Fig 1.
A stimulus is encoded in two ways: (1) a fine-grained representation of the stimulus itself, shown as a (gray) distribution over stimulus space centered at the stimulus’ location in that space, and (2) the language-specific category (e.g. English “green”) in which the stimulus falls, shown as a separate (green) distribution over the same space, centered at the category prototype. The stimulus is reconstructed by combining these two sources of information through probabilistic inference, resulting in a reconstruction of the stimulus (black distribution) that is biased toward the category prototype. Adapted from Fig 11 of Bae et al. (2015) [20].
Fig 2.
Category effects from biased reconstruction.
Model reconstructions tend to be biased toward category prototypes, yielding enhanced distinctiveness for two stimuli that fall on different sides of a category boundary. Categories are shown as distributions in green and blue; stimuli are shown as vertical black lines; reconstruction bias patterns are shown as arrows.
Fig 3.
Screenshots of example trials illustrating (A) simultaneous reconstruction, (B) delayed reconstruction, and (C) green goodness rating.
Fig 4.
Naming and bias data, Study 1.
In both top and bottom panels, the horizontal axis denotes target hue, ranging from yellow on the left to purple on the right. Top panel (naming data): The solid green and blue curves show, for each target hue, the average goodness rating for English green and blue respectively, as a proportion of the maximum rating possible. The dashed green and blue curves show Gaussian functions fitted to the naming goodness data. The dotted vertical lines marked at the bottom with green and blue squares denote the prototypes for green and blue, determined as the means of the green and blue fitted Gaussian functions, respectively. The shaded region in the top panel shows the portion of the spectrum for which bias data were collected. Bottom panel (bias data): Solid curves denote, for each target hue, the average reconstruction bias for that hue, such that positive values denote reconstruction bias toward the purple (here, right) end of the spectrum, and negative values denote reconstruction bias toward the yellow (here, left) end of the spectrum. Units for the vertical axis are the same as for the horizontal axis, which is normalized to length 1.0. The black and red curves show bias under simultaneous and delayed response, respectively. Blue stars at the top of the bottom panel mark hues for which there was a significant difference in the magnitude of bias between simultaneous and delayed conditions. The shaded region in the bottom panel shows the portion of the data that was analyzed statistically, and to which models were fit. In both panels, error bars represent standard error of the mean.
Fig 5.
Bias in color reconstruction, and model fits, Study 1.
Left column: Bias from simultaneous reconstruction, fit by each of the four models. The empirical data (black lines with error bars) in these four panels are the same, and only the model fits (red lines) differ. Within each panel, the horizontal axis denotes target hue, and the vertical axis denotes reconstruction bias. The green and blue prototypes are indicated as vertical lines with green and blue squares at the bottom. Right column: delayed reconstruction, displayed analogously.
Table 1.
Model fits to reconstruction data, Study 1.
LL = log likelihood (higher is better). MSE = mean squared error (lower is better). The best value in each row is shown in bold.
Fig 6.
Color naming across languages, Study 2.
The English categories green and blue (top panel), the Berinmo categories wor and nol (middle panel), and the Himba categories dumbu and burou (bottom panel), plotted against a spectrum of hues that ranges from dark yellow at the left, through green, to blue at the right. Colored squares mark prototypes: the shared prototype for Berinmo wor and Himba dumbu, and the prototypes for English green and blue; the color of each square approximates the color of the corresponding prototype. For each language, the dotted-and-dashed vertical lines denote the prototypes for the two categories from that language, and the dashed vertical line denotes the empirical boundary between these two categories. Black curves show the probability of assigning a given hue to each of the two native-language categories, according to the category component of a 2-category model fit to each language’s naming data. The shaded regions mark the ranges of colors probed in discrimination tasks; these two regions are centered at the English green-blue boundary and the Berinmo wor-nol boundary. Data are from Roberson et al. (2000) [9] and Roberson et al. (2005) [10].
Fig 7.
Color discrimination across languages, Study 2.
Top panels: Discrimination from memory by Berinmo and English speakers for pairs of colors across and within English and Berinmo color category boundaries. Empirical data are from Table 11 of Roberson et al. (2000:392). Empirical values show mean proportion correct 2AFC memory judgments, and error bars show standard error. Model values show mean model proportion correct 2AFC memory judgments after simulated reconstruction with native-language categories. Model results are range-matched to the corresponding empirical values, such that the minimum and maximum model values match the minimum and maximum mean values in the corresponding empirical dataset, and other model values are linearly interpolated. Bottom panels: Discrimination from memory by Himba and English speakers for pairs of colors across and within English and Himba color category boundaries, compared with model results based on native-language categories. Empirical data are from Table 6 of Roberson et al. (2005:400); no error bars are shown because standard error was not reported in that table.
Table 2.
Model fits to cross-language discrimination data, Study 2, reported in mean squared error (lower is better).
The best value in each row is shown in bold. Data are fit better by native-language models than by other-language models.
Fig 8.
Within-category bias, dependent on presentation order.
The category adjustment model predicts: (top panel, good exemplar) easy within-category discrimination in a 2AFC task when the initially-presented target t is closer to the prototype than the distractor d is; (bottom panel, poor exemplar) difficult within-category discrimination with the same two stimuli when the initially-presented target t is farther from the prototype than the distractor d is. Category is shown as a distribution in blue; stimuli are shown as vertical black lines marked t and d; reconstruction bias patterns are shown as arrows.
Fig 9.
Within-category color discrimination across languages, Study 3.
Across: stimulus pair crosses the native-language boundary; GE: within-category pair, target is the good exemplar; PE: within-category pair, target is the poor exemplar. Empirical data are from Figs 2 (English: 10-second retention interval), 3 (Berinmo), and 4 (Himba) of Hanley and Roberson [36]. Empirical values show mean proportion correct 2AFC memory judgments, and error bars show standard error. Model values show mean model proportion correct 2AFC memory judgments after simulated reconstruction using native-language categories, range-matched as in Fig 7. English model compared with English data: 0.00002 MSE; Berinmo model compared with Berinmo data: 0.00055 MSE; Himba model compared with Himba data: 0.00087 MSE.
Fig 10.
The perception of stimulus S = s produces a fine-grained memory M, and a categorical code c specifying the category in which s fell. We wish to reconstruct the original stimulus S = s, given M and c.
Table 3.
Stimulus coordinates, and approximate rendering of stimuli.
All stimuli were presented at lightness 6, saturation 8 in Munsell space.
Table 4.
Debriefing responses by subject, paraphrased as they were reported to the experimenter.
When subjects gave specific examples of color terms used as memory aids, they are reported here.
Table 5.
Hues for probed stimulus pairs within and across the English blue-green, Berinmo wor-nol, and Himba dumbu-burou boundaries.
Any stimulus pair that includes a boundary color is considered to be a cross-category pair. All hues are at value (lightness) level 5, and chroma (saturation) level 8. 1s denotes a 1-step pair; 2s denotes a 2-step pair.
Table 6.
Hues for probed stimulus pairs within and across the English green-blue boundary for Study 3, from Table 1 of Roberson and Davidoff (2000).
Any stimulus pair that includes a boundary color is considered to be a cross-category pair. All hues are at value (lightness) level 4, and chroma (saturation) level 8. 1s denotes a 1-step pair; 2s denotes a 2-step pair.