# Hyperbolic Multimodal Continual Learning

arXiv: https://arxiv.org/abs/2608.09572 · HTML: https://mlsanity.com/paper/2608.09572/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 64 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 30 of 45)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Boosting Continual Learning of Vision-Language Models via Mixture-of-Experts Adapters](https://mlsanity.com/paper/2403.11549/) (2024)
- [VAST: A Vision-Audio-Subtitle-Text Omni-Modality Foundation Model and Dataset](https://mlsanity.com/paper/2305.18500/) (2023)
- [ImageBind-LLM: Multi-modality Instruction Tuning](https://mlsanity.com/paper/2309.03905/) (2023)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models](https://mlsanity.com/paper/2303.06628/) (2023)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [What to align in multimodal contrastive learning?](https://mlsanity.com/paper/2409.07402/) (2024)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Continual Vision-Language Representation Learning with Off-Diagonal Information](https://mlsanity.com/paper/2305.07437/) (2023)
- [Recent Advances of Multimodal Continual Learning: A Comprehensive Survey](https://mlsanity.com/paper/2410.05352/) (2024)
- [Make Continual Learning Stronger via C-Flat](https://mlsanity.com/paper/2404.00986/) (2024)

## Built on by (most cited first, 2 of 2)

- [Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI](https://mlsanity.com/paper/2609.17969/) (2026)
- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)

## Abstract (arXiv)

Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities. Despite this progress, how such representations behave under continual learning poses fundamentally different challenges that remain underexplored. This work provides a geometric perspective on this problem and establishes a theoretical foundation for representation preservation in hyperbolic space, showing that preventing forgetting requires cross-modal invariance under a shared hyperbolic isometry. We further show that forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion, motivating preservation of both cross-modal relational structure and hierarchical geometry. Guided by these insights, a principled continual learning framework is derived that preserves essential geometric structure while allowing effective adaptation to new tasks. Experiments on continual multimodal benchmarks corroborate the effectiveness of the proposed approach.