Is MoE Routing a Huffman Code? Discovering the Frequency-Diversity Law in Chain-of-Thought
A new study reveals that Mixture-of-Experts (MoE) routing in large language models follows a principle similar to Huffman coding, where common tokens are processed by sparse experts and rare, complex tasks engage diverse expert committees. The paper introduces the Frequency-Diversity Law, identifies a redundancy trap in certain models, and proposes Subset Difference Pruning to improve efficiency.
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[Submitted on 8 May 2026]
Title:Is MoE Routing a Huffman Code? Discovering the Frequency-Diversity Law in Chain-of-Thought
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Abstract:Mixture-of-Experts architectures have revolutionized scaling, yet the underlying logic of their routing remains a black box. In this paper, we uncover a fundamental governing principle: MoE routing is not merely selection, but a manifestation of Huffman Coding. We introduce the Frequency-Diversity Law, revealing that state-of-the-art models, such as Phi-3.5-MoE and Gemma-4-27B-A4B, spontaneously act as information-theoretic engines. These models allocate sparse expert resources for common tokens while invoking high-diversity expert committees for rare, complex tasks found in chain-of-thought trajectories. However, we identify a critical redundancy trap in Qwen3.5-35B-A3B: when effective sparsity (k/E_eff) is sufficiently low, load-balancing inadvertently imposes functional redundancy, masking the underlying Huffman efficiency signal. To bridge this gap, we propose Subset Difference Pruning, a surgical strategy to eliminate functional duplicates. We demonstrate that pruning does not degrade reasoning; instead, it unleashes the model's latent Huffman efficiency, forcing the logic to collapse into streamlined, high-density paths. Our findings suggest that the next generation of MoEs should move beyond forced load-balancing toward Minimum Description Length (MDL) optimality, assigning shorter expert-routing codes to high-frequency information and longer, more diverse codes to low-frequency information, thereby transforming routing from a heuristic into a principled compression engine.
Comments: 20 pages, 20 figures
Subjects:
Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Information Theory (cs.IT)
Cite as: arXiv:2607.20427 [cs.CL]
(or arXiv:2607.20427v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2607.20427
arXiv-issued DOI via DataCite
Submission history
From: Ching-Chieh Tsao [view email] [v1] Fri, 8 May 2026 16:55:49 UTC (4,807 KB)
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