View source for Memory graphs (4D)

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[https://help18.supermemo.org/wiki/What's_new_in_SuperMemo_18? SuperMemo 18] or later uses a new spaced repetition algorithm denoted [https://supermemo.guru/wiki/Algorithm_SM-18 Algorithm SM-18]. Unlike all prior algorithms that were either theoretical or "inspired by data", this algorithm has been developed entirely on the basis of prior records of repetitions collected by users of SuperMemo. This data-driven effort required untold hours of analysis while processing millions of repetition samples. '''[[Toolkit menu|Toolkit]] : [[Toolkit menu#Memory|Memory]] : 4D Graphs''' was instrumental in that analysis and debugging process. If you want to understand the algorithm and help improve it further, please study those tools and keep analyzing your own data and your own memory. In a stochastic system of memory, perfection is impossible, but we should always try to come closer to the optimum.

'''Important:''' To see nice graphs as shown in the [[#Pictures|pictures below]], you need to use a [[Glossary:Collection|collection]] with a mature learning process. New collections have no memory data to show.

== Available memory graphs ==

All memory graphs provide a 3-dimensional view with rotation along all 2 axes (X and Y), and a slider for animation in the 3rd dimension along [[Glossary:Difficulty|item difficulty]].

The following memory graphs are available with '''[[Toolkit menu|Toolkit]] : [[Toolkit menu#Memory|Memory]] : 4D Graphs''' on its individual tabs:

* Matrices -
** S90 - stabilization at [[Glossary:Retrievability|retrievability]] of 90%
** SIncMin - minimum stabilization in the stabilization curve
** SIncMax - maximum stabilization in the stabilization curve
** Gain - spacing effect expressed as a stabilization gain in the stabilization curve
** Decay - stabilization decay in the stabilization curve
** OS - optimum stabilization derived from stabilization increase using approximation formulas analogous to those used in deriving the matrix of [[Glossary:O-Factor|O-Factor]]s from the matrix of [[Glossary:R-Factor|R-Factor]]s
** Recall - actual recall measured at the predicted [[Glossary:Retrievability|retrievability]] of 90%
** R90 - predicted [[Glossary:Retrievability|retrievability]] at recall of 90%
** Metric - recall metric that shows the accuracy of recall predictions for different levels of [[Glossary:Stability|stability]] and [[Glossary:Difficulty|difficulty]]
** Cases - repetition cases used in computing the stabilization matrix
** RF - [[Glossary:RF matrix|R-Factor matrix]] of [https://supermemo.guru/wiki/Algorithm_SM-15 Algorithm SM-15]
** OF - [[Glossary:OF matrix|O-Factor matrix]] of [https://supermemo.guru/wiki/Algorithm_SM-15 Algorithm SM-15]
** Intervals - [[Glossary:Optimum interval|optimum interval]]s matrix
** RF Cases - repetition cases used in computing the [[Glossary:RF_matrix|R-Factor matrix]] of [https://supermemo.guru/wiki/Algorithm_SM-15 Algorithm SM-15]
* '''Stabilization''': the function that tells you how much [[Glossary:Stability|memory stability]] increases with a [[Glossary:Repetition|repetition]]. If you click '''Compute''', all [[Repetition history|repetition histories]] will be scanned to compute the [[Glossary:Stability_increase_matrix|SInc[] matrix]]. For a given [[Glossary:Difficulty|item difficulty]], the increase depends on [[Glossary:Stability|stability]] and [[Glossary:Retrievability|retrievabilty]]. To view the 3-rd dimension of [[Glossary:Difficulty|difficulty]], slide the thumb on the '''Difficulty''' slider. See [[#Stability increase function|example]]
* '''SInc Approx''': approximation of the function represented by the [[Glossary:Stability_increase_matrix|stability increase matrix]]. If you click '''Compute''', SuperMemo will look for the best fit to data (which is the SInc[] matrix computed on the '''Stabilization''' tab). See [[#Stability increase function approximation|example]]
* '''Recall''': the function that tells you how well actual recall corresponds with [[Glossary:Retrievability|retrievability]] predicted by SuperMemo. The difference between comes primarily from the difficulty in [http://super-memory.com/articles/20rules.htm formulating perfect items] that would produce purely exponential forgetting. In addition, SuperMemo itself is far from perfect in sorting [[Glossary:Item|items]] by [[Glossary:Difficulty|difficulty]]. See [[#Recall|example]]
* '''Recall Approx''': approximation of the function represented by the [[Glossary:Recall_matrix|Recall[] matrix]]. If you click '''Compute''', SuperMemo will look for the best fit to data (which is the Recall[] matrix computed on the '''Recall''' tab). See [[#Recall approximation|example]]
* '''First Interval''': the function that illustrates [[Glossary:Post-lapse_stability|post-lapse stability]] depending on the number of [[Glossary:Lapse|lapses]] and [[Glossary:Retrievability|retrievability]] at failure. It is the equivalent of the first-interval graph extended into the retrievability dimension. [[Glossary:Retrievability|Retrievability]] is important in that a failure at low retrievability does not need to signify the [[Glossary:Item|item]] is difficult and [[Glossary:Post-lapse_stability|post-lapse stability]] is low. See [[#First interval|example]]
* '''PLS Approx''': approximation of the function represented by post-lapse stability matrix. If you click '''Compute''', SuperMemo will look for the best fit to data (which is the post-lapse matrix computed on the '''First Interval''' tab). See [[#First interval approximation|example]]
* '''Sleep''': correlation between recall and the [[SleepChart#Two-component_sleep_model|two components of sleep]]. This is a 2-dimensional graph that combines [[SleepChart#Alertness|'''Alertness (H)''' and '''Alertness (C)''']] of '''[[Sleep Chart]]'''. As the data is not part of Algorithm SM-18 optimization, you need to click '''Compute''' to collect data needed to display this graph
* '''Forgetting''': 3D [[Glossary:Forgetting_curve|forgetting curves]] collected by [https://supermemo.guru/wiki/Algorithm_SM-15 Algorithm SM-15]. This is the same graph as the one displayed by '''[[Toolkit menu|Toolkit]] : [[Toolkit menu#Statistics|Statistics]] : [[Analysis]] : [[Analysis#3-D Curves|3-D Curves]]''' with the added benefit of 3-axis rotation in space and '''[[Glossary:A-Factor|A-Factor]]''' slider for the 4th dimension.
* '''RF Matrix''': 3D [[Glossary:RF_matrix|RF matrix]] collected by [https://supermemo.guru/wiki/Algorithm_SM-15 Algorithm SM-15]. This is the same graph as the one displayed by '''[[Toolkit menu|Toolkit]] : [[Toolkit menu#Statistics|Statistics]] : [[Analysis]] : [[Analysis#3-D Graphs|3-D Graphs]] : R-Factor Matrix''' with the added benefit of 3-axis rotation in space

== Graph analysis controls ==

* '''X''' and '''Y''' axis rotation (top 2 sliders)
* '''Difficulty''' slider (for animation in the 3rd dimension)
* Repetition cases in consideration
* '''Cases''': the label showing the total number of repetition cases in consideration
* '''Compute''': recompute the graph using the data in the [[Glossary:Collection|collection]]
* '''Reset''': reset the memory matrices
* '''Smoothing''': average neighboring entries in matrices
* '''Subset''': select a [[Glossary:Element_subset|subset of elements]] for which matrices should be computed
* '''Reset Cases''': reset the count of repetition cases without changing the data (i.e. values of entries in matrices)
* '''Export''': export data for analysis in Excel
* '''Average''' checkbox: the "golden mean" average of the data with:
*# the best-fit approximation, and
*# data-rich neighboring entries in proportion to available information

== Pictures ==

=== Stability increase function ===

<div class="center">
[[Image:Stability increase function.png|800px|SuperMemo: 3D graph of SInc[] matrix based on 61,768 repetition cases for items with difficulty=0.8]]
{{:Image:Stability increase function.png}}
</div>

=== Stability increase function contour map ===

<div class="center">
[[Image:Stability increase function contour map.jpg|800px|SuperMemo: A "from above" view at the SInc[] matrix providing a contour map]]
{{:Image:Stability increase function contour map.jpg}}
</div>

=== Stability increase approximation ===

<div class="center">
[[File:Stability increase function approximation.jpg|800px|SuperMemo: Approximating the SInc[] matrix with the best-fit function used by default in SuperMemo to compute the increase in stability (e.g. in cases of lack of data)]]
{{File:Stability increase function approximation.jpg}}
</div>

=== Recall ===

<div class="center">
[[File:Recall.jpg|800px|SuperMemo: The Recall[] matrix graph showing actual recall differs from predicted retrievability]]
{{:File:Recall.jpg}}
</div>

=== Recall approximation ===

<div class="center">
[[File:Recall approximation.jpg|800px|SuperMemo: Approximating the Recall[] matrix with the best-fit function to compute default recall in conditions of data scarcity]]
{{:File:Recall approximation.jpg}}
</div>

=== Recall approximation curve ===

<div class="center">
[[File:Recall approximation curve.jpg|800px|SuperMemo: Approximating the Recall[] matrix with the best-fit function to compute default recall in conditions of data scarcity]]
{{:File:Recall approximation curve.jpg}}
</div>

=== First interval ===

<div class="center">
[[File:Post-lapse stability.jpg|800px|SuperMemo: The relationship between the first interval after failure, retrievability at review, and prior memory lapse count]]
{{:File:Post-lapse stability.jpg}}
</div>

=== First interval approximation ===

<div class="center">
[[File:First interval approximation.jpg|800px|SuperMemo Approximating the impact of retrievability and memory lapses on the post-lapse stability]]
{{:File:First interval approximation.jpg}}
</div>