{
  "id": 18389,
  "url": "https://arxiv.org/abs/2608.05136",
  "title": "The Loss Does Not See the Basis, but Adam Does",
  "summary": "Gradient descent on a factored model W = UV^top is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not. We trace the difference to the gauge symmetry of the loss, its invariance under (U, V) mapsto (UQ, VQ). Gradient flow's low-rank mechanism is available to an optimizer only if that optimizer is gauge-equivariant, a condition necessary for the transfer but not sufficient for low-rank recovery. Gradient descent, momentum, \"shared-scalar\" A",
  "authors": "Devender Singh",
  "category": "research",
  "topics": "bias-fairness",
  "orgs": null,
  "regions": null,
  "published_at": "2026-08-04T20:00:00.000Z",
  "fetched_at": "2026-08-12T05:10:43.828Z",
  "source_slug": "hf-daily",
  "source_name": "HuggingFace Daily Papers",
  "source_homepage": "https://huggingface.co/papers",
  "ethics_ai_record_url": "https://ethics.ai/record/18389",
  "original_url": "https://arxiv.org/abs/2608.05136",
  "evidence_status": "source-only",
  "attribution": "via ethics.ai"
}