arXiv Machine Learning
Jun 16
The Data Manifold under the Microscope
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
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.
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arXiv Machine Learning
Jul 30
Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
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.
arXiv Machine Learning
Jul 3
Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
arXiv Machine Learning
Jun 5
Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations
arXiv:2606. 05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators.
arXiv Machine Learning
Jun 18
Fisher Width: A Geometric Measure of Complexity on Statistical Manifolds
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
arXiv Machine Learning
Jul 7
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
arXiv:2607. 03613v1 Announce Type: new Abstract: We study the implicit bias of noisy stochastic gradient descent in training wide two-layer ReLU networks for multivariate regression.
arXiv Machine Learning
6d ago
A Variational Analysis of Kernel Learning with Learnable Linear Transformations
arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
Hugging Face Trending Papers
Jul 21
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.
arXiv Machine Learning
Jun 18
On the Stability of the Jacobian Matrix in Deep Neural Networks
arXiv:2506. 08764v3 Announce Type: replace Abstract: Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.
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 $\eta$.