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.
arXiv:2609.00870v1 Announce Type: cross Abstract: Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optim...
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.
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.
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...
arXiv:2609. 17298v1 Announce Type: cross Abstract: This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting.
arXiv:2607. 06841v1 Announce Type: cross Abstract: Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process.
arXiv:2608. 17135v1 Announce Type: cross Abstract: Tensor networks are powerful formats for compressing large-scale data.
The paper demonstrates that tree tensor networks (TTNs) can encode arbitrary read‑once Boolean formulas, yielding polynomial‑size targets that are hard for gradient descent to learn in polynomial time, yet their loss landscapes are conditionally benign: every minimum‑norm local minimum is global. This shows that bad local minima are not the source of learning difficulty in TTNs; instead, high‑order degenerate saddle points caused by rank‑deficiency can impede learning. A case study on the parity function illustrates how TTNs can link landscape geometry to computational hardness.
arXiv:2606. 02328v1 Announce Type: new Abstract: We explore Riemannian optimization techniques for rank-factored matrix parameters, targeting contemporary deep learning applications.
arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
arXiv:2608. 07043v1 Announce Type: cross Abstract: Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification.
arXiv:2606. 08871v1 Announce Type: cross Abstract: The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces.