HyperShadow：用于检测高维空间对象3D投影的基准测试
HyperShadow: A Benchmark for Detecting 3D Projections of Higher-Dimensional Spatial Objects
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中文总结 AI 辅助
HyperShadow是用于检测高维空间对象3D投影的基准测试，通过190k参数点网络及零参数刚性见证进行检测，能在不同损坏层级达到高准确率和泛化率，为研究三维解释不兼容性提供工具，数据等已公开。
中文摘要 AI 辅助
机器学习中标记为“4D”的数据集通常表示三个空间维度加时间。我们引入了HyperShadow，这是首个第四、第五和第六维度为空间维度的公共基准测试：任务是判定一个3D点云是原生三维形状还是生活在R^N（N = 4 - 6）中刚性物体的投影，即“阴影”。我们表明此任务与内在维度估计有根本区别，标准估计器准确率仅71 - 73%。检测需要投影特征、密度折叠、具有特征径向轮廓的填充体积和拓扑变化，一个190k参数的点网络在四个损坏层级上准确率达96.6%，对训练中未见的对象家族泛化率为79 - 91%。在刚性旋转物体的时间轨迹上，我们引入了零参数刚性见证：连续帧之间最优刚性3D对齐（Kabsch）的残差，它对任何刚性3D运动必须消失，但对R^N中刚性旋转的阴影不会消失。这个单一可解释统计量在AUROC 0.982时分离了类别。所有数据可从种子可重复生成，数据集、模型和代码已公开发布。HyperShadow并非关于物理现实的断言；它是一种用于研究哪些可观测统计量能证明与纯三维解释不兼容的受控工具。
英文摘要
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.
