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Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks

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

Record details

Published: 28 July 2026
Source: arXiv
Category: Research
Topics: Bias & fairness
Retrieved: 29 July 2026

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How to cite this record

ethics.ai (28 July 2026), “Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks,” evidence record 14144, https://ethics.ai/record/14144 (originally published by arXiv).

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