FSRS (Free Spaced Repetition Scheduler)
FSRS is a modern spaced-repetition scheduling algorithm developed by Jarrett Ye (MaiMemo Inc.). It replaces the heuristic SM-2 scheduler (Anki’s default for roughly three decades) with an explicit, machine-learned model of memory, and is the default scheduler in Anki since 23.10. Where SM-2 nudges an interval up or down by fixed rules, FSRS fits the parameters of a forgetting-curve model to a learner’s actual review history and schedules each card at the moment its predicted recall probability falls to a target. See spaced-repetition for the underlying distributed-practice evidence FSRS operationalizes.
The memory model: DSR
FSRS descends from MaiMemo’s DHP model, a variant of the three-component (DSR) model of memory. Three variables describe the state of one memory: 1
- Retrievability (R) — the probability of recalling the item right now. R decays continuously as time passes since the last review.
- Stability (S) — the time in days for R to fall from 100% to 90%. S is not a half-life; it is the time to a fixed 90% recall point, and it grows after successful reviews and shrinks after lapses.
- Difficulty (D) — an intrinsic scalar (1–10) for how hard the item is to stabilize; higher D means each successful review buys a smaller increase in S.
R changes daily with elapsed time; D and S change only when the card is reviewed. Each card carries its own (D, S, R) memory state. The scheduler’s job reduces to: show the card when its R reaches the learner’s desired retention (typically 90%, reasonable range 70–97%). Higher retention targets mean more reviews per day.
How it is trained
FSRS’s formulas for D, S, and R contain optimizable parameters — 21 in FSRS-6, the current widely-deployed version. These are fit by maximum-likelihood optimization over a user’s review log; users with too few reviews fall back to defaults fit on several hundred million reviews from ~10,000 Anki users. The academic foundation is MaiMemo’s KDD 2022 paper, which collected 220 million memory-behavior logs, built a Markov memory model, and framed scheduling as a stochastic shortest-path problem that provably minimizes review cost — reporting a 12.6% improvement over prior state-of-the-art. A follow-up in IEEE TKDE 2023 (Su, Ye, Nie, Cao, Chen) extends the model. 2
FSRS-6 refines same-day review handling and adds an optimizable parameter controlling the flatness of the forgetting curve, so the curve’s shape differs per user. The forgetting curve is a power law, not the exponential SM-2-style assumption. FSRS-7 (newest, not yet the common default) moves to fractional interval lengths with an 8-parameter curve for realistic same-day predictions. 3
Evidence and honest caveats
The open-spaced-repetition SRS benchmark evaluates schedulers on ~350 million reviews from ~10,000 Anki users, split by time (train on old, test on new) and scored by Log Loss, AUC, and a binned RMSE of calibration. On the no-same-day split: 4
- FSRS-6 (21 params) reaches Log Loss ~0.346, decisively beating SM-2-class heuristics and Duolingo’s HLR (~0.469) and the older FSRS v1–v4 line.
- The margin is about calibration — FSRS’s predicted recall probabilities track real recall rates closely — which is what lets a target retention translate into correct intervals.
- FSRS is not the predictive ceiling. The neural RWKV-P model (~2.7M params) reaches ~0.277 Log Loss, and FSRS-7 variants edge out FSRS-6. FSRS wins on a different axis: it is a small, interpretable, cheap, locally-runnable model whose parameters are few enough to fit per-user.
Two caveats worth keeping attached to the marketing numbers. The oft-quoted “20–30% fewer reviews than SM-2 for the same retention” is, by the authors’ own note, a simulation result, not a head-to-head field trial. And the benchmark’s authors and most contributors are the FSRS developers themselves — the evaluation is well-constructed (time-split, public dataset, multiple baselines) but not independent.
Why it matters
FSRS is the clearest current example of a learning-science effect (spaced-repetition) being turned into a fitted model rather than a hand-tuned rule. Its design also illustrates a broader pattern: a small interpretable model with the right inductive bias (a forgetting-curve survival model) can be more useful than a larger black box even when the black box predicts slightly better, because the small model’s parameters are few enough to personalize and cheap enough to run anywhere. The card-side craft that determines what gets scheduled in the first place is covered in flashcard-design.
Related pages
- spaced-repetition — the distributed-practice evidence base FSRS operationalizes; ISI × retention-interval interaction is why “optimal interval” is a moving target
- flashcard-design — what to put on the cards FSRS schedules (atomicity, cue-leakage, recognition vs production)
- ai-mathematical-practice — both pages concern fitting models to human intellectual practice; the Goodhart caution there applies to over-optimizing a retention target here
Sources
- Ye, J., Su, J., & Cao, Y. (2022). “A Stochastic Shortest Path Algorithm for Optimizing Spaced Repetition Scheduling.” KDD ‘22, 4381–4390. Ye, Su, & Cao 2022 — A Stochastic Shortest Path Algorithm for Optimizing Spaced Repetition Scheduling
- Ye, J. (2026). “ABC of FSRS.” open-spaced-repetition wiki. Jarrett Ye 2026 — ABC of FSRS
- open-spaced-repetition community (2026). “SRS Benchmark.” open-spaced-repetition community 2026 — SRS Benchmark (open-spaced-repetition)