Slow feature analysis yields a rich repertoire of complex cell properties

Abstract

In this study we investigate temporal slowness as a learning principle for receptive fields using slow feature analysis, a new algorithm to determine functions that extract slowly varying signals from the input data. We find a good qualitative and quantitative match between the set of learned functions trained on image sequences and the population of complex cells in the primary visual cortex (V1). The functions show many properties found also experimentally in complex cells, such as direction selectivity, non-orthogonal inhibition, end-inhibition, and side-inhibition. Our results demonstrate that a single unsupervised learning principle can account for such a rich repertoire of receptive field properties.

Analysis and interpretation of quadratic models of receptive fields

“…This development has led to the need for new tools to interpret and visualize non-linear functions. This protocol presents a number of methods that were developed, in the context of a computational model of the visual cortex 1,2 , to analyze quadratic forms as neuronal RFs.…”

“…In addition, several theoretical studies have defined quadratic models of neuronal RFs either explicitly 2,14,15 or implicitly as neural networks [16][17][18] . This choice is justified by the fact that quadratic forms constitute a computationally rich function space that contains interesting elements (e.g., the standard energy model of complex cells 19 ) while still having a reasonably small number of parameters.…”

“…This development has led to the need for new tools to interpret and visualize non-linear functions. This protocol presents a number of methods that were developed, in the context of a computational model of the visual cortex 1,2 , to analyze quadratic forms as neuronal RFs.Quadratic forms are used in experimental studies as quadratic approximations to the input-output function of neurons and can be derived from neural data as Volterra/Wiener approximations up to the second order 3-13 . In addition, several theoretical studies have defined quadratic models of neuronal RFs either explicitly 2,14,15 or implicitly as neural networks [16][17][18] .…”

Invariant Object Recognition with Slow Feature Analysis

“…The slowness principle has been applied in many models of the visual system in the past [11,12,13,5,6,2]. VisNet is the most prominent example of hierarchical feed-forward neural network models of the primate ventral visual system [1].…”

“…In the computationally relevant case where F is finite-dimensional the solution to the optimization problem can be found by means of Slow Feature Analysis [5,6]. This algorithm, which is based on an eigenvector approach, is guaranteed to find the global optimum.…”