发表机构
Universiteit van Amsterdam（阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对残差量化在欧几里得空间忽视层次结构的问题，提出几何感知双曲残差量化，通过前向聚合与后向梯度路由提升稳定性，在层次任务中优于双曲基线，但纯压缩仍以欧氏方法为佳。
AI 中文摘要
残差向量量化将连续表示转换为离散的多级令牌序列。然而，尽管生成的编码具有从粗到细的结构，且许多数据域中存在潜在层次结构，大多数方法仍在欧几里得空间中操作。双曲几何为层次表示提供了一种自然的替代方案，但朴素的双曲扩展引入了几何不一致性：非结合的双曲加法阻碍了一致的残差聚合，而标准的直通梯度估计忽略了潜在空间的几何结构。我们提出了一种几何感知的双曲残差量化方法，在前向和后向传播中均解决了这些问题。在前向传播中，双曲残差聚合恢复了庞加莱球上残差量化的伸缩行为。在后向传播中，折扣双曲直通估计器将重建梯度作为单个几何块通过量化器路由，避免了跨残差阶段的不稳定递归梯度传输。在层次预测、推荐、图像令牌化和神经音频编码任务上的评估表明，与朴素的双曲基线相比，我们的方法提高了双曲残差编码的稳定性和结构组织性。同时，我们观察到一个清晰的结构-压缩权衡：欧几里得残差量化在纯压缩方面仍然更优，而几何感知的双曲量化对于层次组织的离散潜在空间最为有用。
英文摘要
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.
Comments14-page main paper (30 pages total with references and appendix), 3 figures, 8 tables. Accepted at the Beyond Euclidean Workshop, ECCV 2026 (Oral)
