Fig. 4. Relational properties in deep networks.

a Example illustrating the Weber’s law for line length. Although the original statement of Weber’s law is that the just-noticeable difference in length will depend on the baseline length, previous studies have shown that it also applies to perceptual distances²³. In this formulation, the perceptual distance across pairs of lines differing in length will be more correlated with relative changes in length rather than absolute changes in length. b To calculate a single quantity that measures adherence to Weber’s law, we calculated the correlation between distances and relative changes in length and subtracted the correlation between distances with absolute changes in length (see the “Methods” section). A positive difference indicates adherence to Weber’s law (grey region). This difference in correlation is plotted across layers for line length in VGG-16 (blue) and a VGG-16 with random weights (brown). The dashed line indicates the value observed during human performing visual search on the same stimuli. c Schematic of the relative size encoding observed in monkey IT neurons²⁴. Parts are coloured differently for illustration; in the actual experiments we used black silhouettes. For a fraction of neurons, the distance between two-part objects when both parts covary in size is smaller than the distance when they show inconsistent changes in size. Thus, these neurons are sensitive to the relative size of items in a display. d Relative size index across units with interaction effects (averaged across top 7% tetrads, error bars representing s.e.m.) across layers of the VGG-16 network (blue) and a VGG-16 with random weights (brown). The dashed line shows the strength of the relative size index estimated from monkey IT neurons on the same set of stimuli²⁴. e Schematic of the surface invariance index observed in monkey IT neurons²⁵. For a fraction of neurons, the distance between two stimuli with congruent changes in pattern and surface curvature is smaller than between two stimuli with incongruent pattern/surface changes. Thus, these neurons decouple pattern shape from surface shape. f Surface invariance index across units with interaction effects (averaged across top 9% pattern/surface tetrads, error bars representing s.e.m.) across layers of the VGG-16 network (blue) and a VGG-16 with random weights (brown). The dashed line depicts the surface invariance index estimated from monkey inferior temporal neurons on the same set of stimuli²⁵.