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Engineering · scheduling

Spaced-retrieval bottleneck

The Forgetting Curve

Retrievability R = e^(−t/S) decays between reviews. A review at the recall threshold raises S and stretches the next interval.

Memory decays. Ebbinghaus measured the shape of it more than a century ago: the probability of recall falls off roughly exponentially with time since the last review.

R(t)=e−t/S R(t) = e^{-t / S}

where RR is retrievability, tt is elapsed time, and SS is the current memory stability. Decay is biology. The schedule of reviews is not.

A scheduling problem in disguise

A review that lands before you would have forgotten is partly wasted. One that lands after means relearning from scratch. The optimum is to review at the moment retrievability crosses a target threshold. Each successful review then raises SS and stretches the next interval. That is a data-scheduling problem with a clean objective function, and modern spaced-repetition schedulers solve it well.

The bottleneck was never knowing this. It was computing a personalised schedule for every learner against every item, which is exactly the work that just became cheap.