# Task-Stratified Knowledge Scaling Laws for Post-Training Quantized Large Language Models

arXiv: https://arxiv.org/abs/2508.18609 · HTML: https://mlsanity.com/paper/2508.18609/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [Measuring and Improving Consistency in Pretrained Language Models](https://mlsanity.com/paper/2102.01017/) (2021)
- [Evaluating Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2310.19736/) (2023)
- [On the Impact of Calibration Data in Post-training Quantization and Pruning](https://mlsanity.com/paper/2311.09755/) (2023)
- [Knowledge Mechanisms in Large Language Models: A Survey and Perspective](https://mlsanity.com/paper/2407.15017/) (2024)
- [How Does Quantization Affect Multilingual LLMs?](https://mlsanity.com/paper/2407.03211/) (2024)
- [Why Has Predicting Downstream Capabilities of Frontier AI Models with Scale Remained Elusive?](https://mlsanity.com/paper/2406.04391/) (2024)
- [Optimizing Large Language Models through Quantization: A Comparative Analysis of PTQ and QAT Techniques](https://mlsanity.com/paper/2411.06084/) (2024)
- [Scaling Laws for Floating Point Quantization Training](https://mlsanity.com/paper/2501.02423/) (2025)

## Built on by (most cited first, 4 of 4)

- [Which Decisions Low-Bit Quantization Breaks, and How to Predict Them](https://mlsanity.com/paper/2608.06564/) (2026)
- [Quantization Degradation in Large Language Models: A Signal-Noise Perspective](https://mlsanity.com/paper/2608.08188/) (2026)
- [Capability Scaling-Down Laws for LLM Compression](https://mlsanity.com/paper/2610.02462/) (2026)
- [Saying, Not Knowing: Aggressively GGUF-Quantized Small Language Models Still Write Rare Words They Can No Longer Define](https://mlsanity.com/paper/2610.04403/) (2026)

## Abstract (arXiv)

Post-Training Quantization (PTQ) is a critical strategy for efficient Large Language Models (LLMs) deployment. However, existing scaling laws primarily focus on general performance, overlooking crucial fine-grained factors and how quantization differentially impacts diverse knowledge capabilities. To address this, we establish Task-Stratified Knowledge Scaling Laws. By stratifying capabilities into memorization, application, and reasoning, we develop a framework that unifies model size, bit-width, and fine-grained factors: group size and calibration set size. Validated on 293 diverse PTQ configurations, our framework demonstrates strong fit and cross-architecture consistency. It reveals distinct sensitivities across knowledge capabilities: reasoning is precision-critical, application is scale-responsive, and memorization is calibration-sensitive. We highlight that in low-bit scenarios, optimizing these fine-grained factors is essential for preventing performance collapse. These findings provide an empirically-backed foundation for designing knowledge-aware quantization strategies.