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I use Anki for studying. I add 20 new facts each day. Over the past few months, I have noticed that each day, I have slightly more words to review than the previous day. Over time, this is adding up, and it takes several hours to finish all of the reviews.

  • Is it normal for the number of daily reviews to steadily increase?
  • Will the number of daily reviews eventually reach balance?
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2 Answers 2

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Your question is the first thing I have asked when heard of spaced repetition to flatten the exponential forgetting curve

enter image description here

I even considered the mathoverflow to ask for (new words) input rate to compensate the fact that I will have exponential gaps between repetition of learned words. I imagined the gaps like time axis

1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  
1   1       1               1                               1                                                               1                                                                                                                               1       

Here, pulses of 1 indicate the moments of time when you should repeat the idea, starting from two expositions, without any gap between them. The pulse density decreases exponentially as time goes on. This creates ever increasing amount of free slots that you can fill with pulses of new material, say 2:

        1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64
        2   2       2               2                               2                                                               2                                                                                                                               2
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66
1   1   2   2   1   2       1       2                       1       2                                                       1       2                                                                                                                       1       2

The line above shows repetitions 2 introduced and line at the bottom summarizes the instances when you should be exposed to both 1 and 2. Again, it becomes less sparse as time goes on and you can start learn idea3 at later time.

                        1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  
                        3   3       3               3                               3                                                               3                                                                                                               
        1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64
        2   2       2               2                               2                                                               2                                                                                                                               2
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66
1   1   2   2   1   2   3   3   1   2   3           3       1       2               3                                       1       2               3                                                                                                       1       2

You see that in case of conflict, when it is time to repeat two things at once, I prioritize the newly introduced cards because dealaying them causes more memory loss than delaying old familiar material. I am not sure how to resolve the conflicts better. Anyway, you see that my idea is to fill the gaps which appear due to exponential time necessary between repetitions. Which time shift should we use between representing every new idea? Is it possible to fill all gaps exactly, submitting material at constant rate, without causing neither overflow nor underflow? The constant rate of introducing new material is what you are talking you here. And, it was the first question that stroke my head when I first heard about this kind of learning.

Initially I wanted to ask this question at mathoverflow. But school teaches us the geometric series (I used the decay ration of 2 in the example above). Say, thing 1 repetition rate goes down at

1/2     1/4     1/8     1/16        1/32        1/64        ...

This means that we have to repeat a single item once per 2 time units, then once per 4 time units, then once per 8 time units and so on. The thing to notice is that series 1/2+1/4+1/8+.. adds up to 1. It is important because when we introduce repetition of another item, one time unit later, we get

1/2     1/4     1/8     1/16        1/32        1/64        1/128       ...
        1/2     1/4     1/8         1/16        1/32        1/64        ...

and other items at later times on, introducing 1 item every next time unit

1/2     1/4     1/8     1/16    1/32    1/64        1/128       1/256       ...
        1/2     1/4     1/8     1/16    1/32        1/64        1/128       ...
                1/2     1/4     1/8     1/16        1/32        1/64        ...
                        1/2     1/4     1/8         1/16        1/32        ...

Now, we are interested for the vertical column to be 1. And indeed, as time goes on, all your gaps are filled exactly to density 1, which means that at every instance of time you have something to learn/repeat but no more.

I considered it like a rigorous mathematical issue, though reality may be different. It is mentally very intensive to remember and compute all the recalling periods and exact timing is impossible because of conflicting repetition timing and your other daily business. Anki keeps timing as much as possible and, through feedback, adjusts the spacing. I provide mostly the extendnded question rather than answer here. I am curious myself if the anki feedback can reconcile the atomicity of the thoughts with continous decay.

You get this result exactly when exposing a constant amount of material at every instance of time. Might be your constant is too large though. I expected the real Anki experiment to confirm that and provides the constant since in my discussion it is not clear what is the "one item". Is it a book, a chapter, a sentence, a paragraph, a single word? How large is one item?

update I have spotted that the series does not decrease exponentially. The series 1/2+0+1/4+0+0+0+1/8+0+0+0+0+0+0+0+1/16+0+... goes down more slowly than geometric series, 1/2+1/4+1/8+... I could not describe what you will get in the vertical columns when add a new item every n clock cycles and created a program to simulate the case (initially there as a bug). Now, it shows that the amount of material to reherse is accumulating overtime and it is accumulating exponentially, at first guess. Might be that is your problem.

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Yes, it will sort of balance out, but it will take a while. I'm using Anki as well, and as soon as cards are getting into the mature state, and are steadily spreading away further and further, they will ease on your workload. When your workload gets too much, it often helps to take some kind of digestion break, to allow the bulk of cards to spread into the future as you're getting more confident with them. Meaning that you stop introducing new cards, while continuing to review the old ones on a daily base.

It may be that 20 new cards/day on a steady base is too high a load to take into your active deck, so don't feel guilty if you ease that load and reduce it. With Anki, steady gets you further than digging through immense workloads.

In such an overload situation, it also helps not to do the full workload - Anki doesn't really punish you if you're not managing all cards at once. When you're reviewing a card that had actually been due a few days ago, and you manage to recall it, the spacing algorithm will take into account that you have been able to remember it at a greater interval than anticipated, and offer a longer interval for the next review as well, thus easing your load.

The only thing to keep in mind when you don't meet your goal due to high workload would be to avoid introducing too many new cards, and to keep reviewing.

For motivation and to view your progress, watch how the cards spread out in the "Intervals" report. This one will also show you when you are ready to start introducing new cards again (as soon as the high peak of cards with a less-than-a-week interval evens out).

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When I used Anki, I decided upon how many cards I could reasonably do in a day and only added new cards if my reviews were less than that. So if I set a limit of 50 and had 45 reviews, then I added 5 new cards. But if I had 60 reviews, no new cards. That helped a lot to keep things reasonable. –  Belisama Jun 9 '12 at 11:45

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