Organizations: Department of Computer Science, University of Texas at Austin, Austin, TX 78712, USA · Department of Learning Technologies, University of North Texas, Denton, TX 76203, USA
Electroencephalography (EEG) provides a non-invasive insight into the brain's cognitive and emotional dynamics. However, modeling how these states evolve in real time and quantifying the energy required for such transitions remains a major challenge. The Schrödinger Bridge Problem (SBP) offers a principled probabilistic framework to model the most efficient evolution between the brain states, interpreted as a measure of cognitive energy cost. While generative models such as GANs have been widely used to augment EEG data, it remains unclear whether synthetic EEG preserves the underlying dynamical structure required for transition-based analysis. In this work, we address this gap by using SBP-derived transport cost as a metric to evaluate whether GAN-generated EEG retains the distributional geometry necessary for energy-based modeling of cognitive state transitions. We compare transition energies derived from real and synthetic EEG collected during Stroop tasks and demonstrate strong agreement across group and participant-level analyses. These results indicate that synthetic EEG preserves the transition structure required for SBP-based modeling, enabling its use in data-efficient neuroadaptive systems. We further present a framework in which SBP-derived cognitive energy serves as a control signal for adaptive human-machine systems, supporting real-time adjustment of system behavior in response to user cognitive and affective state.
Figures & tables
Fig. 1 : GAN training stability showing convergence of distribution alignment and bounded gradient penalty.
Fig. 2 : Comparison of real and GAN-generated EEG feature distributions for Theta power, Alpha power, and Engagement, showing alignment in distribution shape and variance.
Feature
Real Mean
Real Std
GAN Mean
GAN Std
Theta
0.0797
1.0866
0.1750
0.9550
Alpha
0.0412
0.9363
0.3523
0.8225
Engagement
-0.0627
1.0493
-0.5231
1.0640
TABLE I : Mean and standard deviation of real and GAN-generated EEG features under baseline z -score normalization.
Participant
P1 → P2 Energy
P1 → P3 Energy
Participant 1
0.000391
0.000491
Participant 2
0.000518
0.000549
Participant 3
0.000725
0.000740
Participant 4
0.000692
0.000907
Participant 5
0.000790
0.001063
Participant 6
0.000508
0.000835
TABLE II : Participant-level SBP energies for real EEG across task transitions.
Participant
P1 → P2 Energy
P1 → P3 Energy
Participant 1
0.000845
0.000885
Participant 2
0.000860
0.001127
Participant 3
0.000558
0.000951
Participant 4
0.000753
0.000932
Participant 5
0.000581
0.000830
Participant 6
0.000951
0.000948
TABLE III : Participant-level SBP energies for GAN-generated EEG across task transitions.
Fig. 3 : Group-level comparison of SBP transport energy (mean ± standard deviation) for real and GAN EEG.
Fig. 4 : Participant-level SBP transport energy trends for real and GAN EEG across task transitions.
Fig. 5 : Closed-loop neuroadaptive system framework using EEG-derived cognitive energy as a control signal for real-time human–machine adaptation.
Concordia Institute for Information Systems Engineering (CIISE), Concordia University, Canada. · Department of Electrical and Computer Engineering, University of Toronto, Canada