Learning Neural Antiderivatives
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a continuous analogue of summed-area tables. Although widely used in discrete domains, such cumulative schemes rely on grids, which prevents their applicability in continuous neural contexts. We introduce and analyze a range of neural methods for repeated integration, including both adaptations of prior work and novel designs. Our evaluation spans multiple input dimensionalities and integration orders, assessing both reconstruction quality and performance in downstream tasks such as filtering and rendering. These results enable integrating classical cumulative operators into modern neural systems and offer insights into learning tasks involving differential and integral operators.
Description
CCS Concepts: Computing methodologies → Machine learning algorithms; Image manipulation; Rendering
@inproceedings{10.2312:vmv.20251230,
booktitle = {Vision, Modeling, and Visualization},
editor = {Egger, Bernhard and Günther, Tobias},
title = {{Learning Neural Antiderivatives}},
author = {Rubab, Fizza and Nsampi, Ntumba Elie and Balint, Martin and Mujkanovic, Felix and Seidel, Hans-Peter and Ritschel, Tobias and Leimkühler, Thomas},
year = {2025},
publisher = {The Eurographics Association},
ISBN = {978-3-03868-294-3},
DOI = {10.2312/vmv.20251230}
}