FSRS Algorithm:
The Genetics of Memory
A deep analysis of the data-driven DSR model and its 21 trainable parameters.
The Evolution from SM-2 to FSRS
For decades, the heuristic SuperMemo-2 (SM-2) algorithm dominated learning software. Its significant weaknesses include the inability to dynamically adapt to the specific neuroplasticity of individual users.
Furthermore, SM-2 often leads to the so-called "Ease Hell", where flashcards become trapped in endless cycles of minimal intervals due to negative ratings[2]. FSRS discards these rigid intervals and implements a stochastic, probability-based architecture that originally emerged from the analysis of hundreds of millions of review logs[1].
The DSR Model
The three-dimensional ontology of memory- Retrievability (R)
- The stochastic probability of recalling information at an exact point in time. Expressed mathematically, it is a real number in the interval $[0, 1]$, often communicated as a percentage. R continuously decreases over time.
- Stability (S)
- The primary measure of storage strength in long-term memory. S is exactly the duration in days required for R to drop from an initial 100% to the threshold of exactly 90%[3].
- Difficulty (D)
- Describes the inherent complexity of a piece of information. A high D-value acts as an algorithmic damper, ensuring that complex topics are reviewed at shorter intervals.
The 21-Parameter Genome
The "genome" of FSRS-6 consists of 21 trainable parameters ($w_0$ to $w_{20}$) that are calibrated to the user's learning history through stochastic gradient descent[6].
| Gene Cluster | Indices | Function |
|---|---|---|
| Initialization | $w_0 - w_5$ | Determine the initial DSR values after the very first review. |
| Difficulty Modulation | $w_6 - w_7$ | Control the linear adjustment and "Mean Reversion" to prevent "Ease Hell". |
| SInc Growth | $w_8 - w_{14}$ | Form the parameters of the SInc function and quantify the impact of the spacing effect. |
| Short-term & Retrievability | $w_{17} - w_{20}$ | Handle "Same-Day Reviews" and the exact curvature of the power function ($w_{20}$). |
Machine Learning & Calibration
FSRS formulates interval calculation as a binary classification task. The optimizer utilizes Stochastic Gradient Descent (SGD) to individually adapt the 21 genes to real brain performance.
- Log Loss: Penalizes algorithmic miscalculations extremely harshly, enforcing perfect calibration.
- CMRR (Optimal Retention): Through simulation using Brent's Method, FSRS finds the exact retention rate (often 70%-85%) that minimizes learning effort.
| Algorithm | RMSE Value (lower is better) |
|---|---|
| FSRS v4 | 0.0452 |
| SuperMemo-2 (SM-2) | 0.0618 |
FSRS consistently achieves the lowest RMSE values compared to SM-2.