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This study investigates the performance of Dynamical System Autoencoders (DSAE) for classifying LiDAR point clouds, focusing on the impact of encoder depth on hidden representations. Through experiments with varying depths from 1 to 5, the authors reveal a significant hidden-state collapse at depth 5, where the standard deviation of hidden states drops to $10^{-5}$, leading to a stagnant macro F1 score across classifiers. The findings highlight a critical limitation in DSAE architectures, where increased depth fails to enhance class separation, ultimately undermining classification effectiveness.
Hidden-state representations in DSAE for LiDAR classification collapse at depth 5, revealing a fundamental flaw in deep architectures for this task.
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.