Contrast sensitivity function in deep networks.

The contrast sensitivity function (CSF) is a fundamental signature of the visual system that has been measured extensively in several species. It is defined by the visibility threshold for sinusoidal gratings at all spatial frequencies. Here, we investigated the CSF in deep neural networks using the same 2AFC contrast detection paradigm as in human psychophysics. We examined 240 networks pretrained on several tasks. To obtain their corresponding CSFs, we trained a linear classifier on top of the extracted features from frozen pretrained networks. The linear classifier is exclusively trained on a contrast discrimination task with natural images. It has to find which of the two input images has higher contrast. The network's CSF is measured by detecting which one of two images contains a sinusoidal grating of varying orientation and spatial frequency. Our results demonstrate characteristics of the human CSF are manifested in deep networks both in the luminance channel (a band-limited inverted U-shaped function) and in the chromatic channels (two low-pass functions of similar properties). The exact shape of the networks' CSF appears to be task-dependent. The human CSF is better captured by networks trained on low-level visual tasks such as image-denoising or autoencoding. However, human-like CSF also emerges in mid- and high-level tasks such as edge detection and object recognition. Our analysis shows that human-like CSF appears in all architectures but at different depths of processing, some at early layers, while others in intermediate and final layers. Overall, these results suggest that (i) deep networks model the human CSF faithfully, making them suitable candidates for applications of image quality and compression, (ii) efficient/purposeful processing of the natural world drives the CSF shape, and (iii) visual representation from all levels of visual hierarchy contribute to the tuning curve of the CSF, in turn implying a function which we intuitively think of as modulated by low-level visual features may arise as a consequence of pooling from a larger set of neurons at all levels of the visual system.