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

• URL: http://arxiv.org/abs/2609.07664v2
• Date: Wed, 09 Sep 2026 08:50:36 GMT
• Title: Accuracy is Not Enough: A Divergence-Based Approach to Evaluate Fidelity Loss in Quantized LLMs
• Abstract summary: Deployment of Large Language Models (LLMs) on memory-constrained edge devices relies heavily on aggressive post-training quantization.<n>We introduce a distribution-sensitive evaluation framework quantifying information loss in quantized LLMs.<n>We quantify probability mass displacement and distributional drift relative to the BF16 reference, capturing predictive distribution changes not reflected in top-1 accuracy.
• Score: 13.897073114465094
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers [1.4452289368758382]
  Single-Pass Adaptive Risk is a structured, calibrated, and efficient uncertainty estimate for human motion forecasters.<n>A deterministic backbone predicts the future mean, and a conjugate Bayesian last layer converts time-domain feature leverage into an analytic horizon-wise scale.<n>It ranks first on NLL and on the combined MPJPE+NLL criterion while retaining competitive point accuracy and efficient calibrated tubes.
  arXiv  Detail & Related papers  (2026-08-21T07:20:22Z)
• The Illusion of Equivalency: Statistical Characterization of Quantization Effects in LLMs [5.849736173068869]
  Post-training quantization is widely used to deploy large language models in resource-constrained settings.<n>We show that these metrics fail to capture behavioral changes induced by quantization.<n>We introduce correctness agreement, a decision-level metric that measures overlap in correct predictions between a base model and its quantized variants.
  arXiv  Detail & Related papers  (2026-07-09T17:35:02Z)
• Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation [55.47411235954028]
  We recast imputation under missing completely at random as density estimation from masked observations.<n>We obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method.<n>The resulting PSD Impute model yields both single and multiple imputations from the same fitted density.
  arXiv  Detail & Related papers  (2026-07-08T15:51:05Z)
• Bayesian 3D Steerable CNNs: Enabling Equivariance and Uncertainty Quantification Simultaneously [1.2234742322758416]
  Steerable convolutional neural networks (Steerable-CNNs) guarantee SE(3)-equivariance by parameterizing kernels as linear combinations of steerable basis functions.<n>We propose a Bayesian Steerable-CNN that places posterior distributions over the basis coefficients, yielding kernels while preserving equivariance exactly.<n> Empirically, the model attains competitive classification accuracy alongside an expected calibration error of 0.0263 and outperforms its deterministic counterpart by up to 6.17% under distributional shift induced by additive Gaussian noise.
  arXiv  Detail & Related papers  (2026-06-13T21:28:04Z)
• Quantization of Spiking Neural Networks Beyond Accuracy [3.43677310385818]
  We show that firing activity governs effective sparsity, state storage, and event-processing load in SNNs.<n>We propose Earth Mover's Distance as a diagnostic metric for firing distribution divergence.<n>We find that uniform quantization induces distributional drift even when accuracy is preserved, while LQ-Net style learned quantization maintains firing behavior close to the full-precision baseline.
  arXiv  Detail & Related papers  (2026-04-15T23:55:11Z)
• Mitigating LLM Hallucination via Behaviorally Calibrated Reinforcement Learning [32.32593439144886]
  Behavior-calibrated reinforcement learning allows smaller models to surpass frontier models in uncertainty quantification.<n>Our model's log-scale Accuracy-to-Hallucination Ratio gain (0.806) exceeds GPT-5's (0.207) in a challenging in-domain evaluation.
  arXiv  Detail & Related papers  (2025-12-22T22:51:48Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Regularized Vector Quantization for Tokenized Image Synthesis [126.96880843754066]
  Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. deterministic quantization suffers from severe codebook collapse and misalignment with inference stage while quantization suffers from low codebook utilization and reconstruction objective. This paper presents a regularized vector quantization framework that allows to mitigate perturbed above issues effectively by applying regularization from two perspectives.
  arXiv  Detail & Related papers  (2023-03-11T15:20:54Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)
• Uncertainty Estimation Using a Single Deep Deterministic Neural Network [66.26231423824089]
  We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models.
  arXiv  Detail & Related papers  (2020-03-04T12:27:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.