The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
By Hao Yu
arXiv:2507.19290v2 Announce Type: replace-cross
Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-...
By Noah Amsel, Pratyush Avi, Tyler Chen, Feyza Duman Keles, Chinmay Hegde, Cameron Musco, Christopher Musco, David Persson
arXiv:2407. 00966v3 Announce Type: replace Abstract: In traditional models of supervised learning, the goal of a learner-- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$-- is to output a hypothesis that is competitive (to within $\epsilon$) of the best fitting concept from some class.
By Gautam Chandrasekaran, Adam Klivans, Vasilis Kontonis, Raghu Meka, Konstantinos Stavropoulos
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
By Andrea Montanari, Kangjie Zhou
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.
By Yuanfan Li, Yunwen Lei, Zheng-Chu Guo, Yiming Ying
arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
By Saumya Goyal, Barnab\'as P\'oczos
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
By Haitong Liu, Deepak Narayanan Sridharan, David Steurer, Manuel Wiedmer
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.
By Filip Kova\v{c}evi\'c, Hong Chang Ji, Denny Wu, Mahdi Soltanolkotabi, Marco Mondelli
arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.
By Jiayu Zhang, Tianyi Lin
arXiv:2609.25576v1 Announce Type: cross
Abstract: We study the estimation of a $K$-dimensional simplex from $N$ i.i.d.\ points sampled uniformly from its interior; the observations are convex combina...
By Jun LI, Yanlong Guo, Zhaozhao Zeng
The paper demonstrates that tree tensor networks (TTNs) can encode arbitrary read‑once Boolean formulas, yielding polynomial‑size targets that are hard for gradient descent to learn in polynomial time, yet their loss landscapes are conditionally benign: every minimum‑norm local minimum is global. This shows that bad local minima are not the source of learning difficulty in TTNs; instead, high‑order degenerate saddle points caused by rank‑deficiency can impede learning. A case study on the parity function illustrates how TTNs can link landscape geometry to computational hardness.
By Zach Furman, Stephan W\"aldchen, Yangda Bei, Liam Hodgkinson
arXiv:2609.06430v1 Announce Type: new
Abstract: We study the identity straight-through estimator (STE) for training a two-layer binary-activation network with hinge loss from the perspective of Stati...
By Yiming Ying