Energy Landscapes of Emotion: Quantifying Brain Network Stability During Happy and Sad Face Processing Using EEG-Based Hopfield Energy

TL;DR

This study introduces a Hopfield energy-based framework to quantify brain network stability during emotional face processing using EEG, revealing distinct stability patterns for happy and sad emotions.

Contribution

The paper presents a novel application of Hopfield network energy to empirically derived EEG functional connectivity to measure emotional brain state stability.

Findings

Sad emotional processing shows lower (more negative) energy in delta, theta, and alpha bands.

Alpha-band energy correlates positively with reaction time during sad trials.

Network efficiency is strongly negatively correlated with Hopfield energy, indicating more stable states are hyperconnected.

Abstract

Understanding how the human brain instantiates distinct emotional states is a key challenge in affective neuroscience. While network-based approaches have advanced emotion processing research,they remain largely descriptive,leaving the dynamical stability of emotional brain states unquantified.This study introduces a novel framework to quantify this stability by applying Hopfield network energy to empirically derived functional connectivity. High density EEG was recorded from 20 healthy adults during a happy versus sad facial expression discrimination task. Functional connectivity was estimated using the weighted Phase Lag Index to obtain artifact-robust,frequency-specific matrices, which served as coupling weights in a continuous Hopfield energy model to calculate a scalar energy value per trial. Statistical comparisons showed sad emotional processing was associated with significantly lower(more negative) energy in delta,theta,and alpha bands,with the strongest effect in the alpha band (Cohen's d =0.83). Energy correlated strongly negatively with global efficiency(r=-0.72),indicating hyperconnected,efficient networks correspond to more stable states.Additionally, alpha-band energy correlated positively with reaction time during sad trials(r=0.61),linking deeper network stability to increased cognitive effort. These findings demonstrate emotional valence corresponds to distinct attractor basins in the brain's functional landscape, with sadness occupying a deeper,more stable configuration than happiness.The Hopfield energy metric provides a principled, quantifiable measure of emotional brain state stability, opening new avenues for understanding affective dynamics in health and disease.