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In this study, we propose a novel approach for quantifying brain-to-brain coupling during a hypnosis induction. Our approach uses a multi-output sequence-to-sequence deep neural network applied to raw EEG data recorded from 51 participants using 59 electrodes. Specifically, we use a long short-term memory (LSTM) encoder to extract an embedding, which is then utilized for two downstream heads: one head to predict the hypnotist's brain activity, and the other head to classify the level of hypnotic depth. We found that removing the head that predicted the hypnotist's brain activity substantially decreased the accuracy of the classification head, indicating that this head plays a critical role in achieving better classification performance. These results highlight the importance of shared representations in shaping social interactions. Ultimately, this work can help us better understand the dynamics of verbal communication.