# EEG-Based Multimodal Learning via Hyperbolic Mixture-of-Curvature Experts

arXiv: https://arxiv.org/abs/2604.12579 · HTML: https://mlsanity.com/paper/2604.12579/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 71 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Efficient Low-rank Multimodal Fusion with Modality-Specific Factors](https://mlsanity.com/paper/1806.00064/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [MM-DFN: Multimodal Dynamic Fusion Network for Emotion Recognition in Conversations](https://mlsanity.com/paper/2203.02385/) (2022)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [SalientSleepNet: Multimodal Salient Wave Detection Network for Sleep Staging](https://mlsanity.com/paper/2105.13864/) (2021)
- [Multimodal Multi-loss Fusion Network for Sentiment Analysis](https://mlsanity.com/paper/2308.00264/) (2023)
- [HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts](https://mlsanity.com/paper/2505.24722/) (2025)
- [GA2MIF: Graph and Attention Based Two-Stage Multi-Source Information Fusion for Conversational Emotion Detection](https://mlsanity.com/paper/2207.11900/) (2022)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Hypergraph Multi-Modal Learning for EEG-based Emotion Recognition in Conversation](https://mlsanity.com/paper/2502.21154/) (2025)
- [Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold](https://mlsanity.com/paper/2307.04514/) (2023)
- [Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds](https://mlsanity.com/paper/2510.27391/) (2025)

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

- [Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation](https://mlsanity.com/paper/2609.35128/) (2026)
- [Constant-Curvature Sliced Gromov-Wasserstein for Heterogeneous Cross-Curvature Alignment](https://mlsanity.com/paper/2610.07218/) (2026)

## Abstract (arXiv)

Electroencephalography (EEG)-based multimodal learning integrates brain signals with complementary modalities to improve mental state assessment, providing great clinical potential. The effectiveness of such paradigms largely depends on the representation learning on heterogeneous modalities. For EEG-based paradigms, one promising approach is to leverage their hierarchical structures, as recent studies have shown that both EEG and associated modalities (e.g., facial expressions) exhibit hierarchical structures reflecting complex cognitive processes. However, Euclidean embeddings struggle to represent these hierarchical structures due to their flat geometry, while hyperbolic spaces, with their exponential growth property, are naturally suited for them. In this work, we propose EEG-MoCE, a novel hyperbolic mixture-of-curvature experts framework designed for multimodal neurotechnology. EEG-MoCE assigns each modality to an expert in a learnable-curvature hyperbolic space, enabling adaptive modeling of its intrinsic geometry. A curvature-aware fusion strategy then dynamically weights experts, emphasizing modalities with richer hierarchical information. Extensive experiments on benchmark datasets demonstrate that EEG-MoCE achieves state-of-the-art performance, including emotion recognition, sleep staging, and cognitive assessment. Code is available at https://github.com/zhourunhe/EEG-MoCE.