# The Structure of Quantization Damage in LLMs: Why the Next Bit Should Be Spent Globally

arXiv: https://arxiv.org/abs/2609.01587 · HTML: https://mlsanity.com/paper/2609.01587/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [On the Impact of Calibration Data in Post-training Quantization and Pruning](https://mlsanity.com/paper/2311.09755/) (2023)
- [Task-Circuit Quantization: Leveraging Knowledge Localization and Interpretability for Compression](https://mlsanity.com/paper/2504.07389/) (2025)
- [Scaling Laws for Post Training Quantized Large Language Models](https://mlsanity.com/paper/2410.12119/) (2024)
- [You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations](https://mlsanity.com/paper/2511.06516/) (2025)

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

- [XMerge: Cross-Axis Selection and Reconstructive Layer Merging for LLM Depth Compression](https://mlsanity.com/paper/2609.02083/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) is widely used to reduce the cost of serving large language models (LLMs), but its accuracy cost is uneven and is often tuned per model. We study where quantization damage occurs and how to allocate a small additional precision budget. Using causal mixed-precision intervention as ground truth (raise each layer to 8-bit in turn and measure the accuracy it recovers) across 9 open-weight models in 4 architecture families, we test 3 intuitive hypotheses: that quantization damage lives in task circuits, where the model computes, or in weight statistics. None of them predicts which layers benefit from restored precision. Recovery is instead diffuse: for 8 of 9 models, recovering 75% of the gap takes roughly half the layers; the lone exception, Qwen3-8B, is sharply concentrated. At a matched precision budget, spending it globally on finer quantization granularity beats locally repairing the most recoverable layers for all 8 group-128-compatible models (all but OpenLLaMA, whose width rules out group-128), by 21-52 points, including the concentrated Qwen3-8B. We report 2 secondary findings: the residual is budget-limited (8-bit is near-lossless in our evaluation across RTN, GPTQ, and AWQ), and the location of peak recovery correlates with architecture within a family, though not across families. Within this budget setting, global granularity is a better default than selectively protecting critical layers. More broadly, cheap signals that correlate with quantization damage do not necessarily identify where restoring precision improves accuracy; this must be tested with causal intervention.