Extended Data Fig. 4: Comparisons of fit to memory data for different measured similarity functions.

Comparison of fit to memory data for similarity functions reported in main text. In the current data for color, both the model-based triad psychophysical scaling data and the Likert similarity rating produce extremely similar data (see Fig. 1). Thus, they all produce similar fits to the memory data (shown here are the set size data). It is important to note that depending on the number of trials, a large number of data points (that is subjects) may be necessary in order to obtain reliable estimates of a given stimulus space in the triad and quad scaling tasks (we use the quad task for face similarity). The Likert task requires considerably less data to estimate, and it was in agreement with the results of the triad task for colors, so we rely on it as our primary measure of similarity in the current fits. However, depending on the stimulus space, observers may utilize different strategies in such subjective similarity tasks (particularly for spaces, like orientation, where it is obviously a linear physical manipulation), and ultimately an objective task like the quad task may be best to understand the psychophysical similarity function. This is why for the face space task we used the quad similarity task. The task used to estimate similarity is important in that it is important that participants provide judgments of the absolute interval between stimuli and not rely on categories or verbal labels, or, in the triad task, that participants not rely on a relational or relative encoding of the two choice items rather than their absolute distance to the target item. How best to ensure that participants rely on absolute intervals is represented in a large literature dating to Thurstone⁶³ and Torgerson¹⁵.