Hericium erinaceus contains two classes of bioactive compounds — hericenones in the fruiting body and erinacines in the mycelium. Both stimulate nerve growth factor (NGF) synthesis in vitro. Whether that translates to measurable cognitive improvement in humans is a more careful question.
The best available trials show modest but consistent gains in short-term memory and processing speed at doses of 1000mg+ of standardized extract, over durations of 12–16 weeks. Shorter protocols show nothing.