Rectifying Gradient Trajectories: A Hierarchical Geometric Framework with Structural Constraints for Few-Shot EEG Adaptation

Few-shot EEG domain adaptation faces severe data heterogeneity and optimization instability. While prevalent "symmetric alignment" methods typically seek a compromised shared subspace, they often falter when domain discrepancies are vast, leading to mutual interference and negative transfer. To overcome this, we abandon the pursuit of a middle ground and advocate for a "target-to-source alignment" strategy that explicitly maps target distributions onto the rigid source manifold. To regulate the optimization dynamics of this asymmetric mapping, we present H-GSC (Hierarchical Geometric Framework with Structural Constraints). Specifically, H-GSC employs Feature-Space Guidance (FSG) as a geometric pre-conditioner to reorient adaptation gradients, and Hierarchical Gradient Alignment (H-GA) to filter destructive interference by strictly prioritizing source discriminability. To prevent manifold collapse, we preserve intrinsic manifold structure via a dual-constraint regularization scheme (synergizing Masked Structural Consistency with semantic anchors) and ensure robust early stopping with a Metric-Decoupled Validator. Theoretical analysis confirms that H-GSC aligns with generalization bound minimization. Extensive experiments on CHB-MIT demonstrate state-of-the-art performance (79.54% AUC). Crucially, in rigorous joint cross-dataset scenarios where prior methods suffer from negative transfer, H-GSC achieves a significant 9.65 pp AUC gain, validating that our rectified trajectory effectively bridges vast distributional shifts for scalable clinical deployment.