🧠 Spaced Repetition & Memory Decay

Ebbinghaus forgetting curve R(t) = e^{−t/S} where S is memory strength. SM-2 algorithm schedules reviews at expanding intervals. See how repeated reviews increase retention.

EducationInteractive
Golden line = first card · Click canvas to add a manual review · P pause · R reset

How it Works

The simulator tracks multiple flashcards over time. Each card has a memory strength S that determines how quickly retention decays. When a review occurs (at the threshold or manually), S is multiplied by the ease factor EF, making the next interval longer. The SM-2 algorithm computes: after the nth review, I(n) = I(n-1) × EF.

The chart shows the Ebbinghaus forgetting curve for each card. Review events are marked as vertical lines. Watch how retention at the review threshold rises after each successive review.

Forgetting: R(t) = e^{−t/S} (retention 0-1) Strength: S_new = S_old × EF (after each review) SM-2 intervals: I(1)=1d, I(2)=6d, I(n)=I(n-1)×EF Review when: R(t) < threshold → schedule review

Frequently Asked Questions

What is the Ebbinghaus forgetting curve?

The Ebbinghaus forgetting curve models how retention R decays exponentially over time: R(t) = e^{−t/S}, where t is time since learning and S is memory strength. Ebbinghaus found retention drops to ~58% after 20 minutes and ~33% after 1 day without review.

What is spaced repetition?

Spaced repetition schedules reviews at increasing intervals timed to occur just before the memory would be forgotten. It exploits the spacing effect: memories reviewed at expanding intervals are retained more durably than those reviewed in close succession (cramming).

What is the SM-2 algorithm?

SM-2 (SuperMemo algorithm 2) calculates next review interval as I(n) = I(n-1) × EF, where EF is the ease factor (1.3–2.5) reflecting how easily the card is recalled. EF is adjusted after each review based on performance quality (0–5 scale). EF never drops below 1.3.

What is memory strength (stability) S in the forgetting curve?

Memory strength S is the time constant of the exponential decay. When S is large, the forgetting curve is flat (retention decays slowly). S increases with each successful review and is higher for deeply encoded information (meaning, emotion, repetition).

What is the spacing effect?

The spacing effect is the empirical finding that learning is more effective when study sessions are spread out over time rather than concentrated (cramming). First described by Ebbinghaus, it is one of the most robust findings in cognitive psychology.

What is the ease factor in SM-2?

The ease factor (EF) starts at 2.5 and is adjusted after each review based on response quality. If quality is below 3, the card is lapsed and intervals reset. The ease factor is clamped to a minimum of 1.3 to prevent intervals from shrinking indefinitely.

How does Anki implement spaced repetition?

Anki uses a modified SM-2 algorithm with learning steps, relearning steps, and a fuzz factor to spread due dates. Cards in the review queue are sorted by due date. Anki also tracks lapses (failed reviews) to identify difficult material needing extra reinforcement.

What is the difference between massed and spaced practice?

Massed practice (cramming) concentrates study sessions closely together. Spaced practice distributes sessions over time. While cramming can produce short-term gains, spaced practice produces far more durable long-term retention through consolidation and retrieval practice effects.

What is active recall in spaced repetition?

Active recall means attempting to retrieve information from memory before seeing the answer (the testing effect). It is far more effective than passive re-reading. In spaced repetition systems, each review is an active recall event: question → attempt → answer → self-assess.

What is memory consolidation?

Memory consolidation is the process by which newly acquired memories are stabilised into long-term storage, primarily during sleep. Spaced repetition aligns reviews with consolidation windows, making each review more effective at strengthening the memory trace over time.