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

arXiv: https://arxiv.org/abs/2607.14463 · HTML: https://mlsanity.com/paper/2607.14463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 8 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 2 of 2)

- [Integrating Product Coefficients for Improved 3D LiDAR Data Classification](https://mlsanity.com/paper/2503.11943/) (2025)
- [Integrating Product Coefficients for Improved 3D LiDAR Data Classification (Part II)](https://mlsanity.com/paper/2510.15219/) (2025)

## Abstract (arXiv)

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.