This week’s coverage focused on one recurring question: what remains reusable after a model’s impressive run? The conversation shifted from single-shot capabilities to components and practices that can be reused later — whether formal proofs, repeated processing inside Transformers, or agents that operate within real computer environments.
1. Why Axiom Math built a city out of proofs
Axiom Math has formalized a version of the Stacks Project in Lean, creating a large library of mathematical code. The project represents dependency structure as a city: following a line from one building shows which results support it and which results build upon it.
In a walkthrough video, Ksenia explains the city metaphor and the collaboration behind the work. Lean can verify whether a formal proof logically follows from stated assumptions. However, whether the formal statement captures the mathematician’s intended meaning is a separate issue that still requires careful human review.
2. Looped Transformers: when is another pass worth the cost?
A conventional Transformer proceeds through a stack of layers with different weights. A looped Transformer can execute the same blocks multiple times, updating hidden representations on each pass. For example, six blocks used four times yield 24 block applications without storing 24 separate sets of weights.
That setup raises a practical question: when does an additional pass actually help? The guide examines what information circulates through the loop and why having fewer parameters does not automatically imply lower compute costs or faster inference. It also discusses adaptive stopping: a model’s outputs may stabilize before they are actually correct.
3. Computer-use AI agents: best open-source and closed-source tools in 2026
The landscape of computer-use agents now ranges from ready-made assistants to frameworks for building custom agents. The updated collection compares tools across desktop, browser, and mobile environments, and covers deployment options, pricing, and permission controls.
One important detail when choosing among them is that an app running on your computer does not necessarily mean the model processes everything locally. The guide also looks beyond demos to issues such as recovery, cost, and the level of access an agent requires to handle messy, real-world workflows.
4. FOD#175: The anxiety of abundance
Editorial note: publication timing needs to be checked against the Moscow-time cutoff before this item is included.
Agents can enable more work, but they can also leave us with more outputs to read, more decisions to make, and more processes to supervise. In this issue, Ksenia reflects on that tension and on how it feels when the set of things we could do keeps expanding.
The research roundup moves from the personal question to system-level concerns: how agents recover from failures, how robotic systems adapt, and why measuring partial progress can provide more insight than a simple success-or-failure metric.
Closing thoughts
Across these pieces the recurring message is that reusability in AI requires deliberate design, verification, and workflow support. Without those, impressive single runs rarely translate into reliable, repeatable value.
