I worked with a sleep psychologist and psychiatrist before on my insomnia. From what she told me about the research she was involved in: kind of, but in reverse. If you do not sleep well, the next sleep you do spend more time in deep restorative sleep cycles than if you were not sleep deprived. However if you sleep extra it does not mean more time in deep sleep, in actuality the longer you sleep, the “extra” sleep is spend on lighter sleep cycles so you do not “bank” extra sleep.
There are also medications that can change how much time you spend in deep sleep vs light sleep.
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