Title: Learning Neural Antiderivatives Show Chinese title

Title: 学习神经反导数

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. Show Chinese abstract

Abstract: 神经场提供了超越传统离散格式的连续、可学习表示。 我们研究了从函数中直接学习重复反导数的神经表示问题，这是求和面积表的连续模拟。 尽管在离散领域中广泛使用，这种累积方案依赖于网格，这限制了它们在连续神经环境中的适用性。 我们引入并分析了一系列用于重复积分的神经方法，包括对先前工作的适应和新的设计。 我们的评估涵盖了多种输入维度和积分阶数，评估了重建质量和在过滤和渲染等下游任务中的性能。 这些结果使经典累积算子能够融入现代神经系统，并为涉及微分和积分算子的学习任务提供了见解。