Tianxiao Cao | Search arXiv

arXiv2026

Shared Low-rank Basis Factorization for Data-free Mixture-of-Experts Compression

Mixture-of-Experts (MoE) large language models decouple capacity from compute through sparse routing, but their large parameter count creates storage and serving challenges. We analyze three MoE compression families: expert pruning, expert merging, and weight reconstruction, and derive structural error bounds showing that pruning and merging can incur non-vanishing errors tied to routing and expert heterogeneity. In contrast, weight reconstruction avoids these structural costs by preserving expert structure and routing. Motivated by the analysis, we propose Shared Low-rank Basis Factorization (SLBF), a data-free weight reconstruction method that uses rank-$k$ bases shared among experts, enabling richer cross-expert sharing, faster convergence, and lower reconstruction error. A post-hoc gauge fixing removes redundant parameters at no representational cost. Across five MoE architectures spanning 16B to 122B parameters, SLBF consistently outperforms methods from all three compression families.

cs.LG↗

arXiv2025

Unpacking the Implicit Norm Dynamics of Sharpness-Aware Minimization in Tensorized Models

Sharpness-Aware Minimization (SAM) has been proven to be an effective optimization technique for improving generalization in overparameterized models. While prior works have explored the implicit regularization of SAM in simple two-core scale-invariant settings, its behavior in more general tensorized or scale-invariant models remains underexplored. In this work, we leverage scale-invariance to analyze the norm dynamics of SAM in general tensorized models. We introduce the notion of \emph{Norm Deviation} as a global measure of core norm imbalance, and derive its evolution under SAM using gradient flow analysis. We show that SAM's implicit control of Norm Deviation is governed by the covariance between core norms and their gradient magnitudes. Motivated by these findings, we propose a simple yet effective method, \emph{Deviation-Aware Scaling (DAS)}, which explicitly mimics this regularization behavior by scaling core norms in a data-adaptive manner. Our experiments across tensor completion, noisy training, model compression, and parameter-efficient fine-tuning confirm that DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.

cs.LG↗