[ACT-R-users] Efficient approximation of the Base-Level Learning Equation

[Alex Petrov]

Dear Lynne,

Thanks for this useful information. I used to ruminate about these issues, but 
have since come to the conclusion that the activation function is an emergent 
property of billions of neurons and, as such, does not have a neat entry in 
the mathematical catalog.  It's neither power nor exponential; it's just some 
context-sensitive function affected to individual differences, development, 
medication, etc. So, we are dealing with approximations anyway and the only 
thing that matters is its three qualitative properties: transient boost 
immediately after use, gradual accretion of strength with frequent use, and 
decay in the absence of use. 

The problems with the power function are well documented. (See below for some 
relevant refs). I bet the exponential has similar problems of its own. It's 
hard to beat the elegance of John's rational analysis of memory, though.

The two-page abstract that started this whole discussion does not make any 
claim as to whether the ACT-R proposal is *the* correct function.  It simply 
says, "assuming this is a good function to use, how can we approximate it 
efficiently".

Best regards, and I look forward to seeing you in Pgh :-)

-- Alex

@article{PradhanHoffman63,
    author  = {Pradhan, P. L. and Hoffman, P. J.},
    year    = 1963,
    title   = {Effects of Spacing and Range of Stimuli on Magnitude Estimation 
judgments},
    journal = {Journal of Experimental Psychology},
    volume  = 66,
    pages   = {533--541},
    annote  = {Suggest that the power function is an artifact of data 
averaging},
}

@article{ParkerCaseyZiriaxEtAl88,
    author  = {Parker, S. and Casey, J. and Ziriax, J. M. and Silberberg, A.},
    year    = 1988,
    title   = {Random Monotone Data Fit Simple Algebraic Models:        
                 Correlation is Not Confirmation},
    journal = {Psychological Bulletin},
    volume  = 104,
    number  = 3,
    pages   = {417--423},
    annote  = {Power fun can fit almost any monotonic curve w/in measurement 
errors},
}

@article{PoultonE89,
    author  = {Poulton, E. C.},
    year    = 1989,
    title   = {Uncertain Size of Exponent when Judging without Familiar 
Units},
    journal = {Behavioral and Brain Sciences},
    volume  = 12,
    number  = 2,
    pages   = {286--287},
    annote  = {Commentary to Krueger89},
}
@article{Krueger89,
    author  = {Krueger, L. E.},
    year    = 1989,
    title   = {Reconciling {F}echner and {S}tevens:
               Toward a Unified Psychophysical Law},
    journal = {Behavioral and Brain Sciences},
    volume  = 12,
    number  = 2,
    pages   = {251--320},
    annote  = {Continuing commentary (1991), BBS 14, 187-204.},
}


On Wednesday 15 February 2006 03:14 pm, Lynne Reder wrote:
> Alex, two things:
>
>   first in my step-child version of ACT-R's non-procedural memory
> (called SAC), we use a transient boost in current activation that
> decays exponentially.  I think old versions of ACT did that too, but I
> know longer remember.  In any case,  I've been using a current boost
> that decays exponentially for about a decade or so (first published in
> 1996).  Second, as you may know, Barbara Dosher & co. have evidence
> that power law learning is really an artifact of averaging different
> exponentials from different processes within a person or across people.
>   I heard her give a talk recently.  Perhaps I have mischaracterized
> these things, but thought you might know about this and want to address
> that.
>
> Regards,
> Lynne