Depth-Dependent Hidden-State Collapse in Dynamical System Autoencoders for LiDAR Point-Cloud Classification

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.