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.
By Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko, Sergei Kudriashov, Maxim Rakhuba
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.
The paper introduces chained linear minimization oracles (chained LMOs) as a unified framework for optimizers that compose multiple matrix normalizations, addressing fragmentation in the field. It shows that while many such chains can diverge on smooth convex objectives, chaining can still improve performance under anisotropic embeddings, as demonstrated by the new TensorChain optimizer. TensorChain, which stacks compatible weight matrices across layers and normalizes a 3‑D tensor, achieves a 9.6% token efficiency gain over Muon in Qwen3 0.6B and 1.7B pretraining at matched validation loss.
By Sungyoon Kim, Kaan Ozkara, Youngsuk Park
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.
By Matvei Tarasov, Salman Ahmadi-Asl, Andre L. F. de Almeida, Andrzej Cichocki
arXiv:2602. 17510v2 Announce Type: replace-cross Abstract: We introduce LoRA-CRAFT (\textbf{C}ross-layer \textbf{R}ank \textbf{A}daptation via \textbf{F}rozen \textbf{T}ucker), abbreviated CRAFT throughout, an extremely parameter-efficient fine-tuning (PEFT) method that applies Tucker tensor decomposition to pre-trained attention weight matrices stacked across transformer layers and trains only small square adaptation matrices on the resulting frozen Tucker factors.
By Kasun Dewage, Marianna Pensky, Suranadi De Silva, Shankadeep Mondal
Muon has motivated a growing family of optimizers that compose multiple matrix normalizations, but these methods remain fragmented and lack a unified perspective. We introduce chained linear minimizat...