HyperShadow Benchmark Detects Higher-Dimensional Object Projections in 3D.

The field of machine learning often uses the term "4D" to refer to three spatial dimensions plus time. This new research introduces HyperShadow, a unique benchmark that challenges this convention by defining higher dimensions as purely spatial. The core task is to determine if a given 3D point cloud represents an intrinsically three-dimensional object or if it is the "shadow" – a projection – of a rigid object existing in 4, 5, or 6 spatial dimensions. Traditional methods for estimating intrinsic dimensionality prove inadequate for this task, achieving only 71-73% accuracy. This indicates that detecting higher-dimensional projections requires recognizing specific "projection signatures," including density folds, characteristic radial profiles of filled volumes, and topological changes. A specialized 190k-parameter point network, however, demonstrated remarkable success, reaching 96.6% accuracy across various data corruption levels. For objects undergoing rigid rotation, the researchers also developed a zero-parameter rigidity witness. This involves analyzing the residual of the optimal rigid 3D alignment between consecutive frames, which should vanish for true 3D rigid motion but not for the shadow of a higher-dimensional rotation. This simple statistic achieved an AUROC of 0.982, effectively separating the classes. All data, models, and code for HyperShadow are publicly released.