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
6d ago
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 AI
22h ago
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.
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 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.
arXiv Machine Learning
Aug 4
Smooth Reparameterizations of Functions on Simplicial Product Spaces: Applications to Probabilistic Tensor Decomposition and Functional Data Registration
arXiv:2608. 02576v1 Announce Type: new Abstract: We consider optimization problems defined on product spaces of simplices.
arXiv Machine Learning
Jun 11
Recursive Binding on a Budget: Subspace Carving in Order-p Tensor Memories
arXiv:2606. 11391v1 Announce Type: new Abstract: Tensor Product Representations provide the structural fidelity required for symbolic reasoning in models but suffer from exponential dimensionality growth when encoding deep recursive structures.
arXiv Machine Learning
Jun 2
Riemannian Optimization for Hadamard Products of Low-Rank Matrices
arXiv:2606. 01216v1 Announce Type: new Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors.