Abstract: In this work, we investigate slowness as a coding principle for the primary visual cortex (V1). The slowness principle can be illustrated as follows: the input signals to the cortex originate from the sensory cells by raw, local measurements of the environment. Such measurements are extremely sensitive to small changes in the state of both the environment and the observer, and vary thus on a timescale faster than that of the environment itself. In the specific case of V1, the sources of the visual input are objects and lights and their position in space. Single receptors on the retina measure light intensities at a given position, an information which is very sensitive even to small shifts or rotations of textured objects or the direction of gaze. Our hypothesis is that the cortex extracts slow signals out of its fast varying input in order to reconstruct information about the environment. This is equivalent to optimizing the neurons to have an output that varies in time as little as possible. To test this hypothesis, we considered video sequences derived from natural images and, by applying slow feature analysis (SFA), determined units (functions) that extract the most slowly-varying signals from the sequences. We analyzed the units by computing their optimal stimuli (i.e. the stimulus that maximally excites or inhibits a given unit) and by means of special test images that probe their response to a range of frequencies, orientations and phases as well as their end-inhibition behavior. We also performed experiments with drifting sinusoidal gratings to permit a direct comparison with experimental data in the literature. The analyzed units have many properties in common with complex cells in V1, including not only Gabor-like optimal stimuli and phase-shift invariance but also direction selectivity, non-orthogonal inhibition, end-inhibition and side-inhibition. Our results show that a single unsupervised learning principle can account for such a rich repertoire of receptive field properties.
Keywords: complex cells, slow feature analysis, temporal slowness, model, spatio-temporal receptive fields