HEEGNet: Hyperbolic Embeddings for EEG

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in humancomputer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. While many decoding methods still rely on Euclidean embeddings, recent work has begun exploring hyperbolic geometry for EEG. Hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first empirically demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEG-Net achieves state-of-the-art performance. The code is available at https: //github.com/fightlesliefigt/HEEGNet