arXiv Machine Learning
Jul 31
It's All Just Vectorization: einx, a Universal Notation for Tensor Operations
arXiv:2607. 27987v1 Announce Type: new Abstract: Tensor operations represent a cornerstone of modern scientific computing.
Broadcast Product: Redefining Shape-aligned Element-wise Multiplication and Beyond
arXiv:2409. 17502v2 Announce Type: replace Abstract: Broadcast operations are widely used in scientific computing libraries, yet their mathematical formulation is often implicit and inconsistently represented in machine learning literature.
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arXiv Machine Learning
Jul 20
(MPO)$^2$: Multivariate Polynomial Optimization based on Matrix Product Operators
arXiv:2607. 15916v1 Announce Type: new Abstract: Central to machine learning and signal processing is the ability to perform universal function approximation and learn complex input-output relationships from limited numbers of observations.
arXiv Machine Learning
Jul 1
Online TT-ALS for Streaming Tensor Decomposition with Incremental Orthogonalization
arXiv:2606. 31061v1 Announce Type: cross Abstract: Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data.
arXiv AI
Jul 10
Multi-agent Autoformalization of Tensor Network Theory
arXiv:2607. 07857v1 Announce Type: cross Abstract: We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration.
arXiv Machine Learning
Aug 13
Weaves, Wires, and Morphisms: Formalizing and Implementing the Algebra of Deep Learning
arXiv:2604. 07242v3 Announce Type: replace Abstract: Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures.
arXiv Machine Learning
Jun 9
Integral Formulas for Vector Signal Tensor Products
arXiv:2603. 08630v2 Announce Type: replace Abstract: We derive integral formulas that simplify the Vector Signal Tensor Product recently introduced by Xie et al.
arXiv Machine Learning
Aug 24
Advanced Linear Algebra with Applications - Part I (Numerical linear algebra for PDEs, machine learning, and data assimilation)
arXiv:2608.21234v1 Announce Type: cross Abstract: These lecture notes form the first part of a master's-level course on advanced numerical linear algebra. Their aim is not only to present the classic...
arXiv AI
Aug 19
Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions
arXiv:2608. 17135v1 Announce Type: cross Abstract: Tensor networks are powerful formats for compressing large-scale data.
arXiv Machine Learning
1d ago
A Typed Tensor Language for Shared-State Federated Computation
The paper introduces a typed tensor language designed for shared-state federated computations, distinguishing between client-partitioned data and globally available values through two tensor sorts. It demonstrates that typed one-round programs factor through shared tensors whose shapes are program-dependent but client-independent, and extends this construction to multi-round programs with persistent shared state. The language supports server-side first-order updates, curvature-block updates, and covers federated analytics and FedSGD, while excluding more complex schemes like multi-local-step FedAvg and persistent private client state.
Hugging Face Trending Papers
Jun 24
Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics.
arXiv Computer Vision
Sep 15
Tensor Decomposition Structure Search Framework from an Interaction Perspective
arXiv:2603.02720v2 Announce Type: replace Abstract: Recently, tensor decompositions have attracted increasing attention. Fundamentally, different interactions among factors induce distinct tensor dec...
arXiv Machine Learning
Jun 25
Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
arXiv:2606. 25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models.