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

Despite their ubiquity, variational autoencoders (VAEs) inherently suffer from posterior collapse, a failure mode in which latent variables are effectively ignored. This failure arises because explicit prior imposition drives optimization toward loss landscape regions corresponding to uninformative latent representations. Here, we introduce Entropic Autoencoders (EAEs), a framework in which reconstruction loss is the only explicit objective, and entropy generates the latent variables' prior implicitly through a free energy-minimizing ensemble of encoders. This ensemble biases learning toward high-volume regions of near-optimal solutions, while decoder updates direct the search trajectories toward informative latent representations. We demonstrate that EAEs mitigate posterior collapse by learning non-Gaussian, multimodal latent distributions that yield diverse, data-consistent generations and preserve different forms of underlying structure in the data. As a proof-of-concept, we show that an EAE captures a superposition of the known low-dimensional dynamics of a reaction-diffusion process. Then, we show that an EAE identifies implicit categorical distinctions in MNIST latent representations, and displays a hierarchical understanding of facial structure on the CelebA dataset, from an "all-human" face to individual-dependent features.

LiDAR point cloud compression is vital for autonomous systems to handle massive data from high-resolution sensors. While learned entropy modeling built upon octree structures yields high compression gains, it faces two critical bottlenecks: 1) prohibitive latency, particularly during decoding, caused by causal, multi-stage context modeling; and 2) a rigid performance-latency trade-off, preventing a single model from adapting to varying constraints. These limitations stem from the tight coupling between the context aggregation backbone and probability prediction. To address this, we propose PACE, a new framework that reformulates ancestral context aggregation as a non-causal backbone and confines causality to a lightweight, stage-scalable predictor, eliminating repetitive backbone executions and reducing computational overhead. The predictor supports an arbitrary number of prediction stages, enabling seamless adaptation across diverse performance-latency trade-offs without reloading parameters. Experiments demonstrate that PACE sets a new state-of-the-art in compression efficiency, achieving notable BD-BR savings and reducing decoding latency by over 90% in autoregressive mode, making it attractive for practical applications.

Sparse Autoencoders (SAEs) decompose language-model activations into sparse, interpretable features, but standard encoders usually treat the latent dictionary as a flat set of independent coordinates, leaving hierarchy and feature interactions to emerge only implicitly. We propose KronSAE, a design that factorizes the latent space into heads and forms post-latent features as pairwise compositions of lower-dimensional pre-latents using mAND, a differentiable AND-like interaction. This imposes a compositional co-activation prior while remaining compatible with standard SAE objectives and variants such as TopK, Matryoshka, and Switch SAEs. KronSAE matches strong baselines on the EV-FLOPs frontier, improves interpretability of the latents, better captures the underlying correlated feature structure, and reduces encoder computational cost as an additional benefit. Code is available at https://github.com/corl-team/kronsae.