# Training-Free Dual Hyperbolic Adapters for Better Cross-Modal Reasoning

arXiv: https://arxiv.org/abs/2512.08820 · HTML: https://mlsanity.com/paper/2512.08820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 59 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 12 of 12)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [CLIP-Adapter: Better Vision-Language Models with Feature Adapters](https://mlsanity.com/paper/2110.04544/) (2021)
- [Visual Classification via Description from Large Language Models](https://mlsanity.com/paper/2210.07183/) (2022)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Not All Features Matter: Enhancing Few-shot CLIP with Adaptive Prior Refinement](https://mlsanity.com/paper/2304.01195/) (2023)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [PLOT: Prompt Learning with Optimal Transport for Vision-Language Models](https://mlsanity.com/paper/2210.01253/) (2022)
- [Probing BERT in Hyperbolic Spaces](https://mlsanity.com/paper/2104.03869/) (2021)
- [HyperText: Endowing FastText with Hyperbolic Geometry](https://mlsanity.com/paper/2010.16143/) (2020)
- [Enhancing Vision-Language Few-Shot Adaptation with Negative Learning](https://mlsanity.com/paper/2403.12964/) (2024)
- [Cross-Modal Few-Shot Learning with Second-Order Neural Ordinary Differential Equations](https://mlsanity.com/paper/2412.15813/) (2024)

## Abstract (arXiv)

Recent research in Vision-Language Models (VLMs) has significantly advanced our capabilities in cross-modal reasoning. However, existing methods suffer from performance degradation with domain changes or require substantial computational resources for fine-tuning in new domains. To address this issue, we develop a new adaptation method for large vision-language models, called textitTraining-free Dual Hyperbolic Adapters (T-DHA). We characterize the vision-language relationship between semantic concepts, which typically has a hierarchical tree structure, in the hyperbolic space instead of the traditional Euclidean space. Hyperbolic spaces exhibit exponential volume growth with radius, unlike the polynomial growth in Euclidean space. We find that this unique property is particularly effective for embedding hierarchical data structures using the Poincar'e ball model, achieving significantly improved representation and discrimination power. Coupled with negative learning, it provides more accurate and robust classifications with fewer feature dimensions. Our extensive experimental results on various datasets demonstrate that the T-DHA method significantly outperforms existing state-of-the-art methods in few-shot image recognition and domain generalization tasks.