Continuous First, Discrete Later: VQ-VAEs Without Dimensional Collapse

Abstract:While many approaches to improve VQ-VAE performance focus on codebook size and utilization, the effect of dimensional collapse, where trained VQ-VAE representations live in an extremely low-dimensional subspace (1-2% of full rank), remains unaddressed. We show theoretically and empirically that dimension collapse causes a hard loss lower bound that various codebook improvement techniques fail to surpass. Our analytic framework extends the sequential learning effect of Saxe et al. [2014] by introducing ideas from rate-distortion theory and explains how the latent collapse is caused by the VQ suppressing lower-variance directions. Our theory justifies a simple solution: a "warm-up phase" that trains the model as an (unquantized) autoencoder before introducing VQ. On both synthetic experiments and large-scale image (VQGAN) and audio (WavTokenizer) VQ-VAEs, we show that AE Warm-Up successfully restores representation dimension, leading to lower reconstruction and perceptual loss at the same training budget. Across codebook sizes $K \in$ {$2^{10}, 2^{14}, 2^{16}$}, AE warm-up raises VQGAN codebook effective dimension from 3-5 to 17-19 and reduces rFID by 17-35%; on WavTokenizer at $K \in$ {$2^{13}, 2^{14}$}, it raises codebook dimension from 4 to 17-19 and improves PESQ by 11-14%. We empirically characterize how warm-up duration governs the achievable final loss. In agreement with experiment, our theoretical analysis predicts downstream performance as a function of warm-up length, enabling an adaptive criterion for switching from AE Warm-up to VQ-VAE training.

First two authors contributed equally. Revised to include larger-scale ImageNet-1K experiments

Machine Learning (cs.LG)

arXiv:2605.06870 [cs.LG]

(or arXiv:2605.06870v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.06870 Focus to learn more arXiv-issued DOI via DataCite

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