arXiv Computer Vision
Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery
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Semi-Tensor Product-Based Multi-Term Randomized T-SVD and Its Visual Applications
The paper introduces a new semi‑tensor product for third‑order tensors that relaxes the dimensional constraints of the standard t‑product while preserving the closed‑form nature of T‑SVD. It builds a multi‑term semi‑tensor product singular value decomposition (MSTP‑SVD) that improves low‑rank approximation accuracy, and further accelerates it with randomized projection and power iteration to create the MRSTP‑SVD algorithm. Experiments on image and video compression and completion show that this method balances reconstruction accuracy and computational efficiency.
arXiv Machine Learning
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Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
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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 AI
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Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability
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.
arXiv Machine Learning
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Bayesian Tensor Decomposition with Diffusion Model Prior
arXiv:2606. 03212v1 Announce Type: new Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise.
Hugging Face Trending Papers
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Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability
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...