Beyond Expert Rankings: Contrast Calibration for Mixed-Precision MoE Quantization

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.

Sparse Mixture-of-Experts (MoE) allows scaling of language and vision models efficiently by activating only a small subset of experts per input. While this reduces computation, the large number of parameters still incurs substantial memory overhead during inference. Post-training quantization has been explored to address this issue. Because uniform quantization suffers from significant accuracy loss at low bit-widths, mixed-precision methods have been recently explored; however, they often require substantial computation for bit-width allocation and overlook the varying sensitivity of model performance to the quantization of different experts. We propose a theoretically grounded expert-wise mixed precision strategy that assigns bit-width to each expert primarily based on their change in routers l2 norm during training. Experts with smaller changes are shown to capture less frequent but critical features, and model performance is more sensitive to the quantization of these experts, thus requiring higher precision. Furthermore, to avoid allocating experts to lower precision that inject high quantization noise, experts with large maximum intra-neuron variance are also allocated higher precision. Experiments on large-scale MoE models, including Switch Transformer and Mixtral, show that our method achieves higher accuracy than existing approaches, while also reducing inference cost and incurring only negligible overhead for bit-width assignment.

Mixture-of-Experts (MoE) large language models reduce computation through sparse activation but still incur substantial storage costs. Mixed-precision post-training quantization (PTQ) reduces these costs by quantizing different model components at different bit widths, but existing methods often struggle to preserve generation quality under tight bit budgets. We identify two key challenges: (1) nonlinear quantization errors at extremely low precision are underestimated when cross-layer propagation is ignored; (2) direct router fine-tuning may cause routing drift, and calibration gains may not generalize to downstream tasks. To address these issues, we propose ProQuant, a weight-only PTQ framework for MoE models. Prune-or-Prioritize Mixed-Precision Allocation (PoP) jointly optimizes expert pruning and bit-width assignment. It allows higher-precision experts to substitute for severely degraded ones while improving bit-budget utilization. Routing-Consistent RMSNorm Finetune (RoCo) adapts expert input representations through mathematically equivalent transformations. It compensates for quantization errors to reduce routing drift. Extensive experiments demonstrate that ProQuant outperforms existing methods across diverse generative tasks. Code is available at https://github.com/ThrowBug/ProQuant.git.