Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks
Authors: Safa Hamreras, Sukhbinder Singh, Román Orús
Organizations: Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain · Multiverse Computing, Spadina Ave., Toronto, ON M5T 2C2, Canada · Multiverse Computing, Paseo de Miramón 170, E-20014 San Sebastián, Spain
Abstract
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.
Tensor networks provide efficient representations for compressing large neural networks. By carefully designing shapes and topologies, they can significantly reduce memory and computational costs. However, identifying implicit low-rank structures in large foundation models remains challenging due to their enormous scale and un-structured weight distributions. We propose an adaptive tensorization method that discovers inherent low-rank structure in a target tensor by index ordering. Experiments on weight and KV-cache compression demonstrate improved reconstruction quality compared to baselines.
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the network into slices consisting of either individual layers or blocks (e.g., convolutional layers or MLPs), or small groups of consecutive layers, and tensorizes each slice independently to reproduce the intermediate representations of the original pretrained model. This modular strategy improves accuracy recovery, reduces data requirements, and enables efficient parallel optimization. Experiments on ResNet-34 show significant gains over conventional global tensorization, achieving near-lossless compression at moderate compression rates with faster optimization. Results on GPT-2 XL further demonstrate the scalability of the method and its applicability to large-scale models, particularly in distributed settings.
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