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While self-supervised learning techniques are often used to mining implicit knowledge from unlabeled data via modeling multiple views, it is unclear how to perform effective representation learning in a complex and inconsistent context. To this end, we propose a methodology, specifically consistency and complementarity network (CoCoNet), which avails of strict global inter-view consistency and local cross-view complementarity preserving regularization to comprehensively learn representations from multiple views. On the global stage, we reckon that the crucial knowledge is implicitly shared among views, and enhancing the encoder to capture such knowledge from data can improve the discriminability of the learned representations. Hence, preserving the global consistency of multiple views ensures the acquisition of common knowledge. CoCoNet aligns the probabilistic distribution of views by utilizing an efficient discrepancy metric measurement based on the generalized sliced Wasserstein distance. Lastly on the local stage, we propose a heuristic complementarity-factor, which joints cross-view discriminative knowledge, and it guides the encoders to learn not only view-wise discriminability but also cross-view complementary information. Theoretically, we provide the information-theoretical-based analyses of our proposed CoCoNet. Empirically, to investigate the improvement gains of our approach, we conduct adequate experimental validations, which demonstrate that CoCoNet outperforms the state-of-the-art self-supervised methods by a significant margin proves that such implicit consistency and complementarity preserving regularization can enhance the discriminability of latent representations.