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• A bidirectional distillation strategy is proposed to realize the information interaction between hybrid networks. • BIHN optimizes the performance of both CogN and ComN in EEG cognitive recognition by using a bidirectional feedback mode. • Experimental results show the superior performance of BIHN in cognitive recognition compared to many SOTA models. • The BIHN architecture is suitable for various hybrid network pairs related to cognitive and computational networks. Background and objective: Extracting cognitive representation and computational representation information simultaneously from electroencephalography (EEG) data and constructing corresponding information interaction models can effectively improve the recognition capability of brain cognitive status. However, due to the huge gap in the interaction between the two types of information, existing studies have yet to consider the advantages of the interaction of both. Methods: This paper introduces a novel architecture named the bidirectional interaction-based hybrid network (BIHN) for EEG cognitive recognition. BIHN consists of two networks: a cognitive-based network named CogN (e.g., graph convolution network, GCN; capsule network, CapsNet) and a computing-based network named ComN (e.g., EEGNet). CogN is responsible for extracting cognitive representation features from EEG data, while ComN is responsible for extracting computational representation features. Additionally, a bidirectional distillation-based coadaptation (BDC) algorithm is proposed to facilitate information interaction between CogN and ComN to realize the coadaptation of the two networks through bidirectional closed-loop feedback. Results: Cross-subject cognitive recognition experiments were performed on the Fatigue-Awake EEG dataset (FAAD, 2-class classification) and SEED dataset (3-class classification), and hybrid network pairs of GCN + EEGNet and CapsNet + EEGNet were verified. The proposed method achieved average accuracies of 78.76% (GCN + EEGNet) and 77.58% (CapsNet + EEGNet) on FAAD and 55.38% (GCN + EEGNet) and 55.10% (CapsNet + EEGNet) on SEED, outperforming the hybrid networks without the bidirectional interaction strategy. Conclusions: Experimental results show that BIHN can achieve superior performance on two EEG datasets and enhance the ability of both CogN and ComN in EEG processing as well as cognitive recognition. We also validated its effectiveness with different hybrid network pairs. The proposed method could greatly promote the development of brain-computer collaborative intelligence. [ABSTRACT FROM AUTHOR]