Title: TD-MoE: Tensor Decomposition for MoE Models
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Mixture-of-Experts, Model Compression, Tucker Decomposition

Abstract: Mixture-of-Experts (MoE) architectures have demonstrated remarkable capabilities and scalability for large language models, but incur a prohibitive memory footprint due to duplicated expert parameters. Existing compression approaches, particularly those based on low-rank decomposition, typically operate at the granularity of individual experts. However, such per-expert methods overlook structural redundancies across experts, limiting their compression efficiency and effectiveness. In this work, we introduce TD-MoE (Cross-Expert Tensor Decomposition for MoE Compression), a data-aware framework that jointly holistically factorizes expert weights. Our contributions are threefold: (i) Cross-expert tensorization with joint 3D decomposition, which unifies all experts within a layer into a single tensor and captures shared structure beyond per-expert scope; (ii) A multi-linear whitening strategy, which decorrelates input and output features, yielding a more balanced and data-adaptive decomposition; (iii) A 3D rank allocation mechanism, which dynamically assigns 3D decomposition ranks across dimensions to best meet a target compression ratio while minimizing the reconstruction error. Extensive experiments on Mixtral-8×7B across seven commonsense reasoning benchmarks demonstrate that TD-MoE achieves almost lossless performance under 20\% parameter reduction, and delivers more than 14\% gains over state-of-the-art decomposition-based baselines at 40\% and 60\% compression. Further ablation studies validate the effectiveness of each component, highlighting the importance of cross-expert factorization, whitening, and rank allocation. The code is available at \href{https://anonymous.4open.science/r/TD-MoE}{https://anonymous.4open.science/r/TD-MoE}.