Abstract / Summary
Abstract Cross-patient EEG seizure detection using Riemannian geometry on the symmetric positive definite (SPD) covariance matrix manifold has consistently underperformed eigenvalue-based features, a finding attributed to inter-subject variability without a specific geometric mechanism. We identify patient-specific manifold polarity as the mechanism: seizure-related covariance shifts point in opposite directions for different patients on the SPD manifold. A previously unreported feature-regime interaction governs method comparisons: polarity prevalence scales with feature dimensionality, not method choice. We validate this across 22 CHB-MIT patients (leave-one-subject-out). In the full-feature regime (336 features), AUC reaches 0.952 with zero polarity inversions. In the low-dimensional regime (8–36 features), Riemannian tangent space projection (0.659 calibrated AUC, 36 features), the A-Gate quantum circuit (0.637 calibrated, 8 features), and minimal eigenvalues (0.628 calibrated, 8 features) are statistically indistinguishable (Wilcoxon p = 0.4358). Polarity was discovered not through classical analysis but through quantum hardware experiments. The A-Gate circuit, a quantum geometric probe with a fixed measurement basis, makes polarity an explicit observable: per-patient AUC below 0.50 directly indicates manifold inversion, because the circuit’s architectural rigidity prevents the adaptive absorption of polarity that flexible classifiers perform silently. Statevector simulation of the same circuit performs worse than noisy hardware, a reversal of the standard assumption that simulation provides an optimistic upper bound. Simulation AUC degrades from 0.460 to 0.386 as input quality improves, because better-conditioned features sharpen polarity-induced amplitude cancellation; hardware shot noise partially breaks this cancellation stochastically, though the benefit diminishes as polarity projections strengthen at longer windows. The divergence is a property of the problem geometry, not measurement error. Manifold polarity, defined as the projection of a patient’s covariance shift vector onto the circuit’s measurement basis, is a continuous geometric quantity whose sign is encoding-dependent and whose magnitude determines measurement reliability. Whether the projection structure generalizes across encoding configurations, and what it reveals about the underlying manifold geometry, are the questions that motivate subsequent work.