Abstract
With the daily influx of 3D data on the internet, text-3D retrieval has gained increasing attention. However, current methods face two major challenges: Hierarchy Representation Collapse (HRC) and Redundancy-Induced Saliency Dilution (RISD). HRC compresses abstract-to-specific and whole-to-part hierarchies in Euclidean embeddings, while RISD averages noisy fragments, obscuring critical semantic cues and diminishing the model's ability to distinguish hard negatives. To address these challenges, we introduce the Hyperbolic Hierarchical Alignment Reasoning Network (H\(^\{2\}\)ARN) for text-3D retrieval. H\(^\{2\}\)ARN embeds both text and 3D data in a Lorentz-model hyperbolic space, where exponential volume growth inherently preserves hierarchical distances. A hierarchical ordering loss constructs a shrinking entailment cone around each text vector, ensuring that the matched 3D instance falls within the cone, while an instance-level contrastive loss jointly enforces separation from non-ma