Author

Xin Yang

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#machine learning Preprint Oct 2026

The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective

We study the implicit bias of Riemannian gradient flow for hyperbolic multiclass classification with fixed class prototypes in hyperbolic space $\mathbb{H}^n$. Our framework accommodates general permutation invariant relative margin (PERM) losses, a class that includes cross entropy and other standard multiclass losses...

Xing-Run Li, Sho Kuno, Yusuke Mukuta et al. · 0 citations

#machine learning Preprint Sep 2026

$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition

The $\mathbb{SL}(n)$ space is introduced, a representation geometry defined by the simple $\det(A)=1$ constraint and a left invariant Schatten-$p$ Finsler structure that consistently outperforms a broad range of representation manifold baselines across graph benchmarks at different scales.

Xing-Run Li, Yusuke Mukuta, Xin Yang et al. · 0 citations