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Continual learning requires incremental compatibility with a sequence of tasks. However, the design of model architecture remains an open question: In general, learning all tasks with a shared set of parameters suffers from severe interference between tasks; while learning each task with a dedicated parameter subspace is limited by scalability. In this work, we theoretically analyze the generalization errors for learning plasticity and memory stability in continual learning, which can be uniformly upper-bounded by (1) discrepancy between task distributions, (2) flatness of loss landscape and (3) cover of parameter space. Then, inspired by the robust biological learning system that processes sequential experiences with multiple parallel compartments, we propose Cooperation of Small Continual Learners (CoSCL) as a general strategy for continual learning. Specifically, we present an architecture with a fixed number of narrower sub-networks to learn all incremental tasks in parallel, which can naturally reduce the two errors through improving the three components of the upper bound. To strengthen this advantage, we encourage to cooperate these sub-networks by penalizing the difference of predictions made by their feature representations. With a fixed parameter budget, CoSCL can improve a variety of representative continual learning approaches by a large margin (e.g., up to 10.64% on CIFAR-100-SC, 9.33% on CIFAR-100-RS, 11.45% on CUB-200-2011 and 6.72% on Tiny-ImageNet) and achieve the new state-of-the-art performance.