Towards Training-free Automatic Proxy Discovery via Large Language Models for Mixed Precision Quantization

Many LLM applications require only narrow capabilities, yet standard post-training quantization (PTQ) methods allocate precision without considering the target task. This can waste bits on layers that are less relevant to the task signal while over-compressing layers that are critical for downstream behavior. We propose Task-Aware Quantization (TAQ), a training-free, weight-only mixed-precision PTQ framework that uses a small set of unlabeled task calibration prompts to allocate higher precision to task-relevant transformer layers under a fixed bit budget. TAQ estimates layer importance from hidden representations and output sensitivity, and we instantiate it with three scoring rules: TAQ-IS, based on activation information and stability; TAQ-KL, based on output-distribution sensitivity under a quantization-noise proxy; and TAQ-O, a label-informed oracle diagnostic for analyzing layer sensitivity. Across several benchmarks, TAQ outperforms task-agnostic baselines such in most settings, with especially strong gains in the accuracy--memory ratio. We further validate that these gains translate to real deployment behavior through hardware throughput and latency measurements, and analyze calibration robustness and residual-stream error propagation. Overall, TAQ turns mixed-precision PTQ from a model-centric compression step into a task-conditioned precision-allocation problem. A reference implementation is available at \href{https://anonymous.4open.science/r/TAQ-9217/README.md}{\includegraphics[height=1em]{imgs/github-mark.png}}.

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.

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.