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1-Lipschitz Neural Networks on Hadamard Manifolds

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Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean spaces.

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arXiv Machine Learning
Jul 22

1-Lipschitz Neural Networks on Hadamard Manifolds

arXiv:2607. 19335v1 Announce Type: cross Abstract: Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability.

By Davide Murari, Marta Ghirardelli, Ben Adcock, Elena Celledoni, Brynjulf Owren, Carola-Bibiane Sch\"onlieb
arXiv AI
Jul 24

Riemannian Deep Learning: Modules, Networks, and Geometries

arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.

By Chen Ziheng
arXiv AI
Jul 22

Riemannian Deep Learning:Modules, Networks, and Geometries

arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.

By Chen Ziheng
arXiv Machine Learning
Jun 9

Generalization in Nonlinear Least Squares via Learned Feature Geometry

arXiv:2606. 08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term.

By Ayub Kharel, Ilja Kuzborski, Patrick Rebeschini, Yasin Abbasi-Yadkori
arXiv Machine Learning
Jun 25

Towards Robust EEG Decoding Based on Riemannian Self-Attention

arXiv:2606. 25456v1 Announce Type: new Abstract: Brain-Computer Interface (BCI) based on electroencephalography (EEG) enables direct interaction between the brain and external environments and has significant applications in assistive technologies, medical rehabilitation, and entertainment.

By Shaocheng Jin, Tao Zhou, Rui Wang, Ziheng Chen, Xiaoqing Luo, Xiaojun Wu, Josef Kittler