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Formally proving a calculation with Claude and Lean

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I ran an experiment today to see whether Claude [1] could generate Lean code to prove a calculation at the bottom of this post, six lines of calculus. I started with this prompt This page contains a mathematical proof that a Fourier coefficient, a_n, is given in terms of a Bessel function. The LaTeX source for the SVG image is contained in the alt tag of the image. Generate a formal proof of the result using Lean. and […]

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A Coding Implementation on Microsoft SkillOpt for Instrumented Prompt Optimization, Skill Evolution Analysis, and Baseline Comparison

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In this tutorial, we implement an instrumented workflow for Microsoft SkillOpt. We set up the SkillOpt repository, connect it to OpenAI-compatible model access, configure the optimizer and target models, and run the SearchQA optimization pipeline with a controlled sample limit to keep costs manageable. We first evaluate the original seed skill as a baseline, then run a real optimization loop in which SkillOpt improves the skill through rollout, reflection, aggregation, selection, updating, and validation-based gating. Along the way, […]

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DiffusionGemma

DiffusionGemma

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DiffusionGemma Last May Google briefly released an experimental Gemini Diffusion model. I tried the preview at the time and recorded it running at 857 tokens/second. It was an exciting model, but Google made no further announcements about it. That research has returned in the best possible way: as a new open weight (Apache 2 licensed) Gemma model, google/diffusiongemma-26B-A4B-it. NVIDIA are currently hosting the model for free on their NIM cloud API. I used that API to generate this […]

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Logitech’s foldable mouse is for people who refuse to carry a mouse with them

Logitech’s foldable mouse is for people who refuse to carry a mouse with them

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I see it often. Hardworking professionals in cafés, airports, or parks hunched over a laptop while carefully dragging their fingers over their PC’s trackpad to navigate some email, project, or alert that can’t be ignored. They would prefer a mouse to a trackpad, but are reluctant to travel with one. When you’re on the go, carrying a mouse can seem burdensome or unnecessary. But I’d argue that it’s worth the boost in efficiency and comfort when navigating your […]

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Google DeepMind releases DiffusionGemma, a model that runs local AI 4x faster

Google DeepMind releases DiffusionGemma, a model that runs local AI 4x faster

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Another day, another AI model from Google. This time, Google DeepMind has released a new member of the Gemma 4 open model family, but it’s fundamentally different from the rest of the lineup. DiffusionGemma doesn’t generate outputs linearly like most AI models. Instead, it can produce an entire block of text in parallel. Google says this makes it faster and more efficient when running on local hardware like an Nvidia DGX or a humble gaming GPU. Most AI […]

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Routing LLMs by task verifiability: a small experiment (n=120, 3 models) inspired by Karpathy’s framework [D]

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Full disclosure: this is directional, not a paper. n=120 tasks, one internal evaluator, not peer reviewed. I work at an LLM infrastructure company. This experiment was done on my own time and is not a company claim. Karpathy’s framework classifies tasks by verifiability. Can output be mechanically checked? High verifiability tasks like code compilation and structured JSON extraction are safer because the verifier catches errors. Low verifiability tasks like creative writing are riskier. I wondered if high verifiability […]

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Google AI Releases DiffusionGemma, a 26B MoE Open Model Using Text Diffusion for Up to 4x Faster Generation

Google AI Releases DiffusionGemma, a 26B MoE Open Model Using Text Diffusion for Up to 4x Faster Generation

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Google AI team including the Google DeepMind researchers have just released DiffusionGemma, an experimental open model for text generation. It uses text diffusion instead of standard autoregressive decoding. The model ships under a permissive Apache 2.0 license. Google positions it for devs and researchers exploring speed-critical, interactive local workflows. Examples include in-line editing, rapid iteration, and generating non-linear text structures. Most language models in use today are autoregressive. They generate one token at a time, left to right. […]

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FACTR 2: Learning External Force Sensing for Commodity Robot Arms Improves Policy Learning

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Contact-rich manipulation requires force sensitivity, but many robot arms lack dedicated force sensors due to their high cost. We present Neural External Torque Estimation (NEXT), a data-driven method that estimates external joint torques without needing any dedicated force sensors. NEXT trains in 1 minute from only 10 minutes of free-motion data, yet achieves estimates comparable to dedicated joint-torque sensors. NEXT enables force-feedback teleoperation on low-cost arms and improves policy learning through Force-Informed Re-Sampling Training (FIRST), which up-samples pre-contact […]

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ATLAS: Active Theory Learning for Automated Science

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Advancing scientific understanding through mechanistic modeling requires posing the right experimental questions to yield maximally informative data. To automate this pursuit within cognitive science, we introduce ATLAS (Active Theory Learning for Automated Science), an active learning framework for the data-driven discovery of interpretable behavioral models. ATLAS iterates between generating mechanistic hypotheses–instantiated as a diverse ensemble of sparse neural networks (Disentangled RNNs)–and designing experiments that optimally distinguish between them. We test this approach on the problem of recovering reinforcement […]

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