Fig. 4: Analysis of single-kernel models trained on human gloss judgements.

a, Computational steps of the single-kernel model. Conv., convolution. The input image is convolved with a 15 × 15 × 3 kernel, the resulting activation map is max-pooled to a single value, and a bias term is applied to produce the gloss prediction. b, Consistency check across 24 networks trained in cross-validation. Although the training splits partially overlapped across folds (and, thus, the networks are not fully independent in terms of the data they saw), the networks were trained separately with different random weight initializations. All networks developed a similar pattern of kernels, with a bright blob located at various positions, superimposed on straight elongated, diagonally oriented brown–black–blue ridges. c, Analysis of chromatic tuning of the kernel. The sRGB colour of each pixel in an example kernel was converted to the L*a*b* colour coordinates, and their a*b* distribution is shown. We found that kernel colours are closely aligned along the daylight locus, probably reflecting the typical colour of specular highlights and their contrast with the surrounding bluish ambient light (from skylight reflections in shadows) seen in training images (see example image at the bottom). d, Chromatic distribution of an emergent kernel from a human-like network trained on a new set of 3,888 images under 90° gamut-rotated environmental illuminations. The kernel clearly adapts to the chromatic statistics of specular highlights present in the training data. e, Kernel that emerged from a human-like network trained on images in which the object was rotated by 90° relative to the original orientation. f, Kernel that emerged from a human-like network trained on object images illuminated by light probes whose elevation was lowered by 90°. g, Fitting a 2D Gaussian filter and one or two Gaussian ridges to the kernel’s spatial intensity distribution. For simplicity, fitting was performed on the luminance image after mean subtraction. The bright blob region is well approximated by the 2D Gaussian filter. The diagonal stripe pattern is captured by a 1D Gaussian ridge, and the residual component is also shown. The difference in scale between the two components is indicated by the colour bars. h, Distribution of the fitted parameters for the 2D Gaussian components and ridges across the 24 kernels shown in b. i, Thirty-six image regions that most strongly activated the example kernel for images where both humans and the model judged the surfaces as highly glossy. Although the regions capture a variety of specular reflection geometries, diagonal highlights are comparatively more prevalent. j, Examples of real material photographs, showing enlarged regions of oriented specular highlights that maximally activate our single kernel.