{
  "id": 14851240,
  "title": "When Is Muon Optimal? Radial Fragility and Minimax Geometry",
  "url": "https://urgent.news/2026/10/15/when-is-muon-optimal-radial-fragility-and-minimax-geometry",
  "topic": "ai",
  "section": "AI",
  "published": "2026-10-15T09:13:19.000Z",
  "source": {
    "name": "arXiv cs.AI",
    "slug": "arxiv-cs-ai",
    "url": "https://arxiv.org/abs/2610.21549v1"
  },
  "original_language": "en",
  "account": null,
  "summary": "Muon replaces a matrix gradient by an approximate polar factor and has shown strong empirical performance in neural-network training. The Isotropic Curvature Model (ICM) provides a curvature-based explanation for this update by asking when gradient orthogonalization minimizes a one-step local-loss surrogate. We investigate the stability of this explanation when the fixed input radius of the ICM…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}