Rethinking Spatial Inductive Bias in EEG Transformers: A Geodesic Approach

The generalization capacity of deep learning models depends heavily on embedding the correct inductive bias for the geometry of the underlying data. EEG electrodes are distributed over a near-spherical scalp surface whose natural metric is geodesic distance, yet existing spatial positional encoding schemes for EEG Transformers universally rely on Euclidean or coordinate-decomposed assumptions, creating a systematic mismatch with the true geometry. We provide a rigorous theoretical analysis of this mismatch, proving that several widely adopted encoding families fail to satisfy rotational invariance on the sphere, each with a quantifiable error bound. Building on this analysis, we propose a unified geometric positional encoding framework with two complementary components: one that constructs rotation encodings directly from geodesic distance and achieves exact rotational invariance by design, and one that introduces an attention bias built on a geodesic kernel whose positive-definiteness follows from classical results on spherical harmonic analysis. Across a diverse set of EEG downstream tasks, the resulting framework yields consistent gains over strong existing baselines, and our analysis further clarifies why geometric correctness in positional encoding matters for cross-subject generalization. Code is available at https://anonymous.4open.science/r/georope/.