Abstract
Scarf et al. (Proc Natl Acad Sci 113(40):11272–11276, 2016) demonstrated that pigeons, as with baboons (Grainger et al. in Science 336(6078):245–248, 2012; Ziegler in Psychol Sci. https://doi.org/10.1177/0956797612474322, 2013), can be trained to display several behavioural hallmarks of human orthographic processing. But, Vokey and Jamieson (Psychol Sci 25(4):991–996, 2014) demonstrated that a standard, autoassociative neural network model of memory applied to pixel maps of the words and nonwords reproduces all of those results. In a subsequent report, Scarf et al. (Anim Cognit 20(5):999–1002, 2017) demonstrated that pigeons can reproduce one more marker of human orthographic processing: the ability to discriminate visually presented four-letter words from their mirror-reversed counterparts (e.g. “LEFT” vs. “
”). The current report shows that the model of Vokey and Jamieson (2014) reproduces the results of Scarf et al. (2017) and reinforces the original argument: the recent results thought to support a conclusion of orthographic processing in pigeons and baboons are consistent with but do not force that conclusion.
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Notes
There is no good statistical reason to leave our simulations as under-powered as the pigeon experiments were: we could have, for example, used many more simulated pigeons, and with many more learned items. Instead, we aimed for verisimilitude: could we simulate similar effects with such limited training and memories?
\({\mathbf {X}}^T\) is the matrix transpose of \({\mathbf {X}}\).
Technically, the weight-matrix, \({\mathbf {W}}\), is given by \({\mathbf {W}} = \delta {\mathbf {UU}}^T\), for which \(\delta\) is the vector of corresponding eigenvalues. The effect of Widrow–Hoff error training is to spherize or “whiten” the weight-matrix, rendering each of the eigenvectors the same length; hence, dropping the eigenvalues from the expression produces the Widrow–Hoff error-correction (Abdi et al. 1999).
Which also means that every item stored in memory is necessarily perfectly reconstructed if every eigenvector is used in that reconstruction (which is why we have to resort to the “leave one out” approach for the test of training). That is, every individual training item is perfectly preserved in that memory, as a consequence of Widrow–Hoff learning, much as the original data matrix can be completely reconstructed from its PCA if every component is retained. That is why we characterize such models of memory as instance-based.
Although our model captures the trend in performance as a function of number of reversible letters, the pigeons of Scarf et al. (2017) endorsed as words the tested, mirrored items at a higher rate than our model overall. Unfortunately, Scarf et al. (2017) made a much smaller set of comparisons than we did (e.g. the 80% achieved by their pigeons in the condition in which every letter could be reversed reflected performance on 4 of 5 items over the 4 pigeons for the mirrored words they actually used). Scarf et al. (2017) did not provide the particular words that each pigeon was trained and tested on; consequently, we could not derive a direct comparison to test whether the model not only predicts the relationship but also the particular details of that relationship.
For the pixel maps we used, there are only 31 nonreversible words, 72 words with just 1 reversible letter, 136 with 2, 61 with 3, and only 8 with 4. For nonwords, there are 759 nonreversible nonwords, 3593 nonwords with 1 reversible letter, 2734 with 2, 700 with 3, and 46 with 4. These distributional differences in the base-rates for mirror-reversed words and nonwords result in a significant bias, with words generally having more reversible letters than nonwords (linear trend chi-square test for ordinal data: \(M^{2}(1) = 59.42, p<.0001\), Agresti 1996).
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Funding
This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada to R. K. Jamieson (RGPIN 355882-2013) and a University of Lethbridge Arts and Science research grant to J. R. Vokey.
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Vokey, J.R., Jamieson, R.K., Tangen, J.M. et al. A visual familiarity account of evidence for orthographic processing in pigeons (Columbia livia): a reply to Scarf, Corballis, Güntürkün, and Colombo (2017). Anim Cogn 21, 425–431 (2018). https://doi.org/10.1007/s10071-018-1166-2
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DOI: https://doi.org/10.1007/s10071-018-1166-2