I recently found out about Andrica’s conjecture: the square roots of consecutive primes are less than 1 apart. In symbols, Andrica’s conjecture says that if pn and pn+1 are consecutive prime numbers, then √pn+1 − √pn < 1. This has been empirically verified for primes up to 2 × 1019. If the conjecture is true, it puts an upper bound on how long you’d have to search to find the next prime: pn+1 < 1 + 2√pn + […]
Reinforcement Learning with Verifiable Rewards (RLVR) has become a prominent method for post-training Large Language Models (LLMs). However, verifiers are rarely error-free; even deterministic checks can be inaccurate, and the growing dependence on model-based judges exacerbates the issue. The extent to which RLVR is robust to such noise and the verifier accuracy required for effective training remain unresolved questions. We investigate these questions in the domains of code generation and scientific reasoning by introducing noise into RL training. […]
Multi-task learning for advanced driver assistance systems requires modeling the complex interplay between driver internal states and external traffic environments. However, existing methods treat recognition tasks as flat and independent objectives, failing to exploit the cognitive causal structure underlying driving behavior. In this paper, we propose CauPsi, a cognitive science-grounded causal multi-task learning framework that explicitly models the hierarchical dependencies among Traffic Context Recognition (TCR), Vehicle Context Recognition (VCR), Driver Emotion Recognition (DER), and Driver Behavior Recognition (DBR). […]
In this tutorial, we build a complete Open WebUI setup in Colab, in a practical, hands-on way, using Python. We begin by installing the required dependencies, then securely provide our OpenAI API key through terminal-based secret input so that sensitive credentials are not exposed directly in the notebook. From there, we configure the environment variables needed for Open WebUI to communicate with the OpenAI API, define a default model, prepare a data directory for runtime storage, and launch […]
Z.AI, the AI platform developed by the team behind the GLM model family, has released GLM-5.1 — its next-generation flagship model developed specifically for agentic engineering. Unlike models optimized for clean, single-turn benchmarks, GLM-5.1 is built for agentic tasks, with significantly stronger coding capabilities than its predecessor, and achieves state-of-the-art performance on SWE-Bench Pro while leading GLM-5 by a wide margin on NL2Repo (repo generation) and Terminal-Bench 2.0 (real-world terminal tasks). Architecture: DSA, MoE, and Asynchronous RL Before […]
Training AI agents that can actually use a computer — opening apps, clicking buttons, browsing the web, writing code — is one of the hardest infrastructure problems in modern AI. It’s not a data problem. It’s not a model problem. It’s a plumbing problem. You need to spin up hundreds, potentially thousands, of full operating system environments with actual graphical user interfaces. Each one needs to run real software. Each one needs to handle unpredictable crashes. And you […]
In this tutorial, we explore ModelScope through a practical, end-to-end workflow that runs smoothly on Colab. We begin by setting up the environment, verifying dependencies, and confirming GPU availability so we can work with the framework reliably from the start. From there, we interact with the ModelScope Hub to search for models, download snapshots, load datasets, and understand how its ecosystem connects with familiar tools such as Hugging Face Transformers. As we move forward, we apply pretrained pipelines […]
Last week I wrote about the orbit of Artemis II. The orbit of Artemis I was much more interesting. Because Artemis I was unmanned, it could spend a lot more time in orbit. The Artemis I mission took 25 days while Artemis II will take 10 days. Artemis I took an unusual path, orbiting the moon the opposite direction of the moon’s orbit around earth. This video by Primal Space demonstrates the orbit both from the perspective of […]
Meta announced Muse Spark today, their first model release since Llama 4 almost exactly a year ago. It’s hosted, not open weights, and the API is currently “a private API preview to select users”, but you can try it out today on meta.ai (Facebook or Instagram login required). Meta’s self-reported benchmarks show it competitive with Opus 4.6, Gemini 3.1 Pro, and GPT 5.4 on selected benchmarks, though notably behind on Terminal-Bench 2.0. Meta themselves say they “continue to […]
The Trump administration wants to require health insurance companies to hand over troves of sensitive, detailed, and identifiable medical records from millions of federal workers and retirees, along with their families. The move is raising immediate concern from legal and health policy experts, according to a report by KFF Health News. The unprecedented proposal was quietly revealed in a short notice from the Office of Personnel Management in December, KFF notes. OPM said it is seeking “service use […]
