Spaced Repetition Algorithms Comparison: SuperMemo SM-2 vs. SM-17 Architecture

Dr. Piotr Woźniak, the pioneer of spaced repetition theory, dedicated over four decades to modeling the mathematical decay of human memory. In the late 1980s, he formulated the **SM-2** algorithm. Today, SM-2 remains the foundational engine powering popular platforms like Anki, Quizlet, and our own language learning application Polyvo. However, decades of cognitive research and millions of review data points eventually led to the development of the highly sophisticated **SM-17** model.

Limitations of the Classic SM-2 Model

The SM-2 algorithm calculates the next review interval for each card using linear algebraic formulas. While highly efficient, this classic approach suffers from several key limitations:

• Disregard for Historical Patterns: SM-2 schedules intervals using only the immediate score (q) and the current Easiness Factor (EF). It ignores the user's historical performance stability for that specific item.
• Easiness Factor Volatility (Ease Hell): A few consecutive low scores can drag the EF value down rapidly, scheduling card reviews at redundant, near-instant intervals, leading to review fatigue.
• Hardcoded Initial Steps: Hardcoding the first two intervals to 1 and 6 days assumes all learning materials start with the same baseline difficulty, which is biologically inaccurate.

The Modern SM-17 Paradigm: Three-Dimensional Memory Model

Instead of relying on fixed formulas, the SM-17 algorithm models memory status as a coordinate inside a three-dimensional space defined by three distinct variables:

1. Retrievability (R): The probability of successfully recalling an item at a given moment. It starts at 100% and decays exponentially over time.
2. Stability (S): The strength of the memory trace. A higher stability means Retrievability (R) decays at a much slower rate. Successful reviews increase Stability.
3. Difficulty (D): A value mapped between 0 and 1 indicating the complexity of the item itself.

Using these three metrics, SM-17 plots a customized forgetting curve for each user and schedules the next review at the exact day where Retrievability is predicted to be exactly 90%.

Comparison Matrix

Feature	SM-2 Algorithm	SM-17 Algorithm
Approach	Static Mathematical Formula	Dynamic Memory Simulation
Variables	2 (EF, Repetitions)	3 (Retrievability, Stability, Difficulty)
History Analysis	No (Only last state)	Yes (Full historical records)
Compute Complexity	Extremely low (Client-side friendly)	High (Requires background database analysis)

Implementation in Polyvo

For Polyvo's web deployment, we chose the SM-2 algorithm to ensure fast, offline-first client-side calculations. To address its drawbacks, we optimized it by introducing a lower limit of 1.3 for the Easiness Factor and adding review thresholds. In addition, we built our interactive **Spaced Repetition Simulator** to allow users to manipulate these variables and visualize memory stability curves in real-time. These structural models form the educational backbone of Polimelo.