# Activation Sensitivity as a Unifying Principle for Post-Training Quantization

arXiv: https://arxiv.org/abs/2601.11663 · HTML: https://mlsanity.com/paper/2601.11663/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 13 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (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)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)

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

- [Predicting Quantization Price for Selecting PTQ Configurations Before Deployment](https://mlsanity.com/paper/2609.28270/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) methods for large language models rely on heuristics that implicitly estimate which weight channels most strongly influence model behavior. Two dominant paradigms have emerged: activation-aware methods such as AWQ prioritize channels with large activation magnitudes, while second-order methods such as GPTQ allocate quantization error according to input covariance structure. Despite strong empirical performance, these approaches remain conceptually fragmented, and it is unclear what underlying quantity they are approximating. In this work, we present a unified theoretical framework for PTQ by formalizing activation sensitivity, defined as the expected impact of channel-wise perturbations on the loss. Using a first-order Taylor expansion, we show that sensitivity naturally arises as the squared norm of gradient-weighted activations, yielding a principled measure of channel importance that captures both activation magnitude and downstream error propagation. Within this framework, AWQ and GPTQ can be interpreted as complementary approximations that recover sensitivity under distinct simplifying assumptions. We analyze the design space of sensitivity metrics, connect gradient-based saliency, Fisher information, and Hessian-based criteria, and clarify their relationships to classical pruning methods such as Optimal Brain Damage and Optimal Brain Surgeon. Rather than proposing a new quantization algorithm, this work provides a conceptual foundation for understanding and comparing post-training quantization methods through the lens of sensitivity.