Quanta FSRS Engine

Open-source FSRS Spaced Repetition Engine — the algorithm powering Quanta, the AI-powered STEM learning platform for students in the DACH region.

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What is this?

This is the complete spaced repetition engine extracted from Quanta. It implements the Free Spaced Repetition Scheduler (FSRS) by Ye et al. (2022, ACM KDD), with Quanta-specific extensions for STEM learning:

• FSRS Core — Stability (S), Difficulty (D), Retrievability (R) tracking per card
• STEM-Optimized Weights — Calibrated for academic MINT/STEM content (formulas, proofs, reaction mechanisms)
• Exam-Aware Scheduler — Multi-exam study plan generation with risk-based prioritization
• Interleaving Engine — Topic-interleaved card ordering (Rohrer & Taylor, 2007)
• Readiness Score — FSRS-derived exam readiness metric with confidence intervals
• Mastery Calculation — Per-topic mastery based on stability distribution + answer history

Scientific Foundation

Paper	Key Finding	How Quanta Uses It
Ye et al. 2022, ACM KDD	FSRS is 22% more precise than SM-2 (Log-Loss 0.35 vs 0.45)	Core scheduling algorithm
Karpicke & Roediger 2008, Science	Active Recall improves long-term retention by 50% vs re-reading	Q&A flashcard format
Rohrer & Taylor 2007	Interleaving yields 63% vs 20% on delayed tests	interleaving.ts implementation
Ebbinghaus 1885	Exponential forgetting curve: R(t) = 0.9^(t/S)	calculateRetrievability()

Architecture

src/
├── fsrs.ts              # FSRS core: state updates, retrievability, grades
├── interleaving.ts      # Topic-interleaved card ordering (Rohrer 2007)
└── engine/
    ├── types.ts         # TypeScript interfaces for all engine types
    ├── scheduler.ts     # Multi-exam study plan generator with FSRS simulation
    ├── readiness.ts     # Exam readiness score (composite of mastery + coverage + trend)
    └── mastery.ts       # Per-topic mastery calculation from stability distribution

Key Formulas

Retrievability (Memory Decay)

R(t) = 0.9^(t / S)

Where S = Stability (days until 90% recall probability), t = elapsed days.

Stability Update (Success)

S' = S × (1 + e^w8 × (11-D) × S^(-w9) × (e^(w10×(1-R)) - 1) × hard_penalty × easy_bonus)

Stability Update (Failure)

S' = w11 × D^(-w12) × ((S+1)^w13 - 1) × e^(w14×(1-R))

Difficulty Update (with Mean Reversion)

D' = w7 × D0 + (1 - w7) × (D - w6 × (grade - 3))

What Makes This Different from Other FSRS Implementations

1. STEM-Calibrated Weights — The 17 default weights are optimized for academic STEM content, not casual vocabulary learning
2. Exam-Aware Scheduling — The scheduler doesn't just schedule reviews; it generates multi-day study plans that adapt to exam dates, difficulty, and topic mastery
3. Interleaving Built-In — Most FSRS implementations review one topic at a time. Quanta interleaves topics within study sessions (scientifically proven to improve transfer)
4. Readiness Score — A novel composite metric that tells students whether they're exam-ready, combining mastery, coverage, trend, and time pressure
5. Simulation-First Planning — The scheduler runs FSRS forward-simulations to allocate cards across future days

Used In Production

This engine powers Quanta — a STEM learning platform with:

• FSRS Spaced Repetition for Physics, Chemistry, Math, Biology, Medicine
• AI-powered flashcard generation (Gemini 2.5 Flash)
• LaTeX formula editor (KaTeX) and SMILES molecule builder
• Community deck library with education context filters (university, semester, federal state)
• Quality-controlled content with provenance certificates

License

MIT — use freely in your own learning apps. Attribution appreciated.

Links

• Quanta Platform: quanta-study.de
• FSRS Paper: Ye et al. 2022, ACM KDD
• FSRS Community: open-spaced-repetition/fsrs4anki
• Quanta Community Decks: quanta-study.de/community