The FSRS (Free Spaced Repetition Scheduler) is a modern, probabilistic algorithm designed to schedule memory reviews. Unlike older, deterministic algorithms (like SM-2) that use fixed multipliers, FSRS calculates the specific Memory Stability ($S$) and Retrievability ($R$) of information to predict the precise probability of recall at any given time.

According to the foundational documentation by Jarosz and the FSRS research community, traditional algorithms rely on a simple multiplier logic (e.g., "If you get it right, multiply the interval by 2.5"). This assumes all memories decay at the same rate, which is biologically inaccurate.

FSRS models memory using a more complex "Three-Component Model":

1. Retrievability ($R$): The probability (0%–100%) that the learner can recall the item right now.

2. Stability ($S$): The time (in days) it takes for $R$ to drop from 100% to 90%.

3. Difficulty ($D$): The intrinsic complexity of the specific piece of information .

By separating Stability (how long it lasts) from Difficulty (how hard it is), FSRS can schedule reviews for the exact moment when Retrievability drops to the "Forgetting Threshold" (usually 90%).

The move toward optimal spacing is supported by Cepeda et al. (2008), who demonstrated that as the desired retention interval increases, the optimal gap between study sessions must also increase non-linearly. FSRS operationalizes this by using a decay formula ($P(R) \approx 0.9^{t/S}$) to ensure reviews occur at the "temporal ridgeline" of efficiency.

We utilize a proprietary implementation of FSRS. Our engine tracks the "Stability" of every word you learn. We do not use fixed intervals (Day 1, Day 3, Day 7). Instead, we calculate $R$ daily and only trigger a review when your probability of recall falls below the optimal threshold for consolidation.

1. Jarosz, P., et al. (2023). Optimization of the Spaced Repetition Schedule. (Referenced via FSRS Documentation & SuperMemo Theory).

2. Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in learning: A temporal ridgeline of optimal retention. Psychological Science, 19(11), 1095–1102.