让神经网络直接学习连续累积积分，打通传统表格与神经模型的鸿沟。
Learning Neural Antiderivatives
- 提出多种神经方法实现连续重复积分，突破离散网格限制。
- 在多维输入和高阶积分下保持良好重建质量，支持滤波与渲染任务。
- 为微分积分算子学习提供新思路，适合视觉计算与神经场研究者。
神经场提供了超越传统离散格式的连续可学习表示，广泛应用于视觉计算领域。本文研究从函数中直接学习重复积分的神经表示问题，相当于连续版的累加面积表。尽管在离散领域广泛应用，但传统累积方案依赖网格结构，难以适用于连续神经场景。为此，本文提出并分析了多种神经方法，涵盖对已有工作的改进与新设计。评估覆盖多种输入维度和积分阶数，同时考察重建精度及下游任务（如滤波与渲染）表现。结果表明，该方法可将经典累积算子融入现代神经系统，并为涉及微分与积分算子的学习任务提供新见解。
原文摘要 · Abstract (English)
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.
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