Learning the Brain's Dynamics as a Port-Hamiltonian System

Brain-computer interfaces (BCIs) have been widely used in motor rehabilitation, disease diagnosis, and other neural engineering scenarios. However, conventional neural signal decoding algorithms often suffer from limited generalizability and high adaptation costs, motivating recent interest in BCI foundation models. Existing approaches still struggle to jointly achieve general transferability, accurate decoding, and efficient downstream adaptation. We present STEAM, a hierarchical transfer framework that reconciles general-purpose representation learning with paradigm-specific specialization in EEG foundation models. The framework is instantiated as a dual-branch spatio-temporal encoder in which a shared soft mixture-of-experts (SSMoE) module aligns the spatial and temporal branches, allowing complementary representations to exchange information through a compact set of soft slots. Across seven downstream datasets and fourteen evaluation settings, STEAM attains the best average rank among the compared methods at a competitive inference cost measured in FLOPs. Building upon the Stage-I general initialization, the hierarchical pre-training strategy further specializes the model to a target paradigm without retraining from scratch, yielding consistent gains in paradigm-specific decoding accuracy.

Motor imagery electroencephalography (MI-EEG) decoding offers a non-invasive route for post-stroke rehabilitation, but cross-patient use remains difficult because pathological neural reorganization changes task-related EEG dynamics, aperiodic activity, local excitability, cross-regional coordination, and trial-level brain-state context. This makes source-learned MI representations unreliable for unseen patients. To address this problem, we propose CFSPMNet, a cross-patient adaptation framework that models post-stroke MI-EEG as latent neural-state organization. CFSPMNet combines a Fourier-Reorganized State Mamba Network (FRSM) with Shared-Private Prototype Matching (SPPM). FRSM represents each trial as a latent physiological token sequence, reorganizes token states in the Fourier domain, and uses Fourier-derived trial context to guide Mamba state-space propagation. SPPM improves target pseudo-label updating by combining semantic confidence with shared-private physiological consistency, filtering confident but physiologically inconsistent target predictions. Leave-one-subject-out experiments on two stroke MI-EEG datasets show that CFSPMNet outperforms representative CNN-, Transformer-, Mamba-, and adaptation-based baselines, achieving average accuracies of 68.23% on XW-Stroke and 73.33% on 2019-Stroke, with gains of 5.63 and 8.25 percentage points over the strongest competitors. Ablation, sensitivity, feature-alignment, pseudo-label selection, and neurophysiological visualization analyses further support the roles of Fourier-domain token-state reorganization and calibrated pseudo-label updating. These results suggest that latent neural-state modeling can improve rehabilitation-oriented cross-patient BCI decoding. Code is available at https://github.com/wxk1224/CFSPMNet.

Electroencephalography (EEG) is the dominant non-invasive modality for brain-computer interfaces (BCIs), yet reliable decoding of motor imagery is hampered by inter- and intra-individual variability. A recurring claim is that one decoding pipeline, most often a spatial or Riemannian method, is broadly preferable. We test the weakest version of that claim under the most favourable conditions. Using the Mother of All BCI Benchmarks (MOABB) framework, we evaluated 1,056 decoding configurations (feature extractor x scaler x classifier), >340,000 subject-level model fits, across three public left-versus-right motor-imagery datasets (PhysionetMI, 109 participants; Cho2017, 52; Zhou2016, 4) and two frequency bands (8-15 Hz, 8-30 Hz). Every model is fit and tested within a single session of a single participant, the easiest regime, giving every pipeline its best chance. We apply the statistics standard for multi-classifier comparison: Friedman omnibus tests, Nemenyi critical-difference analysis and Wilcoxon signed-rank tests with effect sizes. Covariance tangent-space projection (cov-tgsp) and Common Spatial Patterns (CSP) are the strongest families, but their ordering is dataset-dependent and, on the largest and most heterogeneous cohort (PhysionetMI), statistically indistinguishable (Nemenyi p = 0.27; Kendall's W = 0.11). At the individual level the single best pipeline is optimal for only 35% of PhysionetMI participants, and nonlinear descriptors are best for roughly one third; matching pipeline to participant adds about seven accuracy points over the best fixed choice. The ranking is not an artefact of dimensionality, and classifier and scaler choices are secondary to the feature representation. Even in the easiest regime, no single pipeline dominates: a lower bound on the personalization problem and a quantitative case for participant-aware model selection rather than a universal decoder.