Features in next version of Parley

[Andreas Xavier]

Feature:  Forgetting curve based training schedules

Note:  The version with the nice .svg plots got bumped.

I want to add training schedules and user assessments based
directly on the forgetting curve time constants.  
Below I will explain what the forgetting curve is, 
how Parley currently schedules training intervals and what the
new method will be and why it is better.  
Please skip the first two sections if have already know how 
Parley works.

I am not really proposing this for release until after the more 
detailed training data is in the data file.

Forgetting Curve:

The forgetting curve measures how fast you forget any new 
information that you learn.  It looks like a slide at children's park.  
When you first learn something you very quickly forget,
the time constant is short or fast, the slide is steep.  
Every time that you learn the material again the time constant 
gets longer, the slide gets flatter and it takes longer for you 
to forget the information.

For more detail see https://en.wikipedia.org/wiki/Forgetting_curve

If you want to learn new material as quickly as possible, then there 
is an optimal place on the curve/slide to relearn the material.  Too 
late and there is risk that you have forgotten too much, too early
and the gain in time constant is smaller than it could be.  Too early 
is not that bad it just means that overall the learning will take longer.

However, if you need to learn something in one week, spending 40
hours in that one week is better than spending 10 hours over 4 months
, even though 10 hours is less total time.

Leitner Boxes:

Currently, Parley uses the Leitner box method to schedule training intervals.
The Leitner box method is an elegant algorithm to approximate optimal
training intervals so that the student doesn't have to calculate time
constants by hand.  The method is simple, every time you get a correct
answer you double the training interval and with every wrong answer
you either halve the interval or go right back to the shortest interval. Simple.

The Leitner method has no provision for intense focused study, like the 
40 hours in one week example above.  If I force Parley to allow me to 
train a word 14 times in a row, it will retire it immediately and it shouldn't

The Leitner box method unduly penalizes late words.  If training of a word 
is very late, then it tells Parley very little about what the student really knows.
But the Leitner box method penalizes the student anyway. 

I think the Leitner method as implemented is too visible in a discouraging
way.  I get one wrong answer and I drop right down to box 0.  In reality
a wrong answer teaches the student almost as much as a correct answer,
but it indicates the student needs to review it sooner.
At the maximum rate of learning before a student approaches mastery there 
are many wrong answers.

New Method:

The new method is simply to use the new training data to directly calculate the
forgetting time constant for each word in reading, listening, speaking and writing.

It is better because it can provide optimal training intervals directly even when the
student practices early, late or often.  It correctly handles short training intervals.

It is easier to set up.  In fact if you do nothing it will end up at optimal training 
intervals for that student.

It can allow the student to do planning.  For example the student can ask the question: 
I would like to be at 90% retention of these words 4 months from now and be able to 
remember them for 1 month.  How much time should I study per day?

This method and the data stored in the new file format makes available a new array
of statistics and plots to track your performance.  Unfortunately, if the visualizers
highlight new words students will have unscheduled training opportunities. =)

The method also allows interactive tailoring of the rate of learning to use preferences.
Simply asking the user if the previous session seemed too hard, too easy or just
right would allow the algorithm to tailor the rate of learning and the intervals to 
the user's desires.  Themaximal rate of learning probably involves more wrong 
answers that most students are comfortable with.  

I made a demo of the method with a mock student.  The code for the new method is
real. The student is simulated.

I have attached two plots of results of fixed interval training, where the student 
practices only the words due up to some time limit each session.  

The first plot is with 10 words over 1 month, 9 training sessions of 30 seconds each. 
You can see the improvement of the time constant by the flattening of the curve
at the end of the month.

The second plot is of 1000 words, 1/2 hour per day over 6 months. 
You can see the gain and then maxing out of performance.  The curve flattens
out before 90% because I stuck in a fudge factor so that I could complete the example
before the end of today.  


Cheers Andreas






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