Regional Simplicial Decomposition and Post-Inversion Empirical Bayes Calibration for Zero-Shot and Few-Shot Topological Neurodynamics in Multichannel EEG
- 1Independent Researcher, Jerusalem, Israel
Abstract
Zero-lag volume conduction and inter-subject baseline shift remain two primary mathematical obstacles to deploying algebraic topological data analysis (TDA) in real-time brain-computer interfaces (BCIs). While Vietoris-Rips filtration over the finite field F_2 induced by Imaginary Coherency (ImCoh) guarantees exact invariance to instantaneous volume conduction, scaling global 20-channel minimum spanning tree (MST) persistence from small homogeneous benchmarks (N=5, AUC=0.764) to heterogeneous cohorts (N=20, 1,160 epochs) causes severe accuracy degradation (AUC=0.650) and sign inversions in 20% of subjects (4/20). In this paper, we prove that this degradation stems from three mechanisms: (i) zero-lag denominator inflation under high-amplitude standing waves, (ii) sub-epoch phase cancellation across 4-second windows, and (iii) combinatorial spatial MST dilution across anterior artifact channels. We introduce the TRR 3.0 Stage 7 architecture to resolve all three bottlenecks. First, we formulate Sub-Window Rectified and Lag-Orthogonalized Imaginary Coherency (rLagImCoh), proving that it preserves exact zero-lag isolation while preventing standing-wave denominator suppression. Second, we introduce an anatomical simplicial decomposition partitioning the 10-20 montage into an 8-channel occipito-parietal complex and a 12-channel anterior reference complex, reducing 2-simplex boundary complexity by 4.13x. Third, we derive a strictly causal Post-Inversion Empirical Bayes Stein Shrinkage Fusion protocol under Leave-One-Subject-Out Cross-Validation (LOSO-CV) that prevents covariance-inversion gate cancellation. Audited across N=20 subjects (1,160 epochs) from the PhysioNet EEGBCI database, the pure F_2 topological spatial gradient elevates zero-shot (0 s) accuracy from 0.650 to 0.837 (mean within-subject AUC = 0.927) and eliminates all subject polarity inversions. Under causal prefix calibration, Pure Topological TRR scales monotonically in pooled accuracy to 0.874 at 22 s (k=10) and 0.895 at 60 s, while the Hybrid Spectral-Topological TRR architecture achieves AUC = 0.869 at zero-shot (0 s), 0.897 at 8 s, 0.928 at 22 s, and 0.954 at 60 s.
Related
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BibTeX
@misc{weinberg2026regional,
title = {{Regional Simplicial Decomposition and Post-Inversion Empirical Bayes Calibration for Zero-Shot and Few-Shot Topological Neurodynamics in Multichannel EEG}},
author = {Ronen Weinberg},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23504184},
url = {https://zenodo.org/records/23504184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regional Simplicial Decomposition and Post-Inversion Empirical Bayes Calibration for Zero-Shot and Few-Shot Topological Neurodynamics in Multichannel EEG
AU - Ronen Weinberg
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23504184
UR - https://zenodo.org/records/23504184
AB - Zero-lag volume conduction and inter-subject baseline shift remain two primary mathematical obstacles to deploying algebraic topological data analysis (TDA) in real-time brain-computer interfaces (BCIs). While Vietoris-Rips filtration over the finite field F_2 induced by Imaginary Coherency (ImCoh) guarantees exact invariance to instantaneous volume conduction, scaling global 20-channel minimum spanning tree (MST) persistence from small homogeneous benchmarks (N=5, AUC=0.764) to heterogeneous cohorts (N=20, 1,160 epochs) causes severe accuracy degradation (AUC=0.650) and sign inversions in 20% of subjects (4/20). In this paper, we prove that this degradation stems from three mechanisms: (i) zero-lag denominator inflation under high-amplitude standing waves, (ii) sub-epoch phase cancellation across 4-second windows, and (iii) combinatorial spatial MST dilution across anterior artifact channels. We introduce the TRR 3.0 Stage 7 architecture to resolve all three bottlenecks. First, we formulate Sub-Window Rectified and Lag-Orthogonalized Imaginary Coherency (rLagImCoh), proving that it preserves exact zero-lag isolation while preventing standing-wave denominator suppression. Second, we introduce an anatomical simplicial decomposition partitioning the 10-20 montage into an 8-channel occipito-parietal complex and a 12-channel anterior reference complex, reducing 2-simplex boundary complexity by 4.13x. Third, we derive a strictly causal Post-Inversion Empirical Bayes Stein Shrinkage Fusion protocol under Leave-One-Subject-Out Cross-Validation (LOSO-CV) that prevents covariance-inversion gate cancellation. Audited across N=20 subjects (1,160 epochs) from the PhysioNet EEGBCI database, the pure F_2 topological spatial gradient elevates zero-shot (0 s) accuracy from 0.650 to 0.837 (mean within-subject AUC = 0.927) and eliminates all subject polarity inversions. Under causal prefix calibration, Pure Topological TRR scales monotonically in pooled accuracy to 0.874 at 22 s (k=10) and 0.895 at 60 s, while the Hybrid Spectral-Topological TRR architecture achieves AUC = 0.869 at zero-shot (0 s), 0.897 at 8 s, 0.928 at 22 s, and 0.954 at 60 s.
ER -