arXiv:2512.04696v3 Announce Type: replace Abstract: We develop a flexible feature selection framework based on deep neural networks that approximately controls the false discovery rate (FDR), a measu...
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures.
arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
arXiv:2206. 04359v3 Announce Type: replace Abstract: One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data.
arXiv:2608. 15982v1 Announce Type: new Abstract: We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces.
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
arXiv:2604. 15613v4 Announce Type: replace-cross Abstract: We present Green-ELM, a non-iterative neural architecture that replaces gradient-based optimization of the output layer with a closed-form analytic solution over a fixed, high-dimensional random feature representation.
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
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:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.