The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
By Matthias C. Caro, Natalie McHugh, Sergii Strelchuk
We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically.
arXiv:2608.29279v1 Announce Type: new
Abstract: Deep learning is often criticized for its theoretical research lagging behind practice. To make deep learning easier to understand, the entropy space t...
By Li Li, Tong Zhang, Wentao Yu, Zuobin Wang
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
By Tong Mao, Jinchao Xu
arXiv:2607. 26699v1 Announce Type: new Abstract: We investigate message-passing graph neural networks with random node features.
By Lukas Gonon, Thilo Meyer-Brandis, Niklas Weber
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
By Martin Carrasco, Caio F. Deberaldini Netto, Vahan A. Martirosyan, Ehimare Okoyomon, Caterina Graziani
arXiv:2608. 17135v1 Announce Type: cross Abstract: Tensor networks are powerful formats for compressing large-scale data.
By Xiao Wang, Tomohiro Hashizume, Pia Siegl, Dieter Jaksch
arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.
By Akram Aldroubi
arXiv:2609.05572v1 Announce Type: new
Abstract: We prove that every strictly positive probability distribution on \(\{-1,1\}^n\) is represented exactly by a sigmoid belief network with finite paramet...
By Gleb Smirnov
arXiv:2608. 10351v1 Announce Type: new Abstract: In this work we present a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN).
By Karl Pierce, Yuehaw Khoo, Haizhao Yang
The paper introduces a general theoretical framework for fibrations on graphs labeled by a commutative monoid, extending the classic theory of graph fibrations to weighted and algebraically labeled graphs. It also accommodates approximate fibrations and demonstrates how this framework can be used to compress arbitrary neural networks, including CNNs, providing a solid theoretical basis for recent findings on fibration symmetries in geometric deep learning.
By Paolo Boldi
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.
By Andrea Agazzi, Eloy Mosig Garc\'ia, Dario Trevisan