arXiv Machine Learning By Alessio Colombo, Melika Ayoughi

Geometry-Aware Hyperbolic Residual Quantization

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The paper introduces Geometry‑Aware Hyperbolic Residual Quantization, a method that adapts residual vector quantization to hyperbolic space while preserving its telescoping structure. It achieves this by using Hyperbolic Residual Aggregation in the forward pass and a discounted Hyperbolic Straight‑Through Estimator in the backward pass, thereby avoiding geometric inconsistencies and unstable gradients. Experiments on hierarchical prediction, recommendation, image tokenization, and neural audio coding demonstrate improved stability and structural organization of hyperbolic residual codes, with a noted trade‑off between compression efficiency and hierarchical organization.

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