A general tensor-structured compression scheme for efficient large language models
Authors: Ying Lu, Peng-Fei Zhou, Qi-Xuan Fang, Pan Zhang, Shi-Ju Ran, Gang Su
Organizations: School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China. · Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China. · Center for Quantum Physics and Intelligent Sciences, Department of Physics, Capital Normal University, Beijing, 100048, China. · Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China.
Large language models (LLMs) are dominated by dense linear transformations, whose storage, memory and computational overheads hinder efficient adaptation and deployment while masking the functional impacts of structural simplification. Here we present Tensor Mixture (MixT), a general tensor-structured compression scheme that replaces targeted dense linear layers with natively executable mixtures of tensor operators. Operating directly on generic linear projections instead of model-specific components, MixT is potentially applicable across Transformer-based LLMs and other dense neural mappings. We evaluate MixT on Qwen3-8B and LLaMA2-7B under a unified recovery protocol, identifying a broad compressible regime in which MMLU accuracy is largely preserved before an abrupt transition at model-specific boundaries. This transition coincides with coordinated shifts in output entropy, prediction entropy and inter-layer geometry. At the LLaMA2-7B transition boundary, MixT reduces full-model parameters by 47.5%, inference FLOPs by 37.1%, training FLOPs by 52.1% and peak inference memory by 60.4%, demonstrating its practical potential for lower-cost LLM compression.
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 underexploited by the conventional matrix-centric view. Tensor decompositions and tensor networks provide a principled algebraic language for this structure, yet the literature often treats them as isolated compression mechanisms. This survey organizes tensor methods for LLMs through two complementary views: a seven-stage lifecycle taxonomy covering tokenization, embeddings, pre-training, adaptation, compression, inference, and interpretability, and a component view covering embeddings, attention, and feed-forward networks. We provide unified notation and theoretical foundations, analyze tensorization strategies for individual Transformer components, and compare methods at each lifecycle stage while making differences in evaluation protocols and model scales explicit. We further connect tensor methods to neighboring efficiency techniques and probabilistic tensor networks. Finally, we synthesize open challenges and introduce ρgap, a metric for the compression-realization gap between theoretical memory reduction and measured system-level speedup. By treating tensorization as a common structural principle, the survey provides a structured entry point to tensorized language models and clarifies when parameter savings can plausibly translate into memory efficiency, computational efficiency, or interpretability. The GitHub page dedicated to this paper is accessible at \href{https://github.com/ma-tt-a/awesome-tensor-methods-for-llms}{this https URL}.
Matvei Tarasov, Salman Ahmadi-Asl, Andre L. F. de Almeida +1
Post-training compression is essential for deploying large language models (LLMs) under tight resource constraints. Tensor decompositions have emerged as a promising direction, offering compact parameterizations well suited to Transformer weight structures. However, existing studies evaluate these methods in narrow settings, leaving unclear whether tensorization is effective at large-scale deployment. We systematically evaluate tensor compression across dense and MoE architectures, establishing performance trade-offs grounded in both empirical analysis and theoretical analysis. We identify a fundamental mismatch between the shared subspaces assumed by tensor decompositions and the heterogeneous representations learned by modern LLMs, thereby delineating their practical limits and clarifying their viable role in large-scale deployment. The code is available at https://github.com/brain-lab-research/TT-LLM.
Artur Zagitov, Alexander Miasnikov, Maxim Krutikov +5
Large Language Models (LLMs) incur significant computational and memory costs when processing long prompts, as full self-attention scales quadratically with input length. Token compression aims to address this challenge by reducing the number of tokens representing inputs. However, existing prompt-compression approaches primarily operate in token space and overlook inefficiencies in the latent embedding space. In this paper, we propose K-Token Merging, a latent-space compression framework that merges each contiguous block of K token embeddings into a single embedding via a lightweight encoder. The compressed sequence is processed by a LoRA-adapted LLM, while generation remains in the original vocabulary. Experiments on structural reasoning (Textualized Tree), sentiment classification (Amazon Reviews), and code editing (CommitPackFT) show that K-Token Merging lies on the Pareto frontier of performance vs. compression, achieving up to 75% input length reduction with minimal performance degradation. Code is available at https://github.com/shsjxzh/K-Token-Merging.