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The full conjecture is stated over abstract fields, but the counterexample is a concrete 3D function that we can explain and visualize using familiar geometric ideas and a little algebra. The post A Simplified View of the Jacobian Conjecture appeared first on Towards Data Science.
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An easier way to find the right beats for your BPM. | Image: Spotify Spotify has introduced a new Running Mode feature that makes it easier to curate playlists around your workout goals, music tastes, and desired beats per minute (BPM). The aim is to help you "spend less time hunting for the right music and more time moving," according to Spotify's announcement, providing customizable running presets and optional coaching features. Running Mode is an AI-powered experience that builds on personalization capabilities that were introduced with Prompted Playlists last year, with Spotify finding that fitness-based prompts have been some of the most popular uses for that feature. It requires a Premium subscription … Read the full story at The Verge.
A security team approving an open-source model for production today starts with a repository page. The page lists the model name, the license, and a tag identifying the base model it descended from. That tag is a string the uploader typed. Hugging Face does not require uploaders to substantiate the claim through weight-level analysis.The ATOM Report, published by Nathan Lambert and Florian Brand at Interconnects AI in April 2026, tracked roughly 1,500 mainline open models. ATOM identifies derivatives through the Hugging Face base_model tag, a field the uploader populates, filtering to models whose base model appears in the tracked list and that have more than five lifetime downloads and excluding GGUF and MLX re-uploads. By that measure, Alibaba’s Qwen family is the declared parent of 69% of new open-model derivatives as of February 2026, up from 1% in January 2024. Chinese labs overall account for 70%. Europe sits at 4%. Cumulative tracked downloads across the three regions reached 2.
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Like other recent DJI products, the Pocket 4P won’t launch in the US. DJI's Osmo Pocket 4P is a pretty simple proposition: an Osmo Pocket 4 with a second camera lens slapped inside. But is that extra lens worth the added size, weight, and cost relative to the regular Pocket 4? And how does it compare to the only rival on the market, Insta360's dual-lens Luna Ultra? It depends on what you're filming. But I think most prospective buyers would get plenty of use out of the 4P's 3x telephoto lens, and its quality is certainly impressive. Meanwhile, DJI has managed to undercut Insta360 on price while at least matching it on quality. For most, this will be the better buy, though the Luna Ultra has one major advanta … Read the full story at The Verge.
How statistical physics explains the transition from deterministic predictions to generative AI. The post How to Decode the Temperature Parameter in LLMs appeared first on Towards Data Science.
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