# Beyond Activation Alignment:The Alignment-Diversity Tradeoff in Task-Aware LLM Quantization

arXiv: https://arxiv.org/abs/2607.00908 · HTML: https://mlsanity.com/paper/2607.00908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 40)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [OWQ: Outlier-Aware Weight Quantization for Efficient Fine-Tuning and Inference of Large Language Models](https://mlsanity.com/paper/2306.02272/) (2023)
- [Not All Layers of LLMs Are Necessary During Inference](https://mlsanity.com/paper/2403.02181/) (2024)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [What is Wrong with Perplexity for Long-context Language Modeling?](https://mlsanity.com/paper/2410.23771/) (2024)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [Quantization Meets Reasoning: Exploring LLM Low-Bit Quantization Degradation for Mathematical Reasoning](https://mlsanity.com/paper/2501.03035/) (2025)
- [APTQ: Attention-aware Post-Training Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2402.14866/) (2024)
- [GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidance](https://mlsanity.com/paper/2505.07004/) (2025)
- [Layer-Wise Quantization: A Pragmatic and Effective Method for Quantizing LLMs Beyond Integer Bit-Levels](https://mlsanity.com/paper/2406.17415/) (2024)
- [Beware of Calibration Data for Pruning Large Language Models](https://mlsanity.com/paper/2410.17711/) (2024)
- [Self-calibration for Language Model Quantization and Pruning](https://mlsanity.com/paper/2410.17170/) (2024)
- [Why Do Some Inputs Break Low-Bit LLM Quantization?](https://mlsanity.com/paper/2506.12044/) (2025)
- [Preserving LLM Capabilities through Calibration Data Curation: From Analysis to Optimization](https://mlsanity.com/paper/2510.10618/) (2025)

## Built on by (most cited first, 1 of 1)

- [Damage Predicts Recovery: When Calibration Data Matters in Compressing Financial LLMs](https://mlsanity.com/paper/2609.26241/) (2026)

## Abstract (arXiv)

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 ≈ 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.