<p>Currently, I am working on various demonstration graphs of various spacing effect algorithms.  From the research it seems like two of the parameters exist to constrain the outputted values...</p>

<blockquote>
  <p>The parameters a and b are also assumed bounded between zero and one,
  and hence R(t) is similarly bounded, which must necessarily be the
  case as R(t) is a probability. Enforcing this bound is important as
  otherwise data fits can be inflated (see Navarro, Pitt, &amp; Myung, 2004,
  for further discussion).</p>
</blockquote>

<p>I think Ebbinghaus' original function R(t) = e ^ -(t/s) (see this <a href="https://psychology.stackexchange.com/questions/5199/which-equation-is-ebbinghauss-forgetting-curve-and-what-do-the-constants-repres?rq=1">thread</a>) can more easily explain things.  t is time and s is the strength of the memory.  After every review, s increases.
If you plot this out, you see that if you increase s, the forgetting curve function flattens out.</p>

CC BY-SA 4.0
2018-12-16T15:14:13.133Z
Welcome to Psychology.SE. You suggested to *"see Navarro, Pitt, & Myung, 2004, for further discussion"* yet there is no reference information in order to find the article.
Chris Rogers
CC BY-SA 4.0
2018-12-17T20:23:50.433Z
@ChrisRogers I quoted a part from the paper that OP referenced.
George Boole
CC BY-SA 4.0
2018-12-15T18:13:18.300Z
2018-12-15T18:13:18.300Z
George Boole
<p>There has been a long debate going on on the actual form of the <em>Forgetting curve</em>, but my question will be about its change when we review a previously memorised fact - Unfortunately, I couldn't seem to find too much information (or perhaps I used wrong terms) on this topic.</p>

<p>Maybe the most up-to-date and least divisive research paper on the topic of the actual form of the Forgetting curve would be <em>Averell, L., &amp; Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology</em>, which I have seen referenced here multiple times. According to it the shape of the curve is best described as
$$R(t) = a + (1-a)*b*(1+t)^{-β}$$
which would yield $1$ at $t=0$ if the encoding happened without a problem (which we assume did). My concrete question would be that how the three parameter change after repeated exposure to the fact (where we assume that at this specific $t_r$ the retention increases to $1$ again). I think it is fair to assume that it is going to be yet another curve describable with a Power function starting at $t_r$ which should have a higher asymptote as the original function.</p>

<p>A picture (although not scientific nor correct in terms of the actual form) illustrating my question has been already posted here at <a href="https://cogsci.stackexchange.com/questions/8377/how-are-these-review-forgetting-curve-calculated">How are these review-forgetting curve calculated?</a>, although for different purposes than mine.</p>

CC BY-SA 4.0
2024-09-11T21:06:38.113Z
Also see: [Evidence of flattening forgetting curves with spaced repetition and formulas to predict them](https://psychology.stackexchange.com/q/30575/7001) - I doubt the equation above has withstood the test of time, and how forgetting curves change with rehearsal likely depends on the type of rehearsal.
Arnon Weinberg
<memory>
How does the Forgetting curve change after repeated exposure to the same item we would like to memorise?
FloriOn
# How does the Forgetting curve change after repeated exposure to the same item we would like to memorise?

(Asked by: username_0 on 2016-08-15)

There has been a long debate going on on the actual form of the *Forgetting curve*, but my question will be about its change when we review a previously memorised fact - Unfortunately, I couldn't seem to find too much information (or perhaps I used wrong terms) on this topic.

Maybe the most up-to-date and least divisive research paper on the topic of the actual form of the Forgetting curve would be *Averell, L., & Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology*, which I have seen referenced here multiple times. According to it the shape of the curve is best described as
$$R(t) = a + (1-a)\*b\*(1+t)^{-β}$$
which would yield $1$ at $t=0$ if the encoding happened without a problem (which we assume did). My concrete question would be that how the three parameter change after repeated exposure to the fact (where we assume that at this specific $t\_r$ the retention increases to $1$ again). I think it is fair to assume that it is going to be yet another curve describable with a Power function starting at $t\_r$ which should have a higher asymptote as the original function.

A picture (although not scientific nor correct in terms of the actual form) illustrating my question has been already posted here at [How are these review-forgetting curve calculated?](https://cogsci.stackexchange.com/questions/8377/how-are-these-review-forgetting-curve-calculated), although for different purposes than mine.

**Tags:** memory

> **Comments:**
> **username_1**: Also see: [Evidence of flattening forgetting curves with spaced repetition and formulas to predict them](https://psychology.stackexchange.com/q/30575/7001) - I doubt the equation above has withstood the test of time, and how forgetting curves change with rehearsal likely depends on the type of rehearsal.  

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## 1 answers

### Answer by username_2 on 2018-12-15. Score: 1

Currently, I am working on various demonstration graphs of various spacing effect algorithms. From the research it seems like two of the parameters exist to constrain the outputted values...

> The parameters a and b are also assumed bounded between zero and one,
> and hence R(t) is similarly bounded, which must necessarily be the
> case as R(t) is a probability. Enforcing this bound is important as
> otherwise data fits can be inflated (see Navarro, Pitt, & Myung, 2004,
> for further discussion).

I think Ebbinghaus' original function R(t) = e ^ -(t/s) (see this [thread](https://psychology.stackexchange.com/questions/5199/which-equation-is-ebbinghauss-forgetting-curve-and-what-do-the-constants-repres?rq=1)) can more easily explain things. t is time and s is the strength of the memory. After every review, s increases.
If you plot this out, you see that if you increase s, the forgetting curve function flattens out.

> **Comments:**
> **username_3**: Welcome to Psychology.SE. You suggested to *"see Navarro, Pitt, & Myung, 2004, for further discussion"* yet there is no reference information in order to find the article.  
> **username_2**: @ChrisRogers I quoted a part from the paper that OP referenced.  

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