The paper presents a formal analysis of the quotient geometry of tree tensor networks (TTNs) and introduces efficient first- and second-order optimization algorithms that leverage this geometry. It also develops a backpropagation method for training TTNs in a kernel learning context. Numerical experiments on a digit classification task demonstrate a tradeoff between two horizontal distributions: one provides clearer geometric insights, while the other yields more efficient algorithms.
By Marius Willner, Marco Trenti, Dirk Lebiedz
The paper introduces a quantum tensor network learning framework that employs matrix product states (MPS) as a machine‑learning architecture, adding a global normalization condition to interpret the MPS as a quantum state. It compares two optimization strategies—gradient descent and a DMRG‑adapted method—to identify locally optimal tensors and evaluates their effectiveness.
By Gustav J L J\"ager, Martin B Plenio, Hans-Martin Rieser
The paper introduces Tensor Network-based Quantum Data Encoding (TNQE), a framework that uses structured unitary tensor network representations to encode classical data into quantum states efficiently. TNQE decomposes each input into tensor cores and compiles them into encoding circuits via two core-to-circuit strategies, with learnable block unitaries ensuring trainability while maintaining unitarity. The method achieves significantly shallower circuits—down to 0.04× the depth of amplitude encoding—and scales to high‑resolution images, demonstrating practical feasibility on real quantum hardware.
By Guang Lin, Toshihisa Tanaka, Qibin Zhao
arXiv:2502. 09928v2 Announce Type: replace-cross Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks.
By Chang Nie
arXiv:2609. 17298v1 Announce Type: cross Abstract: This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting.
By Shiwen An, Konstantinos Slavakis
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
Diffusion Transformers (DiTs) have achieved state-of-the-art (SOTA) performance in visual generative modeling, yet their training remains computationally prohibitive. While the recently proposed Momentum Orthogonalization (Muon) optimizer offers a promising alternative to AdamW, its direct application to DiTs yields suboptimal late-stage convergence.
arXiv:2605.16610v2 Announce Type: replace
Abstract: High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physic...
By Beheshteh T. Rakhshan, Guillaume Rabusseau
The paper discusses tensorizing neural networks by reshaping dense weight matrices into higher-order tensors and approximating them with low-rank tensor network decompositions. This approach offers promising model compression and introduces bond indices that create new latent spaces, potentially enhancing interpretability. Despite encouraging empirical results, tensorized neural networks remain underused, and the authors call for more research to address practical scaling and adoption challenges.
By Safa Hamreras, Sukhbinder Singh, Rom\'an Or\'us
arXiv:2606. 08565v1 Announce Type: cross Abstract: Tensor networks provide efficient representations for compressing large neural networks.
By Toshiaki Koike-Akino, Jing Liu, Ye Wang
arXiv:2608.21700v1 Announce Type: cross
Abstract: Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein...
By Nathan X. Kodama, L. Andrew Wray, Sam Cochran, Chad Rigetti, Shravan Veerapaneni, Michael J. Keiser
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
By Yushun Zhang