# Memory graphs (4D)

## Contents

SuperMemo 17 uses a new spaced repetition algorithm denoted Algorithm SM-17. 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. Tools : 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!

1. At the moment of writing (April 2016), SuperMemo 17 does not use incremental adjustments to optimization matrices in Algorithm SM-17. This is why you should execute Tools : Memory : 4D Graphs : Stability : Compute from time to time to adjust the algorithm to newly available data. In the future, the adjustments will be made at each repetition.
2. To see nice graphs as shown in the pictures below, you also need to use a 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 3 axes (X, Y and Z), and a slider for animation in the 4th dimension along item difficulty.

The following memory graphs are available with Tools : Memory : 4D Graphs on its individual tabs:

## Graph analysis controls

• X, Y, Z axis rotation (top 3 sliders)
• Difficulty slider (for animation in the 4th dimension)
• Repetition cases in consideration (bottom slider)
• Cases: the label showing the total number of repetition cases in consideration
• Compute: recompute the graph using the data in the collection
• Reset: reset the memory matrices
• Smoothing: average neighboring entries in matrices
• Subset: select a 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:
1. the best-fit approximation, and
2. data-rich neighboring entries in proportion to available information

## Pictures

### Stability increase function

Figure: 3D graph of SInc[] matrix based on 60,167 repetition cases for items with difficulty=0.5. The increase is dramatic at low stabilities (17-fold increase is unheard of in earlier SuperMemos), and peaks at retrievability of 0.85. In some cases, the SInc drops below 1.0, which corresponds with a drop in stability (i.e. memory lability). Those low values of SInc do not depend on retrievability. Those huge variations in SInc[] are the main reason why SuperMemo 17 beats SuperMemo 16 in learning metrics by a wide margin..

### Stability increase function contour map

Figure: A "from above" view at the SInc[] matrix providing a contour map. Red zones indicate high stability increase at review. The picture shows that the greatest stability increase occurs for lower stability levels and retrievabilities around 70-90%.

### Stability increase approximation

Figure: 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). The approximation procedure uses a hill-climbing algorithm with parameters A, B, C, D displayed in the picture. Least squares deviation is obtained to asses the progress. Green circles represent the Sinc[] matrix at a chosen difficulty level. Their size corresponds with repetition cases investigated. The blue surface is the best fit of the studied function to the SInc[] data.

### Recall

Figure: The Recall[] matrix graph shows that the actual recall differs from predicted retrievability. For higher stabilities and difficulties, it is harder to reach the desired recall level.

### Recall approximation

Figure: Approximating the Recall[] matrix with the best-fit function to compute default recall in conditions of data scarcity. The approximation procedure uses a hill-climbing algorithm with parameters A, B, C, D displayed in the picture. Least squares deviation is obtained to asses the progress. The circles represent the Recall[] matrix at a chosen difficulty level. Their size corresponds with repetition cases investigated. The red surface is the best fit of the studied function to the Recall[] data.

### Recall approximation curve

Figure: Approximating the Recall[] matrix with the best-fit function to compute default recall in conditions of data scarcity. By choosing the right viewing angle, the curve that reflects the changes to recall with retrievability can be seen in abstraction of stability. In this case the relationship is almost linear (the logarithmic bend is a result of the log scale used for retrievability).

### First interval

Figure: The relationship between the first interval after failure, retrievability at review, and prior memory lapse count.

### First interval approximation

Figure: Approximating the impact of retrievability and memory lapses on the post-lapse stability.