arXiv:2608.23877v1 Announce Type: new
Abstract: We prove a depth hierarchy for ReLU neural networks in which every additional ReLU layer can save exponentially many neurons. For every $\ell\geq 3$, a...
By Itay Safran
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.
By Baicheng Li, Zuowei Shen, Haizhao Yang, Shijun Zhang
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 $\SS^d$.
By Tong Mao, Jinchao Xu
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...
By Xiaoyu Li, Zhizhou Sha, Jiaojiao Jiang, Junbin Gao, Andi Han
arXiv:2607. 16676v1 Announce Type: cross Abstract: How deep does a graph neural network need to be on a sparse graph?
By Aseem Raj Baranwal
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.