Sparse codes and spikes

Bruno A. Olshausen

Dept. of Psychology and Center for Neuroscience
UC Davis

It has been shown that the spatial receptive field properties of cortical simple cells can be accounted for in terms of an efficient coding strategy that has been adapted to the statistics of natural images (Olshausen & Field, 1996; Bell & Sejnowski 1997; van Hateren & van der Schaaf, 1998). Here, I extend this work to the time domain to show how the spatiotemporal receptive field properties of these neurons may also be explained in terms of efficient coding principles. Time-varying natural images are modeled as a superposition of sparse, independent events in both space and time. The events are characterized using an overcomplete set of spatiotemporal basis functions which are assumed to be translation-invariant in the time domain. When adapted to natural movies, the basis functions of the model converge to a set of spatially localized, oriented, bandpass functions that translate over time, similar to the space-time receptive fields of V1 neurons. These results are similar to those obtained previously with ICA (van Hateren & Ruderman, 1998), but there is an important difference in how the output activities of the model are computed due to the use of an overcomplete basis set. Rather than computing the output activities by simply convolving the basis functions with the movie, the outputs are sparsified across both space and time, producing a non-linear code having a spike-like character in time. Thus, continuous, time-varying images are represented as a series of sharp, punctate events in time, similar to neural spike trains (Rieke et al., 1997). These results suggest that both the receptive field structure and the spiking nature of V1 neurons may be accounted for in terms of a single principle of efficient coding. Possibilities for testing this hypothesis shall be discussed.