If a flashcard has a Stability of S = 25 days, what is its expected Retrievability (R) exactly 25 days after the last review?

Exactly 90% (R = 0.90), because Stability in FSRS is normalized around the 90% retention point.

Does rating a card 'Good' (G = 3) in FSRS-6 increase or decrease its Difficulty (D)?

In FSRS-6, rating 'Good' (G = 3) leaves the raw difficulty step unchanged before mean reversion (since G - 3 = 0), and then gently pulls D toward the baseline difficulty D_0(4) via mean reversion.

How do the 'Hard Penalty' (w_15) and 'Easy Bonus' (w_16) modify stability growth on a successful recall?

When G = 2 (Hard), the stability growth increment is multiplied by w_15 (typically 0 1, yielding a larger interval boost).

Summarize the complete lifecycle of a card's DSR state during a single FSRS-6 review event.

1. Compute current R(t, S) from elapsed days t and prior S; 2. Receive user rating G ∈ {1,2,3,4}; 3. Update Difficulty D → D' with linear damping and mean reversion; 4. Update Stability S → S' via recall or lapse formula; 5. Convert S' and Desired Retention into the next interval I.

State the three primary variables that determine the new Stability S'_r(D, S, R, G) after a successful recall (G ∈ {2, 3, 4}).

The new Stability S'_r depends on (1) current Difficulty D, (2) prior Stability S, (3) Retrievability R at the moment of review, and (4) the rating Modifier (Hard penalty w_15 or Easy bonus w_16).

If you change your Desired Retention in FSRS-6 from 90% to 85%, do your cards' Stability (S) or Difficulty (D) values change?

No! Stability (S) is always defined relative to the 90% benchmark; changing Desired Retention only changes the interval multiplier I(r, S) used to convert S into the next scheduled review date.

How does FSRS-6 calculate a card's initial Difficulty D_0(G) on its first review?

Initial Difficulty is computed as D_0(G) = w_4 - exp(w_5 · (G - 1)) + 1, clamped to the interval [1.0, 10.0], so higher initial grades (Good/Easy) start with lower initial Difficulty.

What is 'Mean Reversion of Difficulty' in FSRS-6, and why is it critical?

After updating D based on the latest rating, FSRS-6 blends the updated value with the baseline difficulty D_0(4) using parameter w_7: D' = w_7 · D_0(4) + (1 - w_7) · D_temp, preventing cards from getting permanently stuck at D = 10.0 ('Ease Hell').

How can you interpret the ratio t / S in the FSRS-6 forgetting curve?

The dimensionless ratio t / S measures elapsed time in units of the card's current Stability: when t / S = 1.0, elapsed time equals Stability and Retrievability is exactly 90%.

How do the three DSR variables map onto Bjork's New Theory of Disuse?

Stability (S) corresponds to Storage Strength, Retrievability (R) corresponds to Retrieval Strength, and Difficulty (D) captures item-specific resistance to stability growth.

What is the 'Stabilization Decay' phenomenon in long-term human memory?

As a memory trace becomes more stable (higher S), each additional review still increases S in absolute days, but the multiplicative ratio S'/S gradually diminishes rather than remaining constant forever.

What are the numerical bounds and meaning of Difficulty (D) in FSRS-6?

Difficulty D is bounded on the closed interval [1.0, 10.0], where D = 1.0 represents the easiest possible card and D = 10.0 represents the most difficult card.

What are the four inputs to FSRS-6's Post-Lapse Stability formula S'_f(D, S, R) when you forget a card (Grade = 1, Again)?

When a card lapses (G = 1), its new stability S'_f is computed from (1) baseline scale w_11, (2) Difficulty factor D^(-w_12), (3) prior Stability factor (S + 1)^(w_13) - 1, and (4) Retrievability factor exp(w_14 · (1 - R)), capped so S'_f never exceeds prior S.

In the post-lapse formula S'_f, why does higher Difficulty (D) lead to a shorter post-lapse interval?

Because the term D^(-w_12) decreases as D increases, giving genuinely difficult leech cards a shorter relearning interval after a lapse.

What happens to Stability in FSRS-6 if you review a card 5 minutes after studying it (when R ≈ 0.999)?

Because R is nearly 1.0, the long-term spacing term exp(w_10 · (1 - R)) - 1 approaches zero, preventing artificial interval inflation from premature cramming.

When t = 0 days (immediately after studying a card), what is the theoretical value of Retrievability R(0, S)?

R(0, S) = (1 + F · 0 / S)^(-w20) = 1^(-w20) = 1.0 (100% probability of immediate recall).

What do the three letters D, S, and R stand for in the DSR Memory Model underlying FSRS-6?

D = Difficulty (inherent item complexity), S = Stability (memory storage duration for 90% recall), and R = Retrievability (instantaneous probability of recall at elapsed time t).

How does a card's Difficulty (D) affect its future Stability (S) growth on subsequent successful reviews?

Higher Difficulty (D closer to 10) reduces the stability growth factor SInc, meaning a high-difficulty card's interval grows more slowly than a low-difficulty card's interval even when both are rated 'Good'.

Why does FSRS-6 assign four distinct initial Stability parameters (w_0, w_1, w_2, w_3) for a card's first rating?

Because a learner's prior familiarity with a new card varies widely: a card rated 'Easy' on first sight already has multi-day stability (w_3), whereas a card rated 'Again' requires sub-day or next-day reinforcement (w_0).

Why does FSRS-6 include prior Stability (S + 1)^(w_13) - 1 in the post-lapse formula instead of resetting S to w_0?

Because forgetting a card after 180 days does not erase the entire synaptic trace back to a brand-new card; preserving a fraction of prior S allows mature lapsed cards to recover much faster than unseen cards.

In FSRS-6, how is a brand-new card's initial Stability S_0(G) assigned after its very first review?

Initial Stability S_0(G) is determined directly by the first rating Grade G ∈ {1=Again, 2=Hard, 3=Good, 4=Easy} using the first four trainable parameters: S_0(G) = w_{G-1} (i.e., w_0, w_1, w_2, w_3).

How does prior Stability (S) influence the relative multiplier (SInc = S'_r / S) during a successful review in FSRS-6?

Because the stability growth formula includes the factor S^(-w_9) (where w_9 > 0), cards with higher existing Stability experience a slightly smaller relative multiplier—reflecting the empirical 'stabilization decay' effect as memories mature.

How does current Retrievability (R) influence the stability gain in FSRS-6 when you successfully recall a card?

The growth term includes exp(w_10 · (1 - R)) - 1: the lower R is at the moment of successful recall (i.e., the longer you waited or the more overdue the card was), the exponentially larger the stability gain upon successful retrieval!

What is the exact quantitative definition of Memory Stability (S) in FSRS-6?

Stability (S) is the time interval in days required for a card's Retrievability (R) to decay from 100% (1.0) immediately after a review down to 90% (0.90).

How is 'Estimated Total Knowledge' of a flashcard collection calculated using Retrievability (R)?

By summing the instantaneous Retrievability R_i(t) across all learned cards i in the collection: E[Knowledge] = ∑ R_i(t), which predicts the exact number of cards you would answer correctly if tested on the entire collection today.

Why is 'Sum of Retrievability (∑ R_i)' a better metric of mastery than 'Total Number of Cards Reviewed'?

Total reviews can be inflated by futile cramming or low-retention churning, whereas ∑ R_i directly measures how many facts are actually accessible in your memory right now.

What are the numerical bounds and meaning of Retrievability (R) in FSRS-6?

Retrievability R lies in (0, 1] (or 0% to 100%), representing the predicted probability of successful recall at elapsed time t days since the last review.

Why does recalling an overdue card at R = 0.70 yield a much bigger Stability jump than reviewing the same card early at R = 0.98?

At R = 0.98, 1 - R is only 0.02, so exp(w_10 · (1 - R)) - 1 is near zero (minimal retrieval effort); at R = 0.70, successful recall proves the memory survived a long delay and triggers strong reconsolidation.

What is 'Linear Damping' in FSRS-6's difficulty update equation?

Before applying a difficulty increase ΔD = -w_6 · (G - 3), FSRS-6 multiplies ΔD by (10 - D) / 9 so that as D approaches the ceiling of 10.0, further difficulty increases taper off smoothly.

What is the role of the DSR state vector in decoupling 'Memory Modeling' from 'Review Scheduling'?

The DSR state vector (D, S) completely summarizes the learner's memory of a card independent of any scheduling policy; the scheduler simply queries R(t, S) to pick the next review date that satisfies the user's chosen Desired Retention.

What does it mean if a deck has a high average Stability (mean S = 120 days) and a high average Retrievability (mean R = 93%)?

It means the deck is both deeply consolidated in long-term memory (high S) and currently well-maintained with very few forgotten cards (high R).

Guaranteeing monotonicity: Can a successful recall in FSRS-6 ever reduce a card's Stability (S'_r < S)?

No. In the long-term recall formula S'_r = S · (1 + ...), the additive growth term is strictly non-negative, ensuring S'_r ≥ S for any successful recall.

FSRS-6 & Spaced Repetition — The DSR Model: Difficulty (D), Stability (S) & Retrievability (R)

Deep dive into the Three-Component Model of Memory (DSR): exact definitions, units, bounds, and state transitions of Difficulty (D), Memory Stability (S), and Retrievability (R) in FSRS-6.

Level: basic
Languages: en → en
Cards: 32
Markdown: FSRS-6 & Spaced Repetition — The DSR Model: Difficulty (D), Stability (S) & Retrievability (R) (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	If a flashcard has a Stability of S = 25 days, what is its expected Retrievability (R) exactly 25 days after the last review?	Exactly 90% (R = 0.90), because Stability in FSRS is normalized around the 90% retention point.
2	Does rating a card 'Good' (G = 3) in FSRS-6 increase or decrease its Difficulty (D)?	In FSRS-6, rating 'Good' (G = 3) leaves the raw difficulty step unchanged before mean reversion (since G - 3 = 0), and then gently pulls D toward the baseline difficulty D_0(4) via mean reversion.
3	How do the 'Hard Penalty' (w_15) and 'Easy Bonus' (w_16) modify stability growth on a successful recall?	When G = 2 (Hard), the stability growth increment is multiplied by w_15 (typically 0 < w_15 < 1, yielding a smaller interval increase); when G = 4 (Easy), it is multiplied by w_16 (typically w_16 > 1, yielding a larger interval boost).
4	Summarize the complete lifecycle of a card's DSR state during a single FSRS-6 review event.	1. Compute current R(t, S) from elapsed days t and prior S; 2. Receive user rating G ∈ {1,2,3,4}; 3. Update Difficulty D → D' with linear damping and mean reversion; 4. Update Stability S → S' via recall or lapse formula; 5. Convert S' and Desired Retention into the next interval I.
5	State the three primary variables that determine the new Stability S'_r(D, S, R, G) after a successful recall (G ∈ {2, 3, 4}).	The new Stability S'_r depends on (1) current Difficulty D, (2) prior Stability S, (3) Retrievability R at the moment of review, and (4) the rating Modifier (Hard penalty w_15 or Easy bonus w_16).
6	If you change your Desired Retention in FSRS-6 from 90% to 85%, do your cards' Stability (S) or Difficulty (D) values change?	No! Stability (S) is always defined relative to the 90% benchmark; changing Desired Retention only changes the interval multiplier I(r, S) used to convert S into the next scheduled review date.
7	How does FSRS-6 calculate a card's initial Difficulty D_0(G) on its first review?	Initial Difficulty is computed as D_0(G) = w_4 - exp(w_5 · (G - 1)) + 1, clamped to the interval [1.0, 10.0], so higher initial grades (Good/Easy) start with lower initial Difficulty.
8	What is 'Mean Reversion of Difficulty' in FSRS-6, and why is it critical?	After updating D based on the latest rating, FSRS-6 blends the updated value with the baseline difficulty D_0(4) using parameter w_7: D' = w_7 · D_0(4) + (1 - w_7) · D_temp, preventing cards from getting permanently stuck at D = 10.0 ('Ease Hell').
9	How can you interpret the ratio t / S in the FSRS-6 forgetting curve?	The dimensionless ratio t / S measures elapsed time in units of the card's current Stability: when t / S = 1.0, elapsed time equals Stability and Retrievability is exactly 90%.
10	How do the three DSR variables map onto Bjork's New Theory of Disuse?	Stability (S) corresponds to Storage Strength, Retrievability (R) corresponds to Retrieval Strength, and Difficulty (D) captures item-specific resistance to stability growth.
11	What is the 'Stabilization Decay' phenomenon in long-term human memory?	As a memory trace becomes more stable (higher S), each additional review still increases S in absolute days, but the multiplicative ratio S'/S gradually diminishes rather than remaining constant forever.
12	What are the numerical bounds and meaning of Difficulty (D) in FSRS-6?	Difficulty D is bounded on the closed interval [1.0, 10.0], where D = 1.0 represents the easiest possible card and D = 10.0 represents the most difficult card.
13	What are the four inputs to FSRS-6's Post-Lapse Stability formula S'_f(D, S, R) when you forget a card (Grade = 1, Again)?	When a card lapses (G = 1), its new stability S'_f is computed from (1) baseline scale w_11, (2) Difficulty factor D^(-w_12), (3) prior Stability factor (S + 1)^(w_13) - 1, and (4) Retrievability factor exp(w_14 · (1 - R)), capped so S'_f never exceeds prior S.
14	In the post-lapse formula S'_f, why does higher Difficulty (D) lead to a shorter post-lapse interval?	Because the term D^(-w_12) decreases as D increases, giving genuinely difficult leech cards a shorter relearning interval after a lapse.
15	What happens to Stability in FSRS-6 if you review a card 5 minutes after studying it (when R ≈ 0.999)?	Because R is nearly 1.0, the long-term spacing term exp(w_10 · (1 - R)) - 1 approaches zero, preventing artificial interval inflation from premature cramming.
16	When t = 0 days (immediately after studying a card), what is the theoretical value of Retrievability R(0, S)?	R(0, S) = (1 + F · 0 / S)^(-w20) = 1^(-w20) = 1.0 (100% probability of immediate recall).
17	What do the three letters D, S, and R stand for in the DSR Memory Model underlying FSRS-6?	D = Difficulty (inherent item complexity), S = Stability (memory storage duration for 90% recall), and R = Retrievability (instantaneous probability of recall at elapsed time t).
18	How does a card's Difficulty (D) affect its future Stability (S) growth on subsequent successful reviews?	Higher Difficulty (D closer to 10) reduces the stability growth factor SInc, meaning a high-difficulty card's interval grows more slowly than a low-difficulty card's interval even when both are rated 'Good'.
19	Why does FSRS-6 assign four distinct initial Stability parameters (w_0, w_1, w_2, w_3) for a card's first rating?	Because a learner's prior familiarity with a new card varies widely: a card rated 'Easy' on first sight already has multi-day stability (w_3), whereas a card rated 'Again' requires sub-day or next-day reinforcement (w_0).
20	Why does FSRS-6 include prior Stability (S + 1)^(w_13) - 1 in the post-lapse formula instead of resetting S to w_0?	Because forgetting a card after 180 days does not erase the entire synaptic trace back to a brand-new card; preserving a fraction of prior S allows mature lapsed cards to recover much faster than unseen cards.
21	In FSRS-6, how is a brand-new card's initial Stability S_0(G) assigned after its very first review?	Initial Stability S_0(G) is determined directly by the first rating Grade G ∈ {1=Again, 2=Hard, 3=Good, 4=Easy} using the first four trainable parameters: S_0(G) = w_{G-1} (i.e., w_0, w_1, w_2, w_3).
22	How does prior Stability (S) influence the relative multiplier (SInc = S'_r / S) during a successful review in FSRS-6?	Because the stability growth formula includes the factor S^(-w_9) (where w_9 > 0), cards with higher existing Stability experience a slightly smaller relative multiplier—reflecting the empirical 'stabilization decay' effect as memories mature.
23	How does current Retrievability (R) influence the stability gain in FSRS-6 when you successfully recall a card?	The growth term includes exp(w_10 · (1 - R)) - 1: the lower R is at the moment of successful recall (i.e., the longer you waited or the more overdue the card was), the exponentially larger the stability gain upon successful retrieval!
24	What is the exact quantitative definition of Memory Stability (S) in FSRS-6?	Stability (S) is the time interval in days required for a card's Retrievability (R) to decay from 100% (1.0) immediately after a review down to 90% (0.90).
25	How is 'Estimated Total Knowledge' of a flashcard collection calculated using Retrievability (R)?	By summing the instantaneous Retrievability R_i(t) across all learned cards i in the collection: E[Knowledge] = ∑ R_i(t), which predicts the exact number of cards you would answer correctly if tested on the entire collection today.
26	Why is 'Sum of Retrievability (∑ R_i)' a better metric of mastery than 'Total Number of Cards Reviewed'?	Total reviews can be inflated by futile cramming or low-retention churning, whereas ∑ R_i directly measures how many facts are actually accessible in your memory right now.
27	What are the numerical bounds and meaning of Retrievability (R) in FSRS-6?	Retrievability R lies in (0, 1] (or 0% to 100%), representing the predicted probability of successful recall at elapsed time t days since the last review.
28	Why does recalling an overdue card at R = 0.70 yield a much bigger Stability jump than reviewing the same card early at R = 0.98?	At R = 0.98, 1 - R is only 0.02, so exp(w_10 · (1 - R)) - 1 is near zero (minimal retrieval effort); at R = 0.70, successful recall proves the memory survived a long delay and triggers strong reconsolidation.
29	What is 'Linear Damping' in FSRS-6's difficulty update equation?	Before applying a difficulty increase ΔD = -w_6 · (G - 3), FSRS-6 multiplies ΔD by (10 - D) / 9 so that as D approaches the ceiling of 10.0, further difficulty increases taper off smoothly.
30	What is the role of the DSR state vector in decoupling 'Memory Modeling' from 'Review Scheduling'?	The DSR state vector (D, S) completely summarizes the learner's memory of a card independent of any scheduling policy; the scheduler simply queries R(t, S) to pick the next review date that satisfies the user's chosen Desired Retention.
31	What does it mean if a deck has a high average Stability (mean S = 120 days) and a high average Retrievability (mean R = 93%)?	It means the deck is both deeply consolidated in long-term memory (high S) and currently well-maintained with very few forgotten cards (high R).
32	Guaranteeing monotonicity: Can a successful recall in FSRS-6 ever reduce a card's Stability (S'_r < S)?	No. In the long-term recall formula S'_r = S · (1 + ...), the additive growth term is strictly non-negative, ensuring S'_r ≥ S for any successful recall.