arXiv:2610.30729v2 Announce Type: replace-cross
Abstract: Recent work established that the infinite-width and infinite-depth limits of residual networks commute at initialization when residual branch...
By Ruijia Zhang, Soufiane Hayou
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
By Shijun Zhang, Zuowei Shen, Yuesheng Xu
The paper presents a nonasymptotic generalization theory for multilayer fully connected neural networks trained with path regularization, covering both underparameterized and overparameterized regimes without assuming bounded loss, sparsity, or width/depth limits. It explicitly models approximation error, resolves an open problem on approximation rates in generalized Barron spaces, and establishes matching upper and lower bounds that show the error curve is non‑monotone—descending, rising, then descending again—as width increases. The analysis reveals that the rise is due to shrinkage imposed by regularization rather than overfitting, and this effect cannot be eliminated by width‑independent regularization.
By Hao Yu
arXiv:2610.31783v1 Announce Type: new
Abstract: We study the early training dynamics of nonlinear residual networks with blocks of zero hidden layers as a model of more general residual networks. We...
By Vladimir Narovlansky, Boris Hanin
arXiv:2607. 04597v1 Announce Type: new Abstract: In this paper, we study the universal approximation property of residual neural networks, and obtain some new results.
By Qi Zhou, Xuan Zhou, Xiao-Song Yang
arXiv:2602. 07697v3 Announce Type: replace-cross Abstract: Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights.
By Francesco Innocenti, El Mehdi Achour, Rafal Bogacz