Vector-Quantized Variational Autoencoders (VQVAEs) have enabled strong performance in generative modeling by mapping continuous data to learnable codes. In this work, we identify a surprising yet consistent phenomenon that we term dimensional collapse: despite using high-dimensional embeddings, VQVAEs tend to compress their representations into a much smaller subspace, typically only 4 to 10 dimensions. We provide an in-depth analysis of this phenomenon and reveal its relation to model performance and learning dynamics. Interestingly, VQVAEs naturally gravitate toward this low-dimensional regime, and enforcing higher-dimensional usage (e.g., via rank regularization) could lead to degraded performance. To overcome this low-dimensionality limitation, we propose Divide-and-Conquer VQ (DCVQ), which partitions the latent space into multiple low-dimensional subspaces, each quantized independently. By design, each subspace respects the model's preference for low dimensionality, while their combination expands the overall capacity. Our results show that DCVQ overcomes the inherent dimensional bottleneck and achieves improved reconstruction quality across image datasets.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds.

Self-supervised learning (SSL) has rapidly advanced in recent years, approaching the performance of its supervised counterparts through the extraction of representations from unlabeled data. However, dimensional collapse, where a few large eigenvalues dominate the eigenspace, poses a significant obstacle for SSL. When dimensional collapse occurs on features (e.g.

Graph Collaborative Filtering (GCF) is widely used in personalized recommendation systems. However, GCF suffers from a fundamental problem where features tend to occupy the embedding space inefficiently (by spanning only a low-dimensional subspace).

Contrastive learning has emerged as a powerful method in deep learning, excelling at learning effective representations through contrasting samples from different distributions. However, dimensional collapse, where embeddings converge into a lower-dimensional space, poses a significant challenge, especially in semi-supervised and self-supervised setups. In this paper, we first identify a critical learning-rate threshold, beyond which standard contrastive losses converge to collapsed solutions. Building on these insights, we propose CLOP, a novel semi-supervised loss function designed to prevent dimensional collapse by promoting the formation of orthogonal linear subspaces among class embeddings. Through extensive experiments on real and synthetic datasets, we demonstrate that CLOP improves performance in image classification and object detection tasks while also exhibiting greater stability across different learning rates and batch sizes.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality.