Computing the geometry of phase-amplitude coupling: A new moment-based framework
- 1University of Cambridge
Abstract
Phase-amplitude coupling (PAC) is widely used to quantify interactions between neural oscillations, yet cannot establish whether two coupling profiles share the same geometry, phase polarity or modal structure. Here we demonstrate that commonly-used PAC metrics constitute many-to-one mappings from phase-amplitude distributions to low-dimensional summaries. This results in distinct coupling geometries yielding identical PAC values. We propose formalising PAC as a hierarchy of representations, introducing a circular-moment decomposition that preserves richer geometric information. Simulations demonstrate that distinct coupling geometries produce identical Modulation Index (MI) values. Analyses of EEG data acquired during adult language listening reveal substantial geometric variability among PAC profiles with matched MI values, validating the moment-based approach. Applied to a child-language dataset, the framework identifies differences in phase geometry of delta-low gamma PAC in children with developmental language disorder, potentially uniting competing neuroscientific theories. We propose a representation-selection framework for future PAC research.
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BibTeX
@misc{keshavarzi2026computing,
title = {{Computing the geometry of phase-amplitude coupling: A new moment-based framework}},
author = {M. Keshavarzi and U. Goswami},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.15.751789},
url = {https://www.biorxiv.org/content/10.64898/2026.09.15.751789v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Computing the geometry of phase-amplitude coupling: A new moment-based framework
AU - M. Keshavarzi
AU - U. Goswami
PY - 2026
DA - 2026/09/15
PB - bioRxiv
DO - 10.64898/2026.09.15.751789
UR - https://www.biorxiv.org/content/10.64898/2026.09.15.751789v1
AB - Phase-amplitude coupling (PAC) is widely used to quantify interactions between neural oscillations, yet cannot establish whether two coupling profiles share the same geometry, phase polarity or modal structure. Here we demonstrate that commonly-used PAC metrics constitute many-to-one mappings from phase-amplitude distributions to low-dimensional summaries. This results in distinct coupling geometries yielding identical PAC values. We propose formalising PAC as a hierarchy of representations, introducing a circular-moment decomposition that preserves richer geometric information. Simulations demonstrate that distinct coupling geometries produce identical Modulation Index (MI) values. Analyses of EEG data acquired during adult language listening reveal substantial geometric variability among PAC profiles with matched MI values, validating the moment-based approach. Applied to a child-language dataset, the framework identifies differences in phase geometry of delta-low gamma PAC in children with developmental language disorder, potentially uniting competing neuroscientific theories. We propose a representation-selection framework for future PAC research.
ER -