arXiv:2609. 25710v1 Announce Type: cross Abstract: The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data.
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.
arXiv:2607. 06781v1 Announce Type: new Abstract: In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations.
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:2607. 07778v1 Announce Type: new Abstract: Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that fits $n$ noisy labels must have Lipschitz constant at least of order $\sqrt{n/m}$, with no restriction on the size of the weights.
The paper establishes high‑probability bounds on mixed input derivatives for wide random neural networks whose activation derivatives grow factorially, with a focus on anh networks initialized with Xavier weights. For scalar‑output anh networks with Gaussian weights, the authors prove that when the hidden width exceeds a depth‑dependent threshold, the derivative of any order satisfies a bound that is independent of depth for first‑order derivatives and grows at most polynomially with depth for higher‑order mixed derivatives. These results yield high‑probability estimates for the Euclidean Lipschitz constant and weighted Sobolev norms, linking the regularity of network realizations to quasi‑Monte Carlo integration and its potential impact on QMC‑based training.
arXiv:2602. 17596v2 Announce Type: replace Abstract: We study pathwise connectivity of sublevel sets for one-hidden-layer ReLU networks with constrained first-layer weights and an $\ell_1$ penalty on the output layer.
arXiv:2510. 04060v3 Announce Type: replace-cross Abstract: We establish two related but logically distinct results for shallow ReLU$^k$ neural networks on the unit sphere $\SS^d$.
arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
arXiv:2607. 16676v1 Announce Type: cross Abstract: How deep does a graph neural network need to be on a sparse graph?
arXiv:2608.31157v1 Announce Type: new Abstract: Many parameter-efficient methods generate the parameters of a large neural network from a low-dimensional latent representation. Given an architecture...
An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al.
arXiv:2608. 17434v1 Announce Type: new Abstract: We study Gaussian regression over the explicit vector-valued Parhi--Nowak deep-RBV^2 architecture with depth L, width w, layer-sum variation budget A, and output bound B.