Error Aware Distribution Prediction for Lightweight Implicit Neural Representations

Jul 16, 2026

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Implicit neural representations (INRs) provide compact volume encodings, but their lossy approximation introduces prediction errors that can limit scientific reliability. The study introduces an INR training approach that predicts uncertainty distributions to capture relative error scales without expensive ensembles or restrictive parametric assumptions. Regression training is reformulated as classification by discretizing targets into bins. The paper analyzes the reconstruction–uncertainty trade-off and shows classification-based settings deliver high reconstruction quality and competitive error awareness versus regression-based methods.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages7

Reading Time18 min

Introduction

Motivation: localized error vs global metrics

Lightweight uncertainty estimation challenges

Proposed Method

Reformulating regression as classification via binning

Training objective and distribution modeling

Related Work

Uncertainty estimation for INRs

Error Aware Distribution Prediction for Lightweight Implicit Neural Representations Zhimin Li* Vanderbilt University Jake D. Balla† University of Arizona Joshua A. Levine‡ University of Arizona arXiv :2607 . 10068v 1 [ cs .LG] 11 Jul 2026 CE CE + MSE MSE evidential Heteroscedastic Figure 1: Error and uncertainty fields for classification- and regression-based methods on the aneurism dataset. From left to right:cross-entropy(CE), cross-entropy+ mean-squared-error (CE+MSE), mean-squared-error (MSE) in the classification setting, heterocadastic regression, and evidential regression in the regression setting. For volume reconstructed from the heteroscedasticand evidential regression, the corresponding uncertainty fields fail to capture critical features in the error field, indicating the potential limitation of using their predicted uncertainty for error analysis. In contrast, the uncertainty fields produced by CE and CE+MSE show better alignment with the error fields. ABSTRACT Implicit neural representations (INRs) offer compact encoding of volumes, but as lossy approximators, inevitably have prediction errors. We consider INRs that can simultaneously encode relative error scales by predicting distributions using tools from uncertainty estimation. Typically, uncertainty estimation relies on computationally expensive approaches or on predefined parametric assumptions about the predictive distribution (e.g., Gaussian) . In this study, we propose a lightweight method that reformulates regression-based INR training as a classification task by discretizing continuous targets into bins, enabling flexible distribution modeling to capture complex multimodal behaviors. We analyze the trade-off between regression and classification for INR training and demonstrate that the classification setting tends to achieve high reconstruction quality and competitive error awareness through uncertainty estimation, compared to regression-based approaches. Index Terms: Scientific Visualization, Implicit Neural Representation, Uncertainty Quantification 1 INTRODUCTION Implicit neural representations (INRs) have emerged as a powerful tool for compactly representing scientific data, such as 3D volumes * e-mail: [zhimin.li@vanderbilt.edu](zhimin.li@vanderbilt.edu)[ ](zhimin.li@vanderbilt.edu)†e-mail: [jakeballa@arizona.edu](jakeballa@arizona.edu)[ ](jakeballa@arizona.edu)‡e-mail: [josh@cs.arizona.edu](josh@cs.arizona.edu) and time-varying scalar fields, due to their flexibility and expressiveness. As approximations of the data, INRs achieve impressive compression ratios [5, 6, 7, 8, 9, 16, 30, 32] and outperform prior state-of-the-art lossy compression methods [2] . However, their approximating nature introduces errors that can affect the reliability of downstream scientific analysis and raise concerns among domain experts about their use in scientific workflows. Common error metrics, such as peak signal-to-noise ratio (PSNR), provide a global error estimate for the data approximation but fail to capture localized inaccuracies that are critical for scientific interpretation. Without access to the raw data, which is often unavailable, measuring prediction error is challenging. Recently, prediction uncertainty has been used as a potential indicator of the relative error scale of INR predictions [24, 31] . Classical uncertainty quantification approaches, such as deep ensemble [15] and Monte Carlo dropout [4] provide uncertainty estimates but introduce significant computational overhead or may compromise prediction accuracy. Lightweight solutions, heteroscedastic [11, 26] or evidential regression [1], enable single-pass uncertainty estimation but rely on restrictive distribution assumptions, limiting their ability to model complex scientific data with long-tailed or multi-modal distributions. In this study, we propose a new lightweight approach for INRbased scientific data modeling that does not rely on predefined parametric assu

FAQs

Why is prediction uncertainty important for implicit neural representations in scientific workflows?

INRs approximate data and can introduce errors that affect downstream scientific interpretation. When raw data is unavailable, uncertainty helps indicate relative error scale and supports more reliable analysis.

How does the proposed method avoid expensive uncertainty estimation or restrictive parametric assumptions?

It reframes INR regression training as a classification problem by discretizing continuous targets into bins, enabling flexible distribution modeling without relying on predefined distributions like Gaussian.

What trade-off between reconstruction quality and error awareness is investigated?

The study compares regression-based and classification-based INR training to assess how well each captures reconstruction fidelity and aligns uncertainty fields with the observed error fields.

Jul 16, 2026

Upload by Quinn