# A Fully Hyperbolic Neural Model for Hierarchical Multi-Class Classification

arXiv: https://arxiv.org/abs/2010.02053 · HTML: https://mlsanity.com/paper/2010.02053/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 23 of 23)

- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Modeling Fine-Grained Entity Types with Box Embeddings](https://mlsanity.com/paper/2101.00345/) (2021)
- [Hyperbolic Deep Reinforcement Learning](https://mlsanity.com/paper/2210.01542/) (2022)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Fine-grained Entity Typing via Label Reasoning](https://mlsanity.com/paper/2109.05744/) (2021)
- [Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2110.13475/) (2021)
- [HyperExpan: Taxonomy Expansion with Hyperbolic Representation Learning](https://mlsanity.com/paper/2109.10500/) (2021)
- [Extracting Event Temporal Relations via Hyperbolic Geometry](https://mlsanity.com/paper/2109.05527/) (2021)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classification](https://mlsanity.com/paper/2306.14822/) (2023)
- [Generative Entity Typing with Curriculum Learning](https://mlsanity.com/paper/2210.02914/) (2022)
- [Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings](https://mlsanity.com/paper/2505.18973/) (2025)
- [Modeling Label Correlations for Ultra-Fine Entity Typing with Neural Pairwise Conditional Random Field](https://mlsanity.com/paper/2212.01581/) (2022)
- [Augmenting the User-Item Graph with Textual Similarity Models](https://mlsanity.com/paper/2109.09358/) (2021)
- [Hyperbolic Disentangled Representation for Fine-Grained Aspect Extraction](https://mlsanity.com/paper/2112.09215/) (2021)
- [Hyperbolic recurrent neural network as the first type of non-Euclidean neural quantum state ansatz](https://mlsanity.com/paper/2505.22083/) (2025)
- [Type-enriched Hierarchical Contrastive Strategy for Fine-Grained Entity Typing](https://mlsanity.com/paper/2208.10081/) (2022)
- [Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces](https://mlsanity.com/paper/2209.05635/) (2022)
- [New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures](https://mlsanity.com/paper/2604.24337/) (2026)
- [Two-dimensional Hyperbolic RNN Neural Quantum State](https://mlsanity.com/paper/2606.25600/) (2026)
- [Graceful Degradation and Related Fields](https://mlsanity.com/paper/2106.11119/) (2021)
- [sHGCN: Simplified hyperbolic graph convolutional neural networks](https://mlsanity.com/paper/2506.14438/) (2025)

## Abstract (arXiv)

Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of symbolic data. However, it is not clear how to integrate hyperbolic components into downstream tasks. This is the first work that proposes a fully hyperbolic model for multi-class multi-label classification, which performs all operations in hyperbolic space. We evaluate the proposed model on two challenging datasets and compare to different baselines that operate under Euclidean assumptions. Our hyperbolic model infers the latent hierarchy from the class distribution, captures implicit hyponymic relations in the inventory, and shows performance on par with state-of-the-art methods on fine-grained classification with remarkable reduction of the parameter size. A thorough analysis sheds light on the impact of each component in the final prediction and showcases its ease of integration with Euclidean layers.