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Composite-database micro-expression recognition is attracting increasing attention as it is more practical to real-world applications. Though the composite database provides more sample diversity for learning good representation models, the important subtle dynamics are prone to disappearing in the domain shift such that the models greatly degrade their performance, especially for deep models. In this paper, we analyze the influence of learning complexity, including the input complexity and model complexity, and discover that the lower-resolution input data and shallower-architecture model are helpful to ease the degradation of deep models in composite-database task. Based on this, we propose a recurrent convolutional network (RCN) to explore the shallower-architecture and lower-resolution input data, shrinking model and input complexities simultaneously. Furthermore, we develop three parameter-free modules (i.e., wide expansion, shortcut connection and attention unit) to integrate with RCN without increasing any learnable parameters. These three modules can enhance the representation ability in various perspectives while preserving not-very-deep architecture for lower-resolution data. Besides, three modules can further be combined by an automatic strategy (a neural architecture search strategy) and the searched architecture becomes more robust. Extensive experiments on MEGC2019 dataset (composited of existing SMIC, CASME II and SAMM datasets) have verified the influence of learning complexity and shown that RCNs with three modules and the searched combination outperform the state-of-the-art approaches.