Brain function relies on the ability to quickly process incoming information while being capable of forming memories of past relevant events through the formation of novel synaptic connections. Synaptic connections are functionally strengthened or weakened to form new memories through synaptic plasticity rules that strongly rely on neuronal rhythmic activities. Brain information processing, on the other hand, is shaped by fluctuations in these neuronal rhythmic activities, each defining distinctive brain states, which poses the question of how such fluctuations in brain states affect the outcome of memory formation. This question is particularly relevant in the context of sleep-dependent memory consolidation, wakefulness to sleep transitions being characterized by large modifications in global neuronal activity. By combining computational models of neuronal activity switches and plasticity rules, we show that switches to rhythmic brain activity reminiscent of sleep lead to a reset in synaptic weights towards a basal value. This reset is shown to occur both in phenomenological and biophysical models of synaptic plasticity, and to be robust to neuronal and synaptic variability and network heterogeneity. Analytical analyses further show that the mechanisms of the synaptic reset are rooted in the endogenous nature of the sleep-like rhythmic activity. This sleep-dependent reset in synaptic weights permits regularizing synaptic connections during sleep, which could be a key component of sleep homeostasis and has the potential to play a central role in sleep-dependent memory consolidation.