AlphaQ: Calibration-Free Bit Allocation for Mixture-of-Experts Quantization

2026-06-03

AI Summary

This work addresses the high memory overhead of deploying Mixture-of-Experts (MoE) models, which stems from the need to load all expert weights, and the suboptimal performance of existing mixed-precision quantization methods that rely on calibration data for bit allocation. The authors propose a calibration-free, expert-level bit allocation strategy that introduces heavy-tailed self-regularization theory into MoE quantization for the first time. By analyzing the heavy-tailed spectral properties of expert weights to assess their training quality, the method optimizes quantization error under a global bit budget constraint. This approach eliminates dependence on private training distributions and significantly outperforms calibration-based baselines across multiple MoE models—achieving near full-precision accuracy with an average of 3.5 bits per expert on Qwen1.5-MoE while reducing memory usage by more than 4×.

Abstract

Mixture-of-Experts (MoE) architectures scale model capacity through sparse expert activation, but their deployment remains memory-bound because all expert weights must reside in memory. Mixed-precision quantization can substantially reduce this footprint by assigning different bit-widths to different experts. Existing approaches, however, typically rely on calibration data to estimate expert importance and determine bit allocation. For frontier MoE LLMs, the original training data, and hence the true training distribution, is proprietary and inaccessible. As a result, calibration sets are inevitably imperfect surrogates, and this can misestimate expert utilization and lead to suboptimal bit allocation. Motivated by the substantial cross-expert quality variability observed in modern MoE models, and by the success of Heavy-Tailed Self-Regularization (HT-SR) theory at predicting neural network model quality without access to training or testing data, we propose AlphaQ, a calibration-free bit-allocation method for MoE quantization. AlphaQ draws on HT-SR theory and follows a simple principle: experts with more heavy-tailed weight spectra are typically better trained and hence should receive higher bit-widths, while experts with weaker heavy-tailed structure can be quantized more aggressively. AlphaQ operationalizes this principle by measuring expert-wise spectral heavy-tailedness and solving a budget-constrained optimization problem that minimizes total quantization error under a global bit-budget constraint. Across several MoE models, AlphaQ consistently outperforms calibration-based baselines under matched bit budgets. Notably, on Qwen1.5-MoE, AlphaQ achieves near full-precision accuracy with an average expert precision of only 3.5 bits, while delivering more than 4$\times$ memory compression. Our code is available at https://github.com/Superone77/AlphaQ.

Problem

• Mixture-of-Experts
• quantization
• bit allocation
• calibration-free
• memory compression

Innovation

• Mixture-of-Experts
• calibration-free quantization
• bit allocation
• Heavy-Tailed Self-Regularization
• mixed-precision