# HyperShadow: A Benchmark for Detecting 3D Projections of Higher-Dimensional Spatial Objects

arXiv: https://arxiv.org/abs/2607.14419 · HTML: https://mlsanity.com/paper/2607.14419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [OmniWorld: A Multi-Domain and Multi-Modal Dataset for 4D World Modeling](https://mlsanity.com/paper/2509.12201/) (2025)
- [A Survey of Dimension Estimation Methods](https://mlsanity.com/paper/2507.13887/) (2025)
- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [Learning Significant Persistent Homology Features for 3D Shape Understanding](https://mlsanity.com/paper/2602.14228/) (2026)
- [Intrinsic Dimension Estimating Autoencoder (IDEA) Using CancelOut Layer and a Projected Loss](https://mlsanity.com/paper/2509.10011/) (2025)

## Abstract (arXiv)

Machine-learning datasets labelled "4D" universally denote three spatial dimensions plus time. We introduce HyperShadow, the first public benchmark in which the fourth, fifth, and sixth dimensions are spatial: the task is to decide whether a 3D point cloud is a native three-dimensional shape or the projection, the "shadow", of a rigid object living in R^N (N = 4-6). We show this task is fundamentally distinct from intrinsic-dimension estimation: a shadow is still at-most-3-dimensional data, and standard estimators (TwoNN, Levina-Bickel MLE) reach only 71-73% accuracy. Detection instead requires projection signatures, density folds, filled volumes with characteristic radial profiles, and topology changes, which a 190k-parameter point network recovers at 96.6% accuracy across four corruption tiers, generalizing at 79-91% to object families never seen in training. On a temporal track of rigidly rotating objects we introduce a zero-parameter rigidity witness: the residual of the optimal rigid 3D alignment (Kabsch) between consecutive frames, which must vanish for any rigid 3D motion but cannot vanish for the shadow of a rigid rotation in R^N. This single interpretable statistic separates the classes at AUROC 0.982. All data are generated reproducibly from seeds; the dataset, models, and code are released publicly. HyperShadow makes no claim about physical reality; it is a controlled instrument for studying which observable statistics can certify incompatibility with a purely three-dimensional explanation.