Invariant encoding of spatial stimulus topology in the temporal domain

Abstract

Invariant representations emerge as a central topic in vision research. Here we investigate a transformation of visual spatial patterns by an ensemble of laterally coupled neurons into the temporal domain. The central property of the network leading to this transformation is the monotonic relationship of transmission delays between neurons with increasing distance. We show that stimuli become encoded in the temporal population activity and that this representation is invariant with respect to translations, rotations and small distortions. Furthermore, the proposed model provides a rapid encoding in accordance with physiological results.

Introduction

Primates excel at tasks like visual object recognition, tolerating considerable changes in images, for instance, due to different viewing angles and deformations. Elucidating the mechanisms of such invariant pattern recognition is an active field of research in neuroscience [10], [12], [6], [4]. However, still very little is known about the underlying algorithms and mechanisms. A number of models have been proposed which aim to reproduce capabilities of the biological visual system, such as invariance to shifts in position, rotation, scaling and distortion [9], [19], [7].

Recently, however, the importance of the temporal dynamics of neuronal activity in representing visual stimuli has shifted into the focus of neuroscience [2], [11], [8]. Several modeling studies have addressed the properties of temporal codes [1], [17], [5]. For instance, Buonomano and Merzenich [3] proposed a model for position-invariant pattern recognition, using temporal coding. Here, we build on these concepts and investigate the formation of invariant representations by the dynamics of activity of neuronal populations.

We investigate a simplified model of primary visual cortex consisting of a map of integrate-and-fire neurons with local excitatory interactions. A central feature of this model is the monotonic relationship between transmission delays in this lateral coupling and the distance between pre- and post-synaptic neurons. We hypothesize that this network property induces dynamics of neuronal activity which is specific to the geometrical shape of a stimulus and invariant with respect to translations and rotations. Such a representation would emerge naturally without the need for training a stimulus repeatedly at different positions or orientations. In order to investigate the validity of this approach we determine the amount of information contained in the temporal population responses of this network for different parameters and stimulus sets. This is done statistically, using a clustering algorithm combined with temporal correlation as a similarity measure. The resulting temporal structure of network activity provides a representation which is position as well as rotation invariant. Moreover, it is robust with respect to synaptic noise and under local and global stimulus distortions. These results suggest that for invariant pattern recognition temporal coding is important, however, not at the level of single neurons, but at the population level.