This paper proposes a quick sequential learning system with model selection, which memorizes each instance completely when the system encounters it. Although the Nearest Neighbor methods achieves the quick sequential learning, the system needs a large amount of resource to memorize all instances. On the other hand, the model based learning methods with model selection need a long time-interval for the optimization of parameters. The aim of this study is to solve this dilemma. The system has two phases, daytime learning phase and nighttime learning phase. During the daytime learning phase, the system recognizes known input patterns and memorizes unknown patterns quickly. During the nighttime learning phase, the system constructs a compact model of the set of memorized patterns using a model selection algorithm. Probably, the nighttime learning phase corresponds to the sleep in biological systems. However, there are cases that the system cannot get enough time interval for the nighttime learning phase. In such the cases, the system cannot complete the learning. This paper also shows the technique to solve the problem caused by the restricted nighttime learning time.
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