ArcVQ-VAE: A Spherical Vector Quantization Framework with ArcCosine Additive Margin

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

Vector quantization is central to modern generative modeling pipelines, but large-codebook VQ models often suffer from codebook collapse. We identify encoder drift as a key driver of this failure: as the encoder moves the latent distribution, sparsely updated code vectors can lag behind, lose assignments, and increase quantization error, creating a feedback loop through the straight-through estimator. We propose NSVQ, a non-stationary-aware VQ training strategy that combines a dense non-stationary embedding loss, codebook replacement, and stage-wise encoder freezing. NSVQ first helps the codebook track encoder drift during early training, then freezes the encoder to consolidate the codebook under a fixed latent geometry, and finally reintroduces adversarial refinement. Experiments on ImageNet-1k show that NSVQ improves reconstruction quality while maintaining full codebook utilization. On ImageNet-1k at 128$\times$128 with 65,536 codes, NSVQ reduces rFID from 2.39 to 2.10 compared with SimVQ, while both methods maintain 100% utilization. Additional latent diffusion experiments show that NSVQ also improves downstream ImageNet generation FID.

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.