Stiefel Manifold Routing Boosts Cross-Subject EEG Accuracy by 5-6%

A team of researchers from academia introduces dynamic Stiefel routing, a novel method for cross-domain EEG decoding that addresses a fundamental challenge: covariance matrices from different subjects occupy distinct regions of the symmetric positive definite (SPD) manifold. Existing domain adaptation methods either require target-domain calibration data or learn subject-specific components that fail to generalize. The proposed solution uses a pool of K expert projection filters on the Stiefel manifold, each specialized for a different region of the SPD manifold. A cross-attention mechanism routes each input covariance to the most appropriate filter, adapting the subspace projection per sample.

The paper identifies a critical degeneracy: a naive implementation collapses to simple ensemble averaging, indistinguishable from a single fixed filter. To break this, the team introduces three structural properties: a symmetric anchor that removes proximity bias among experts, a frozen domain-discriminative query encoder that decouples routing from task optimization, and a decoupled key alignment loss that trains expert keys toward stable domain attractors. This produces the first genuinely committed and domain-structured routing on SPD manifolds. Results show consistent balanced accuracy gains of 5-6% on three EEG datasets, with alignment strategy determined automatically by a single data-driven rule—no dataset-specific hyperparameter search needed.