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The Heilbronn problem asks how to place n points in a unit‑area shape so the smallest triangle formed by any three points is as large as possible. This site logs the best known minimal‑triangle areas for squares, triangles and convex regions, with recent record‑breaking configurations and exact coordinates.
The paper presents PMOPD, a projection-based method that tracks low-dimensional subspaces of task-specific parameter updates during multi-teacher on-policy distillation and removes interfering components. Experiments on Qwen2.5-7B and Llama-3.1-8B show consistent 2-point gains across code, reasoning, and math tasks.
GEAR is a geometry‑enabled attention routing framework for long‑horizon camera‑controlled video generation. It treats per‑frame geometry as token‑level addresses, uses Geometric Correspondence Attention and an Invisible Octree to retrieve visual memory, achieving state‑of‑the‑art quality and consistent control over minute‑long videos.
