{
  "id": 14144,
  "url": "https://arxiv.org/abs/2607.25624v1",
  "title": "Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks",
  "summary": "Positive quadratic networks admit the low-rank representation f_U(x)=x^top UU^top x, where Uinmathbb{R}^{dtimes r} is identifiable only up to right orthogonal multiplication, representing a rank-r PSD matrix Q=UU^top. We study how this quotient structure governs training dynamics, curvature, recovery, and interpolation bias. On the full-column-rank stratum, we identify mathbb{R}^{dtimes r}_*/O(r) with the rank-r PSD manifold. For smooth objectives L(U)=ell(UU^top), the Euclidean factor gradient",
  "authors": "Pengcheng Cheng",
  "category": "research",
  "topics": "bias-fairness",
  "orgs": null,
  "regions": null,
  "published_at": "2026-07-28T12:04:46.000Z",
  "fetched_at": "2026-07-29T05:10:12.205Z",
  "source_slug": "arxiv-ethics",
  "source_name": "arXiv",
  "source_homepage": "https://arxiv.org",
  "ethics_ai_record_url": "https://ethics.ai/record/14144",
  "original_url": "https://arxiv.org/abs/2607.25624v1",
  "evidence_status": "source-only",
  "attribution": "via ethics.ai"
}