arXiv:2610. 31663v1 Announce Type: cross Abstract: Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing.
arXiv:2610. 11475v1 Announce Type: new Abstract: Population gradient flow is a common tool for reasoning about how neural networks adapt, including after pretraining.
arXiv:2610.02253v1 Announce Type: new Abstract: The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realizatio...
Population gradient flow is a common tool for reasoning about how neural networks adapt, including after pretraining. We show that it can mispredict finite-batch stochastic gradient descent (SGD) qualitatively, and we trace the discrepancy to a specific mechanism.
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:2610. 25116v2 Announce Type: replace Abstract: We study positive, bias-free, one-hidden-layer ReLU networks under standard Gaussian inputs.
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:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.
The paper demonstrates that neural networks can maintain perfect training accuracy while their training cross‑entropy remains nearly flat at a positive level, a phenomenon observed on modular addition tasks. Using ReLU networks with supported‑Polar hidden updates, normalized output‑layer updates, and weight decay, the authors show that hidden features evolve and held‑out accuracy can rise from zero to above 90% even as cross‑entropy stays flat. Theoretical results for one‑hidden‑layer networks and empirical evidence from deeper networks and transformers confirm that correct classification need not coincide with minimal cross‑entropy, challenging conventional assumptions about loss plateaus.
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:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2609.09130v1 Announce Type: new Abstract: An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input...
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.