Geometric and Spectral Characterization of 3D Point Cloud Representations in Contrastive and Asymmetric Self-Supervised Learning

Despite the empirical success of self-supervised learning (SSL), the geometric structure of the representations it learns remains insufficiently understood, particularly for 3D point clouds. We present a controlled geometric and spectral analysis of contrastive and asymmetric SSL paradigms under identical architectural and training conditions. Rather than focusing solely on downstream accuracy, we examine intrinsic properties of the learned embeddings through alignment-uniformity trade-offs, class-aware separation, effective dimensionality, spectral decay, feature redundancy, and robustness under controlled geometric perturbations. Our analysis reveals consistent structural differences between objectives: contrastive learning produces more uniformly distributed and semantically organized embeddings, whereas asymmetric methods enforce stronger positive alignment at the cost of reduced global separation and increased redundancy. Robustness experiments further show distinct stability behaviors when generalizing to unseen categories under geometric noise. These results demonstrate that latent space geometry, beyond benchmark performance alone, critically shapes semantic organization and robustness in self-supervised 3D representation learning.