GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets

Mixed-precision quantization improves the accuracy of post-training quantization by allocating higher bitwidths to sensitive layers, but existing methods solve the allocation for a single fixed memory budget. In practice the budget varies across deployments and is unknown at calibration time. Adaptive quantization addresses this with one offline calibration that serves any budget, yet current methods score layer sensitivity in a manner that does not consider its dependency on quantization levels of other layers. We show that a layer's sensitivity depends strongly on the bitwidths of its upstream layers and that this dependence shifts the resulting preferred bit allocation. We propose MixQuant, a technique-agnostic adaptive framework that wraps any base quantizer. MixQuant marginalizes each layer's distortion over random quantized upstream configurations to obtain budget-agnostic scores, calibrates the quantizer's parameters on plans the allocator itself produces, and penalizes allocations that leave layers at the lowest bitwidths. A single greedy pass then serves any budget at deployment. Across Llama-3.2-3B, Llama-2-7B, and Mistral-7B under AWQ and GPTQ, MixQuant outperforms adaptive and mixed-precision baselines in every setting, improving average accuracy by up to 8 points and reducing perplexity from 12.43 to 10.70 at the tightest budget, while matching an ILP solver at negligible deployment cost.

Mixed-precision quantization (MPQ) has become a key technique for deploying large language models under stringent memory and compute constraints. We first identify a phenomenon that we term the Perplexity Illusion: layers ranked as important by perplexity-based sensitivity show little rank correlation with those that are most influential for complex reasoning performance, with Kendall $τ\approx 0$ in our analysis. We further reveal an Alignment-Diversity Tradeoff: using only target-task calibration data can degrade post-quantization performance, whereas incorporating general-domain data stabilizes sensitivity estimation and improves robustness across tasks. Based on these observations, we propose TASA (Task-Aware Sensitivity Analysis), a two-level framework that jointly optimizes calibration-data composition and mixed-precision bit allocation. Specifically, TASA searches for a calibration-data mixture using a training-free gradient-trace alignment criterion, and then aggregates perplexity and reasoning-oriented sensitivity signals to guide both inter-layer and intra-layer bit allocation. Experiments on LLaMA-3-8B and Qwen2.5-7B reveal a precision inversion: appropriately allocated 3.5-bit models can match or surpass less task-aware 4-bit baselines. At an average precision of 3.5 bits, TASA matches or outperforms several competitive 4-bit uniform baselines in aggregate accuracy, and improves over the strongest W3 baseline on GSM8K by more than 20 absolute points on LLaMA-3-8B. These results show that calibration-data composition substantially affects task-sensitive quantization, a factor underexplored in prior work.

Quantization is an effective approach to reduce the memory footprint and inference cost of large language models (LLMs), yet maintaining performance in the ultra-low-bit regime remains challenging. Existing post-training methods often suffer from severe accuracy degradation, while quantization-aware training requires costly retraining and additional resources. Moreover, most mixed-precision strategies rely on coarse-grained or heuristic sensitivity analysis that overlooks fine-grained variations within weight matrices. We propose WINDQuant, a reinforcement-learning-based allocation controller for ultra-low-bit LLM quantization. Rather than introducing another low-level quantization operator, WINDQuant learns how to assign bit-widths and quantization treatments to fine-grained column chunks under a global storage budget. By operating at the column-chunk level, WINDQuant enables flexible and fine-grained precision assignment within layers under a global target bit-width. The implementation combines PPO with activation-aware calibration, lightweight per-unit quantizer fitting, and explicit effective-bit accounting of the learned mixed-precision plan. Experiments on LLaMA models demonstrate that WINDQuant achieves competitive performance in ultra-low-bit settings while reducing optimization overhead relative to retraining-based approaches, highlighting reinforcement learning as a practical controller for adaptive mixed-precision quantization.