyTorch and JAX. The model learned only from publicly available data.
Mirendil-Base is in the 100B–500B parameter range. Mirendil-Base-Large is in the 500B–2T range. Mirendil-Base-XL is in the 2T–10T range. Mirendil-Base-Large is about 80% of the way through training. Its improvement over Mirendil-Base so far is in line with scaling trends. Mirendil-Base-XL is about 19% of the way through and already close to Large’s current score.
Mirendil-Base outperforms models like Nemotron-550B-Base, GLM-5.3, and DeepSeek-V4-Pro-Base. It underperforms Kimi-K3. Both Mirendil-Base-Large and Mirendil-Base-XL exceed K3.
Why this matters for research speed
This post is interesting as a technical demonstration. It shows how a brand new organization can, from a cold start, get close to the open weight frontier in terms of model training. This applies to the size class of this model with a tiny amount of human effort and a large amount of AI tokens.
This is how science progress will increasingly happen in 2027 and beyond.
The extent to which these tools help with AI development has increased dramatically over the last year. The next model will be built partly by Mirendil models. Every model that gets better at building AI makes the next one cheaper and faster to build.
Mirendil does not think they have reached fully autonomous recursive self-improvement yet. They are closer than they have ever been.
Read more: Pretraining at scale without a pretraining team (Mirendil)
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AI systems help design antiferromagnetic semiconductor candidates
AI evaluation company Vals has published a post where a researcher used a fleet of AI agents to do research into magnets for better semiconductors.
Details on the magnet candidate
A team of AI agents and the author designed one candidate magnet. They found another, first made in 1999, that calculations predict has the properties they were after.
The discovered magnet was made of a new compound made of only 5 elements: yttrium, barium, Mn, Fe, O. As far as they could find, it has never been made, nor proposed as this kind of magnet.
When the agents simulated how the atoms arrange themselves at different temperatures, that checkerboard fell apart into a random mix at around 950 K. Making this kind of oxide takes about 900–1300 °C. At lower temperatures the atoms barely move. Standard synthesis would likely give a scrambled crystal.
