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Whitepaper 02

Modeling Memory Decay with FSRS

The brain forgets on a predictable curve. Lumi's scheduler estimates the exact moment a fact is about to slip — and schedules the review there, where a single recall does the most work.

The forgetting curve is not your enemy

Retrievability — the probability you can recall a fact right now — decays roughly exponentially with the time since your last review. Review too early and you waste effort on something you already know; review too late and you've forgotten it and must relearn from scratch. Both are expensive.

R(t) = (1 + t / (9 · S))−1Retrievability R after t days, given memory stability S.

Three numbers per card

FSRS tracks a small memory state for every flashcard and updates it after each review based on how the recall actually went.

Stability (S)

How many days until retrievability falls to 90%. Every successful review stretches stability — the core mechanism behind expanding intervals.

Difficulty (D)

How inherently hard this card is for you. Difficult cards gain stability more slowly, so they resurface more often.

Retrievability (R)

The live probability of recall right now. The scheduler targets the day R crosses your desired retention (e.g. 90%).

Scheduling at the edge of forgetting

When you rate a review — Again, Hard, Good, or Easy — Lumi updates that card's stability and difficulty, then solves for the next interval that lands retrievability on your retention target. A card you find easy might jump from 4 days to 15; one you stumble on collapses back to a short interval and climbs again.

Across thousands of cards this compounds: the same study minutes buy far more retained knowledge than fixed-interval review, because no minute is spent on a fact that wasn't about to be forgotten.

Study less. Remember more.

FSRS-scheduled review is built into every Lumi deck — for students and for the institutions that run on our platform.