interbrain-networks-geometry

name	interbrain-networks-geometry
description	Geometric framework for analyzing inter-brain networks in social neuroscience. Uses discrete geometry and curvature distributions to identify critical transitions in neural connectivity during social interactions, moving beyond correlation-based synchrony metrics. Activation: inter-brain networks, hyperscanning, social neuroscience, discrete geometry, curvature, network topology, synchrony, social interaction, EEG, fNIRS
metadata	{"arxiv_id":"2509.10650","published":"2025-09-12","authors":"Nicolás Hinrichs, Noah Guzmán, Melanie Weber","tags":["inter-brain-networks","discrete-geometry","hyperscanning","social-neuroscience","curvature","network-topology"]}

Interbrain Networks Geometry

Overview

Geometric framework for analyzing inter-brain connectivity during social interactions using discrete geometry and curvature distributions, replacing traditional correlation-based synchrony metrics.

Core Innovation

Beyond Correlation-Based Synchrony

Traditional inter-brain synchrony analysis relies on fixed correlation metrics that only provide descriptive observations. This framework introduces geometric insights to capture dynamic reconfigurations in neural interactions.

Discrete Geometry Approach

• Models inter-brain networks as discrete geometric structures
• Tracks evolving topology during social exchanges
• Identifies critical transitions using entropy metrics from curvature distributions

Methodology

Pipeline

1. Network Construction: Build inter-brain connectivity graphs from hyperscanning data (EEG/fNIRS)
2. Geometric Embedding: Map networks to discrete geometric space
3. Curvature Analysis: Compute curvature distributions across network nodes
4. Entropy Computation: Calculate entropy metrics from curvature distributions
5. Transition Detection: Identify critical connectivity changes via entropy peaks

Key Metrics

• Curvature Distribution: Quantifies local network geometry
• Geometric Entropy: Measures topological complexity
• Transition Points: Entropy maxima indicate critical reconfigurations

Applications

• Hyperscanning studies (dyadic interactions, group dynamics)
• Social cognition research (theory of mind, empathy, cooperation)
• Clinical applications (autism, social anxiety, schizophrenia)
• Human-AI interaction studies

Advantages Over Traditional Methods

• Captures dynamic reconfigurations, not just static correlations
• Provides mechanistic insights into network topology changes
• Identifies critical transition points in social processing
• Compatible with multiple imaging modalities (EEG, fNIRS, fMRI)

Biological Interpretation

Geometric transitions may reflect:

• Shifts in social cognitive strategies
• Alignment of mental models between interactants
• Emergence of shared representations
• Breakdown/recovery of social rapport

Pitfalls

• Requires sufficient temporal resolution to capture transitions
• Geometric embedding choices affect curvature computations
• Entropy metrics sensitive to network density and thresholding
• Interpretation of geometric features requires domain expertise

Related Concepts

• Hyperscanning
• Inter-brain synchrony
• Social neuroscience
• Network topology
• Discrete differential geometry
• Critical transitions in complex systems