Algorithmic
Memory Control
A comparative analysis of the classic SuperMemo-2 (SM-2) and the modern Free Spaced Repetition Scheduler (FSRS). Understand the mathematics behind your learning success.
The Paradox of Forgetting
The architecture of human memory is both fascinating and frustrating. While we excel at recognizing complex patterns, our factual knowledge is subject to rapid, unstoppable decay. This process, often stigmatized as "forgetting," is neurobiologically a necessary filtering mechanism.
As early as 1885, Hermann Ebbinghaus quantified this process [1]. His research demonstrated that memory contents are subject to exponential decay [1]. Without active repetition, knowledge is lost.
Fig 1: Visualization of exponential decay & the restoration effect
Computer science's answer to this biological problem is algorithms. Two giants dominate this field: the historical standard SM-2 and the modern challenger FSRS.
The Deterministic Paradigm: SM-2
Developed in 1987 by Piotr WoźniakSM-2 marked the transition from analog flashcard boxes to computer algorithms. It is a heuristic system based on rigid rules.
Knowledge is broken down into "items". Each item is assigned an individual Easiness Factor (EF), which dictates how quickly the intervals grow [2].
The Algorithm
I(2) = 6 Days
I(n) = I(n-1) * EF
Starting value EF = 2.5. Thus, the interval grows by a standard 150% per successful repetition.
The Problem: "Ease Hell"
SM-2 suffers from mathematical rigidity. If a user frequently marks a card as "Hard", the EF drops to its minimum value of 1.3. The card becomes permanently trapped in a state of slow growth, even if the user masters the content later [2]. This leads to a massive accumulation of unnecessary reviews.
The Paradigm Shift: FSRS
Free Spaced Repetition SchedulerFSRS replaces rigid rules with probability theory and machine learning. It is based on the DSR Model, which views memory three-dimensionally [3]:
How hard is the info? FSRS separates difficulty from stability. A fact can be hard (D=9) but remain stable in memory.
The time span in days until the probability of recall drops to 90%.
The probability of recalling it right now. FSRS utilizes a power function ("Power Law") for this instead of exponential decay [4].
The Mathematics of "Desirable Difficulty" [5]
Formula for calculating Retrievability.
FSRS rewards you mathematically for taking risks. When you review a card just before you would have forgotten it (low R), the gain in stability is greatest [5]. The system optimizes your learning schedule for maximum efficiency.
Head-to-Head Comparison
| Feature | SM-2 | FSRS (v5) |
|---|---|---|
| Model Basis | Deterministic Heuristic | Stochastic DSR Model |
| Adaptivity | Low (EF only) | High (19+ trainable parameters) |
| Efficiency | Standard | -20% to -30% study load |
| Cold Start | Instantly perfect | Requires data (~1000 reviews) |
Data based on benchmark studies of the FSRS-20k dataset.
Conclusion & Recommendation
For High-Performers
If you study >300 cards daily, FSRS is mandatory [3]. The 30% time savings add up to over 150 hours per year.
For Casual Learners
With <50 cards per day, the efficiency advantage is negligible. SM-2 works solidly "out of the box" and without complex configuration [2].
"SM-2 was the diesel engine of spaced repetition: robust, loud, but reliable. FSRS is the modern electric motor: more efficient, quieter, more adaptive."