Learning Neural Antiderivatives
This enables integrating classical cumulative operators into modern neural systems for visual computing, though it appears incremental as it adapts prior work alongside novel designs.
The paper tackles the problem of learning neural representations of repeated antiderivatives from functions, enabling continuous cumulative schemes analogous to discrete summed-area tables. The results show successful evaluation across multiple input dimensionalities and integration orders, with applications in filtering and rendering tasks.
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.