# Accuracy is Not Enough: A Divergence-Based Approach to Evaluate Fidelity Loss in Quantized LLMs

arXiv: https://arxiv.org/abs/2609.07664 · HTML: https://mlsanity.com/paper/2609.07664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (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)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [What Do Compressed Deep Neural Networks Forget?](https://mlsanity.com/paper/1911.05248/) (2019)
- [Privacy in Deep Learning: A Survey](https://mlsanity.com/paper/2004.12254/) (2020)
- [Accuracy is Not All You Need](https://mlsanity.com/paper/2407.09141/) (2024)
- [Teuken-7B-Base & Teuken-7B-Instruct: Towards European LLMs](https://mlsanity.com/paper/2410.03730/) (2024)
- [When LLMs get significantly worse: A statistical approach to detect model degradations](https://mlsanity.com/paper/2602.10144/) (2026)
- [The Illusion of Equivalency: Statistical Characterization of Quantization Effects in LLMs](https://mlsanity.com/paper/2607.08734/) (2026)
- [Alignment Collapse Under KV Cache Quantization: Diagnosis and Mitigation](https://mlsanity.com/paper/2606.09864/) (2026)
- [How Small Can You Go? Compact Language Models for On-Device Critical Error Detection in Machine Translation](https://mlsanity.com/paper/2511.09748/) (2025)

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

- [How Divergence Becomes Decision Flips in Compressed Language Models](https://mlsanity.com/paper/2610.00694/) (2026)

## Abstract (arXiv)

Deployment of Large Language Models (LLMs) on memory-constrained edge devices relies heavily on aggressive post-training quantization. However, evaluating these models is largely based on zero-shot task accuracy, which depends solely on argmax predictions and is insensitive to changes in the underlying predictive distribution. Consequently, accuracy can exhibit unstable, non-monotonic behavior under progressive quantization, masking substantial fidelity loss relative to the BFloat16 (BF16) uncompressed base model and providing misleading deployment signals. We introduce a distribution-sensitive evaluation framework quantifying information loss in quantized LLMs as the divergence between full-vocabulary predictive distributions at the token decision boundary. We compute statistical distances, including Jensen-Shannon Divergence and Total Variation Distance, between outputs of full-precision and quantized models, enabling a fine-grained analysis of distributional shift. Using this framework, we quantify probability mass displacement and distributional drift relative to the BF16 reference, capturing predictive distribution changes not reflected in top-1 accuracy. We conduct a 120-run experimental matrix across five foundation architectures and four reasoning benchmarks under progressive quantization regimes, from uncompressed BF16 to Q2_K, providing a systematic fidelity analysis. Our results show divergence metrics generally increase under stronger quantization, complementing task accuracy with a fidelity signal. Across tested llama-cpp schemes, mixed-precision Q4_K generally yields lower divergence than uniform Q4_0 at similar memory footprints. These findings motivate distribution-aware evaluation as a practical diagnostic complement to task accuracy; they do not directly establish correctness, calibration, safety, or user-perceived quality.