arXiv:2505. 18113v2 Announce Type: replace Abstract: Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem.
arXiv:2608. 11479v1 Announce Type: new Abstract: We establish convergence guarantees of gradient descent for general feedforward neural networks of arbitrary width or depth, with no special requirements on the initialization or dataset.
arXiv:2609. 07997v1 Announce Type: new Abstract: We characterize the sharp structure-agnostic minimax risk for coefficient estimation in the partial linear model when the outcome and treatment nuisances are learned by two distinct black-box learners, which resolves the open problem in double machine learning posed by Gu (2025).
The paper introduces a method for adversarial training that avoids computing input gradients by using a low‑rank Householder expansion (LRHE) to directly generate small‑norm adversarial examples from a network’s parameters. This approach requires only forward passes and standard back‑propagation, eliminating the inner maximization loop and reducing computational cost to roughly 2.8 PGD steps per epoch. The resulting models achieve comparable robustness to multi‑step PGD training for small relative ε budgets, demonstrating the feasibility of gradient‑free adversarial training.
arXiv:2606. 06934v1 Announce Type: new Abstract: We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding.
arXiv:2609.07755v1 Announce Type: new Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
This paper investigates the ρ^p-Lipschitz constants of deep ReLU neural networks with random weights drawn from a He‑style initialization. For zero‑bias networks, it provides high‑probability upper and lower bounds that differ by at most a logarithmic factor in depth, and shows a sharp contrast between the regimes p∈[1,2) and p∈[2,∞], with the former behaving like the Euclidean norm of a Gaussian vector and the latter like its dual norm. The analysis is extended to networks with non‑zero biases from symmetric distributions, yielding bounds that differ by a logarithmic factor in width and a linear factor in depth.
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
arXiv:2608.22636v1 Announce Type: cross Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
arXiv:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.