EinSort: Sorting is All We Need for Tensorizing LLM

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.

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 $ρ_{\rm gap}$, 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}.

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression strategy for large-scale neural networks. However, despite encouraging empirical results, tensorized neural networks (TNNs) remain underutilized in mainstream deep learning. In this position paper, we offer a perspective on both the potential and current limitations of TNNs. We argue that TNNs represent a powerful yet underexplored framework for deep learning--one that deserves greater attention from both engineering and theoretical communities. Beyond compression, we highlight the value of TNNs as a flexible class of architectures with distinctive scaling properties and increased interpretability. A central feature of TNNs is the presence of bond indices, which introduce new latent spaces not found in conventional networks. These internal representations may provide deeper insight into the evolution of features across layers, potentially advancing the goals of mechanistic interpretability. We conclude by outlining several key research directions aimed at overcoming the practical barriers to scaling and adopting TNNs in modern deep learning workflows.