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
arXiv:2609.23774v1 Announce Type: new
Abstract: Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings....
By Sagad Hamid, Tanya Braun
arXiv:2610.27010v1 Announce Type: cross
Abstract: We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix,...
By Chuansen Peng, Xiaojing Shen
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
By Charles Dufour, Ulysse Naepels, Leonardo V. Santoro
The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
By Manuel Fernandez V, Yizhe Zhu
arXiv:2609. 11606v1 Announce Type: cross Abstract: Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families.
By Haoming Wang, Ming Yuan
arXiv:2510. 25591v2 Announce Type: replace-cross Abstract: We study the Sobolev IPM problem for probability measures supported on a graph metric space, where critic function is constrained to lie within the unit ball defined by Sobolev norm.
By Tam Le, Truyen Nguyen, Hideitsu Hino, Kenji Fukumizu
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
By Violet Zheng, Jean Honorio
arXiv:2610. 32147v1 Announce Type: cross Abstract: We propose a neural exploratory framework for variational problems over graphons, i.
By Taeyoung Kim, Jineon Baek, Joonkyung Lee, Hongseok Yang
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
By Rajath Rao K. N., Jens Schl\"oter, Sami Davies, Amira Ouchene, Yasamin Nazari
arXiv:2609.20520v2 Announce Type: replace-cross
Abstract: We prove sharp spectral-norm bounds and construct a mean-fitting regularization procedure for sparse random tensors of fixed order $k$. For a...
By Zhixin Zhou, Yizhe Zhu