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  "builder_plan": {
    "scenario": "You already need task-specific training and want to reduce its memory or compute cost.",
    "change": "Change only the training technique on a small controlled run after checking prerequisites.",
    "baseline": "Your current training recipe with the same model, data split, and evaluation.",
    "steps": [
      "Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.",
      "Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.",
      "Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.",
      "Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test."
    ],
    "measure": "Held-out quality, peak memory, training time, and full compute cost to the target quality.",
    "decision": "Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation."
  },
  "builder_review": null,
  "arxiv_id": "2610.30280",
  "title": "A Quadratic Lens on Muon's Polar Update: Benefits, Pitfalls, and the Role of Newton-Schulz",
  "summary": "The paper does not propose a replacement method; it analyzes the PolarGD orthogonalization inside Muon, showing it acts as iterate-dependent preconditioning whose speed depends on the conditioning of the iterate rather than the Hessian. The practical cost implication is that the Newton-Schulz iterations in Muon are not merely an approximation to be maximized: fewer iterations treat tiny singular values like gradient descent and can converge faster than exact orthogonalization. The identified failure mode is a slow regime where the iterate has tiny singular values, making PolarGD much slower than gradient descent; in a transformer trained with Muon, about a quarter of attention-matrix singular values fall in this regime.",
  "rationale": "This is closed-form analysis on matrix quadratics plus one transformer observation, so it informs how to set Newton-Schulz iteration counts for teams already using Muon, but it provides no directly deployable technique or validated gain on constrained infrastructure.",
  "technique": "Analysis of Muon's orthogonalized (PolarGD) update",
  "family": "treino_eficiente",
  "recommendation": "observar",
  "published": "2026-10-21",
  "as_of": "2026-10-24",
  "editorial_status": "indexed",
  "source_url": "https://arxiv.org/abs/2610.30280",
  "independent_implementations": 0,
  "total_implementations": 1,
  "stars": 4,
  "citations": 0,
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