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Sleep is very important to our lives. For example, we cannot learn/memorize new experiences well without sleep. This suggests that the sleep is very important for our learning and memory. Although sleep is seemingly biological system-specific constraint, a sleep-like period is often needed for artificial learning systems. This paper describes the cases in which a sleep-like period, when the system stops learning new instances, is needed for refining the internal representation of knowledge in incremental/online learning tasks. Through several benchmark tests, we show that the incremental learning system with sleep (ILS) proposed by the authors generates a more compact data model than those of other incremental learning systems, that do not always need a sleep-like period.