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:2606. 05042v1 Announce Type: new Abstract: Marginal inference in discrete graphical models forces a choice between exactness and scalability: exact algorithms are intractable for high-treewidth graphs, while iterative approximations (Belief Propagation, variational methods) sacrifice convergence guarantees on frustrated topologies.
By Zehua Cheng, Wei Dai, Jiahao Sun
This survey reviews tensor methods applied to large language models, framing them through a seven‑stage lifecycle (tokenization, embeddings, pre‑training, adaptation, compression, inference, interpretability) and a component view (embeddings, attention, feed‑forward networks). It offers unified notation, theoretical foundations, and comparative analyses of tensorization strategies for Transformer components, while highlighting evaluation protocol differences and model scale effects. The paper also introduces a new metric, ρ_gap, to quantify the gap between theoretical memory savings and actual system‑level speedup, and connects tensor techniques to related efficiency and probabilistic methods.
By Matvei Tarasov, Salman Ahmadi-Asl, Andre L. F. de Almeida, Andrzej Cichocki
arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
By Qi Shao, Hao Guo, Jiawen Chen, Duxin Chen, Wenwu Yu
Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is unde...
arXiv:2606. 19366v1 Announce Type: cross Abstract: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain.
By Haizi Yu, Lav R. Varshney
arXiv:2404.17763v3 Announce Type: replace-cross
Abstract: Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn...
By Yujie Chen, Anindya Bhadra, Antik Chakraborty
arXiv:2609.15992v1 Announce Type: new
Abstract: Recent advances in large language models (LLMs) have rendered them necessary for Natural Language Processing (NLP) tasks, and their high inference cost...
By Foivos Charalampakos, Md Ibrahim Ibne Alam, Iordanis Koutsopoulos, Koushik Kar
The paper introduces JSP-GFN, a Generative Flow Network that jointly infers the structure and parameters of a Bayesian Network. It sequentially generates a directed acyclic graph edge by edge and then samples the corresponding conditional probability parameters once the full structure is known. Experiments on simulated and real data show that JSP‑GFN accurately approximates the joint posterior and outperforms existing methods.
By Tristan Deleu, Mizu Nishikawa-Toomey, Jithendaraa Subramanian, Esmeralda S. Whitammer, Laurent Charlin, Yoshua Bengio
arXiv:2607. 04650v1 Announce Type: cross Abstract: Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size.
By Pei Heng, Xinyi Hu, Yi Sun
arXiv:2608.24602v1 Announce Type: cross
Abstract: Probabilistic models of Directed Acyclic Graphs (DAGs) with latent variables impose equality constraints on the observed data distribution beyond ord...
By Razieh Nabi, Anna Guo, Lin Liu
arXiv:2609.24942v1 Announce Type: new
Abstract: A model generalizes outside its training distribution only when it computes a representation structurally equivalent to the generating mechanism, not a...
By Filipe Marinho Rocha, In\^es Dutra, V\'itor Santos Costa, Lu\'is Paulo Reis