Addressing Representation Collapse in Vector Quantized Models with One Linear Layer

Abstract: Vector Quantization (VQ) is a widely used method for converting continuous representations into discrete codes, which has become fundamental in unsupervised representation learning and latent generative models. However, VQ models are often hindered by the problem of representation collapse in the latent space, which leads to low codebook utilization and limits the scalability of the codebook for large-scale training. Existing methods designed to mitigate representation collapse typically reduce the dimensionality of latent space at the expense of model capacity, which do not fully resolve the core issue. In this study, we conduct a theoretical analysis of representation collapse in VQ models and identify its primary cause as the disjoint optimization of the codebook, where only a small subset of code vectors are updated through gradient descent. To address this issue, we propose \textbf{SimVQ}, a novel method which reparameterizes the code vectors through a linear transformation layer based on a learnable latent basis. This transformation optimizes the \textit{entire linear space} spanned by the codebook, rather than merely updating \textit{the code vector} selected by the nearest-neighbor search in vanilla VQ models. Although it is commonly understood that the multiplication of two linear matrices is equivalent to applying a single linear layer, our approach works surprisingly well in resolving the collapse issue in VQ models with just one linear layer. We validate the efficacy of SimVQ through extensive experiments across various modalities, including image and audio data with different model architectures. Our code is available at \url{https://github.com/youngsheen/SimVQ}.

• The paper introduces SimVQ, which addresses representation collapse in VQ models using a single, efficient linear transformation layer.
• It reparameterizes code vectors without reducing latent dimensionality, ensuring nearly full codebook utilization across various codebook sizes.
• Empirical results demonstrate superior performance, including lower FID scores on ImageNet and improved reconstruction across modalities.

Addressing Representation Collapse in Vector Quantized Models with One Linear Layer: A Technical Overview

In the context of unsupervised representation learning and latent generative models, vector quantization (VQ) is pivotal for transforming continuous datasets into discrete codes. Despite its notable achievements, VQ models encounter significant challenges, particularly the representation collapse issue. This paper addresses the representation collapse in VQ models by introducing a novel and efficient technique, SimVQ, which leverages a linear transformation layer.

SimVQ tackles the representation collapse problem without the drawbacks associated with existing methods, such as reduced latent space dimensionality. Representation collapse is characterized by low codebook utilization, resulting from the disjoint optimization of codebooks. The paper's theoretical analysis identifies it as the main cause, where only a fraction of the codebook is activated and updated during training, leading to suboptimal scalability.

SimVQ enhances the traditional VQ approach by reparameterizing the code vectors using a linear transformation layer defined by a learnable latent basis. This method is designed to optimize the latent space spanned by the codebook, thus overcoming the limitations of merely optimizing individual code vectors. Unlike traditional VQ models or other strategies that attempt to alleviate collapse by shrinking latent dimensions, SimVQ maintains model capacity and adapts effectively to varying codebook sizes.

Empirical evidence is provided through extensive experimentation across modalities, including image and audio datasets. SimVQ consistently achieves nearly full codebook utilization, irrespective of size, and establishes superior state-of-the-art performance benchmarks on reconstruction tasks. For instance, in the ImageNet dataset, SimVQ achieves a reduced FID score compared to existing models, demonstrating its effectiveness across different codebook sizes.

SimVQ's adaptability underscores its potential utility in various machine learning contexts. It ensures nearly complete codebook utilization, efficiently managing large-scale data without compromising model capacity. Furthermore, it addresses theoretical aspects of representation collapse with practical implications for improving VQ model architectures.

The research suggests possible future routes for expansion in several key areas. It opens pathways for further exploration of latent space transformations, specifically how simple linear transformations can lead to more sophisticated model improvements. Additionally, the general approach of SimVQ could potentially be extended to other forms of representation learning and quantization challenges, further improving efficiency and scalability in machine learning models.

This methodological advancement provides a significant stride in resolving representation collapse in VQ models, positioning SimVQ as a broadly applicable solution to enhance the performance of unsupervised learning frameworks. The practicality of implementing a single linear transformation phase in VQ models presents a compelling case for its integration into future VQ-based architectures and research endeavors.