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 Quantized Variational Autoencoder (VQ-VAE) has become a fundamental framework for learning discrete representations in image modeling. However, VQ-VAE models must tokenize entire images using a finite set of codebook vectors, and this capacity limitation restricts their ability to capture rich and diverse representations. In this paper, we propose ArcCosine Additive Margin VQ-VAE (ArcVQ-VAE), a novel vector quantization framework that introduces a spherical angular-margin prior (SAMP) for the codebook of a conventional VQ-VAE. The proposed SAMP consists of Ball-Bounded Norm Regularization, which constrains all codebook vectors within a time-dependent Euclidean ball, and ArcCosine Additive Margin Loss, which encourages greater angular separability among latent vectors. This formulation promotes more discriminative and uniformly dispersed latent representations within the constrained space, thereby improving effective latent-space coverage and leading to improved codebook utilization. Experimental results on standard image reconstruction and generation tasks show that ArcVQ-VAE achieves competitive performance against baseline models in terms of reconstruction accuracy, representation diversity, and sample quality. The code is available at: https://github.com/goals4292/ArcVQ-VAE
Representation Autoencoders (RAEs) leverage frozen vision foundation models (VFMs) as tokenizer encoders, providing robust high-level representations that facilitate fast convergence and high-quality generation in latent diffusion models. However, freezing the VFM inherently constrains its spatial reconstruction capacity, limiting fine-grained generation and image editing; in contrast, incorporating reconstruction-oriented signals via fine-tuning disrupts the pretrained semantic space and degrades generative fidelity. To address this trade-off, we propose DecQ, a simple yet effective framework for RAEs. Specifically, DecQ introduces lightweight detail-condensing queries that extract fine-grained information from intermediate VFM features through condenser modules. These queries are incorporated into the decoder to support reconstruction and are jointly generated with patch tokens during generative modeling. By aggregating information from both shallow and deep layers, DecQ effectively mitigates the reconstruction--generation trade-off, improving both reconstruction quality and generative performance. Our experiments demonstrate that: (1) with only 8 additional queries and 3.9% extra computation, DecQ improves reconstruction over the frozen DINOv2-based RAE, increasing PSNR from 19.13 dB to 22.76 dB; and (2) for generative modeling, DecQ achieves 3.3× faster convergence than RAE, attaining an FID of 1.41 without guidance and 1.05 with guidance.
Residual Vector Quantization turns continuous representations into discrete, multi-level token sequences. Yet most methods operate in Euclidean space, despite the coarse-to-fine structure of the resulting codes and the latent hierarchies present in many data domains. Hyperbolic geometry offers a natural alternative for hierarchical representations, but naive hyperbolic extensions introduce geometric inconsistencies: non-associative hyperbolic addition prevents consistent residual aggregation, while standard straight-through gradient estimation ignores the geometry of the latent space. We propose a geometry-aware hyperbolic residual quantization that addresses these issues in both the forward and backward passes. In the forward pass, Hyperbolic Residual Aggregation restores the telescoping behavior of residual quantization on the Poincare ball. In the backward pass, a discounted Hyperbolic Straight-Through Estimator routes the reconstruction gradient through the quantizer as a single geometric block, avoiding unstable recursive gradient transport across residual stages. Evaluations on hierarchical prediction, recommendation, image tokenization, and neural audio coding tasks show that our method improves the stability and structural organization of hyperbolic residual codes over naive hyperbolic baselines. At the same time, we observe a clear structure-compression trade-off: Euclidean residual quantization remains preferable for pure compression, while geometry-aware hyperbolic quantization is most useful for hierarchically organized discrete latent spaces.