arXiv:2607. 06290v1 Announce Type: new Abstract: We study the infinite-width Gaussian-process limit of random neural networks through the lens of tensor programs, and we provide a quantitative convergence theory in Wasserstein distance.
arXiv:2606. 00130v1 Announce Type: cross Abstract: We study Automatically Differentiable Nonlinear Tensor Networks (ADNTNs), a family of structured weight generators whose compact core tensors are trained end-to-end by reverse-mode automatic differentiation (AD).
arXiv:2608. 17135v1 Announce Type: cross Abstract: Tensor networks are powerful formats for compressing large-scale data.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2210. 16286v2 Announce Type: replace Abstract: To understand the training dynamics of neural networks, prior studies have considered the mean-field limit of two-layer neural networks as the width tends to infinity, establishing theoretical guarantees for its convergence under gradient flow training as well as approximation and generalization capabilities.
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
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:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
arXiv:2508. 11522v4 Announce Type: replace Abstract: Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks.
arXiv:2608. 08350v1 Announce Type: new Abstract: The initialisation of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive.
arXiv:2410. 09973v2 Announce Type: replace-cross Abstract: We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity.
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv:2607. 23397v1 Announce Type: new Abstract: Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood.