AI 中文总结
研究用DSAE对激光雷达点云分类，通过实验比较不同编码器深度下的表现，发现深度为\(K = 5\)时存在隐藏状态坍缩，乘积系数不能改善坍缩前指标及防止坍缩，确定大深度表示坍缩是DSAE激光雷达分类的失败模式。
AI 中文摘要
我们研究了使用空间坐标和乘积系数特征增强的动态系统自动编码器（DSAE）用于激光雷达点云分类。实验分别比较了在编码器深度\(K = 1,\ldots,5\)下单独训练的DSAE架构，并使用随机森林、kNN和多数类虚拟基线评估所得的隐藏表示。主要发现是在\(K = 5\)时存在隐藏状态坍缩。对于xyz和xyz加乘积系数输入，隐藏状态标准差降至\(10^{-5}\)量级，而所有三个分类器的宏观F1分数均为\(0.224688\)。我们证明类间隐藏散度受总隐藏散度限制，而总隐藏散度又由报告的隐藏状态方差控制。因此，几乎恒定的隐藏表示无法保留大量的类分离结构。在当前DSAE设置中，乘积系数既不能提高坍缩前的宏观F1分数，也不能防止\(K = 5\)时的坍缩。这些结果将大深度表示坍缩确定为DSAE激光雷达分类的一种具体失败模式。
英文摘要
We study Dynamical System Autoencoders (DSAE) for LiDAR point-cloud classification using spatial coordinates and Product Coefficient feature augmentations. The experiments compare separately trained DSAE architectures at encoder depths $K=1,\ldots,5$ and evaluate the resulting hidden representations with Random Forest, kNN, and a majority-class Dummy baseline. The main finding is a hidden-state collapse at $K=5$. For both xyz and xyz plus Product Coefficient inputs, the hidden-state standard deviation falls to the order of $10^{-5}$, while all three classifiers attain the same macro F1 score of $0.224688$. We prove that between-class hidden scatter is bounded by total hidden scatter, which in turn is controlled by the reported hidden-state variance. Thus a nearly constant hidden representation cannot retain substantial class-separating structure. Product Coefficients neither improve pre-collapse macro F1 nor prevent the $K=5$ collapse in the present DSAE setting. These results identify large-depth representation collapse as a concrete failure mode for DSAE LiDAR classification.
Comments6 pages, 2 figures, 1 table. Submitted to the 2026 IEEE High Performance Extreme Computing Conference (HPEC 2026)
