Hugging Face Trending Papers

1-Lipschitz Neural Networks on Hadamard Manifolds

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.

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
arXiv Machine Learning
1d ago

Iso-Riemannian Optimization on Learned Data Manifolds

arXiv:2510. 21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited.

By Willem Diepeveen, Melanie Weber
arXiv Machine Learning
Jun 30

Non-Euclidean Gradient Descent Operates at the Edge of Stability

arXiv:2603. 05002v3 Announce Type: replace Abstract: The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian approaches and then hovers near the stability threshold $2/\eta$ during gradient descent (GD) with step size $\eta$.

By Rustem Islamov, Michael Crawshaw, Jeremy Cohen, Robert Gower
arXiv Machine Learning
Aug 11

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.

By Bruno Aristimunha, Ce Ju, Antoine Collas, Florent Bouchard, Ammar Mian, Bertrand Thirion, Sylvain Chevallier, Reinmar Kobler
arXiv Machine Learning
Jun 19

Fisher-Geometric Sharpness and the Implicit Bias of SGD toward Flat Minima

arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.

By Md Sakir Ahmed, Kumaresh Sarmah, Hemen Dutta
arXiv Machine Learning
Jun 2

Riemannian Optimization for Hadamard Products of Low-Rank Matrices

arXiv:2606. 01216v1 Announce Type: new Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors.

By Pratik Jawanpuria, Ankish Chandresh, Bamdev Mishra