# H2em: Learning Hierarchical Hyperbolic Embeddings for Compositional Zero-Shot Learning

arXiv: https://arxiv.org/abs/2512.20029 · HTML: https://mlsanity.com/paper/2512.20029/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 59 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 30 of 47)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Prompt Distribution Learning](https://mlsanity.com/paper/2205.03340/) (2022)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Task-Driven Modular Networks for Zero-Shot Compositional Learning](https://mlsanity.com/paper/1905.05908/) (2019)
- [Learning Graph Embeddings for Compositional Zero-shot Learning](https://mlsanity.com/paper/2102.01987/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Open World Compositional Zero-Shot Learning](https://mlsanity.com/paper/2101.12609/) (2021)
- [Symmetry and Group in Attribute-Object Compositions](https://mlsanity.com/paper/2004.00587/) (2020)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Learning to Compose Soft Prompts for Compositional Zero-Shot Learning](https://mlsanity.com/paper/2204.03574/) (2022)
- [Learning Graph Embeddings for Open World Compositional Zero-Shot Learning](https://mlsanity.com/paper/2105.01017/) (2021)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [KG-SP: Knowledge Guided Simple Primitives for Open World Compositional Zero-Shot Learning](https://mlsanity.com/paper/2205.06784/) (2022)
- [Learning Attention as Disentangler for Compositional Zero-shot Learning](https://mlsanity.com/paper/2303.15111/) (2023)
- [Troika: Multi-Path Cross-Modal Traction for Compositional Zero-Shot Learning](https://mlsanity.com/paper/2303.15230/) (2023)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)

## Built on by (most cited first, 1 of 1)

- [Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation](https://mlsanity.com/paper/2602.20479/) (2026)

## Abstract (arXiv)

Compositional zero-shot learning (CZSL) aims to recognize unseen state-object compositions by generalizing from a training set of their primitives (state and object). Current methods often overlook the rich hierarchical structures, such as the semantic hierarchy of primitives (e.g., apple fruit) and the conceptual hierarchy between primitives and compositions (e.g, sliced apple apple). A few recent efforts have shown effectiveness in modeling these hierarchies through loss regularization within Euclidean space. In this paper, we argue that they fail to scale to the large-scale taxonomies required for real-world CZSL: the space's polynomial volume growth in flat geometry cannot match the exponential structure, impairing generalization capacity. To this end, we propose H2em, a new framework that learns Hierarchical Hyperbolic EMbeddings for CZSL. H2em leverages the unique properties of hyperbolic geometry, a space naturally suited for embedding tree-like structures with low distortion. However, a naive hyperbolic mapping may suffer from hierarchical collapse and poor fine-grained discrimination. We further design two learning objectives to structure this space: a Dual-Hierarchical Entailment Loss that uses hyperbolic entailment cones to enforce the predefined hierarchies, and a Discriminative Alignment Loss with hard negative mining to establish a large geodesic distance between semantically similar compositions. Furthermore, we devise Hyperbolic Cross-Modal Attention to realize instance-aware cross-modal infusion within hyperbolic geometry. Extensive ablations on three benchmarks demonstrate that H2em establishes a new state-of-the-art in both closed-world and open-world scenarios. Our codes will be released.