# Learning Neural Antiderivatives

arXiv: https://arxiv.org/abs/2509.17755 · HTML: https://mlsanity.com/paper/2509.17755/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 78 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [Inverse Path Tracing for Joint Material and Lighting Estimation](https://mlsanity.com/paper/1903.07145/) (2019)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [Plateau-reduced Differentiable Path Tracing](https://mlsanity.com/paper/2211.17263/) (2022)
- [Neural Field Convolutions by Repeated Differentiation](https://mlsanity.com/paper/2304.01834/) (2023)
- [Accurate Differential Operators for Hybrid Neural Fields](https://mlsanity.com/paper/2312.05984/) (2023)
- [Neural Gaussian Scale-Space Fields](https://mlsanity.com/paper/2405.20980/) (2024)
- [Zero Grads: Learning Local Surrogate Losses for Non-Differentiable Graphics](https://mlsanity.com/paper/2308.05739/) (2023)
- [Computing Anti-Derivatives using Deep Neural Networks](https://mlsanity.com/paper/2209.09084/) (2022)
- [Continuous Levels of Detail for Light Field Networks](https://mlsanity.com/paper/2309.11591/) (2023)

## Abstract (arXiv)

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.