  Identifying causal relationships among distinct brain areas, known as
effective connectivity, holds key insights into the brain's information
processing and cognitive functions. Electroencephalogram (EEG) signals exhibit
intricate dynamics and inter-areal interactions within the brain. However,
methods for characterizing nonlinear causal interactions among multiple brain
regions remain relatively underdeveloped. In this study, we proposed a
data-driven framework to infer effective connectivity by perturbing the trained
neural networks. Specifically, we trained neural networks (i.e., CNN, vanilla
RNN, GRU, LSTM, and Transformer) to predict future EEG signals according to
historical data and perturbed the networks' input to obtain effective
connectivity (EC) between the perturbed EEG channel and the rest of the
channels. The EC reflects the causal impact of perturbing one node on others.
The performance was tested on the synthetic EEG generated by a
biological-plausible Jansen-Rit model. CNN and Transformer obtained the best
performance on both 3-channel and 90-channel synthetic EEG data, outperforming
the classical Granger causality method. Our work demonstrated the potential of
perturbing an artificial neural network, learned to predict future system
dynamics, to uncover the underlying causal structure.
