_version_ 1866901984402997248
author Rodriguez, Rod
author_facet Rodriguez, Rod
contents <p>This paper presents the first systematic application of Riemannian manifold analysis to the study of dynamical transitions in human EEG covariance structure. Using the affine-invariant metric on symmetric positive-definite matrices, we demonstrate that multichannel EEG covariance evolves through metastable geometric phases—discrete quasi-stable states separated by abrupt transitions—during sustained attention tasks. Across 20 subjects and 40 recording sessions from the publicly available COG-BCI dataset, plus an independent 60-minute driving simulation, we document heavy-tailed speed distributions (Fisher combined p = 7.32 × 10⁻8), 2.21-fold enrichment of dimensionality changes at transition boundaries (90% replication), and a dissociation between stochastic transition timing and deterministic regime identity consistent with Kramers escape theory. Geometric speed increases monotonically with working memory load and correlates modestly with reaction times, establishing functional relevance without circularity. These findings connect to recent geometric analyses of transformer neural networks, suggesting that metastable phase structure may be a convergent computational architecture across biological and artificial information-processing systems. All analyses use publicly available datasets and standard open-source tools.</p>
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id zenodo_https___doi_org_10_5281_zenodo_19043484
institution Zenodo
language
publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Metastable Geometric Phase Structure in Human EEG: Riemannian Manifold Analysis of Covariance Dynamics During Sustained Attention
Rodriguez, Rod
metastability
Riemannian geometry
EEG
covariance matrices
symmetric positive-definite manifold
sustained attention
brain states
manifold speed
effective rank
Kramers escape theory
phase transitions
psychomotor vigilance task
geometric deep learning
transformer neural networks
brain-computer interface
Cognitive Neuroscience
Cognitive neuroscience
Cognitive Neuroscience
Cognitive Neuroscience/instrumentation
Cognitive Neuroscience/methods
Computational Neuroscience
Signal Processing
Differential Geometry
Brain-Computer Interfaces
Brain-Computer Interfaces
Dynamical systems
Dynamical Systems
Geometric Contrast Imaging
<p>This paper presents the first systematic application of Riemannian manifold analysis to the study of dynamical transitions in human EEG covariance structure. Using the affine-invariant metric on symmetric positive-definite matrices, we demonstrate that multichannel EEG covariance evolves through metastable geometric phases—discrete quasi-stable states separated by abrupt transitions—during sustained attention tasks. Across 20 subjects and 40 recording sessions from the publicly available COG-BCI dataset, plus an independent 60-minute driving simulation, we document heavy-tailed speed distributions (Fisher combined p = 7.32 × 10⁻8), 2.21-fold enrichment of dimensionality changes at transition boundaries (90% replication), and a dissociation between stochastic transition timing and deterministic regime identity consistent with Kramers escape theory. Geometric speed increases monotonically with working memory load and correlates modestly with reaction times, establishing functional relevance without circularity. These findings connect to recent geometric analyses of transformer neural networks, suggesting that metastable phase structure may be a convergent computational architecture across biological and artificial information-processing systems. All analyses use publicly available datasets and standard open-source tools.</p>
title Metastable Geometric Phase Structure in Human EEG: Riemannian Manifold Analysis of Covariance Dynamics During Sustained Attention
topic metastability
Riemannian geometry
EEG
covariance matrices
symmetric positive-definite manifold
sustained attention
brain states
manifold speed
effective rank
Kramers escape theory
phase transitions
psychomotor vigilance task
geometric deep learning
transformer neural networks
brain-computer interface
Cognitive Neuroscience
Cognitive neuroscience
Cognitive Neuroscience
Cognitive Neuroscience/instrumentation
Cognitive Neuroscience/methods
Computational Neuroscience
Signal Processing
Differential Geometry
Brain-Computer Interfaces
Brain-Computer Interfaces
Dynamical systems
Dynamical Systems
Geometric Contrast Imaging
url https://doi.org/10.5281/zenodo.19043484