Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition

Abstract

Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e͑N 2 1͒!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output. DOI: 10.1103/PhysRevLett.87.068102 PACS numbers: 87.10. +e, 05.45. -a, 87.18.Bb Information about the environment is generally encoded into spike sequences by neurons in animal sensory nervous systems [1]. There is a growing body of evidence [2][3][4][5][6] that, in some systems, the representation of information comes through both identity and temporal encoding: each stimulus is characterized by a specific and reproducible sequence of firing across specific neurons [7]. To build a reasonable dynamical theory of such an encoding, we must first understand the principles on which the dynamics of these sensory networks is based and predict some advantages that such stimulus representation has for further processing.We explore a class of dynamical systems that we call competitive networks or winnerless competition (WLC) networks. These produce identity-temporal or spatiotemporal coding in the form of deterministic trajectories moving along heteroclinic orbits that connect saddle fixed points or saddle limit cycles in the system's state space. These saddle states correspond to the activity of specific neurons or groups of neurons, and the separatrices connecting these states correspond to sequential switching from one state to another.We use observed features of olfactory processing networks [2] as a guide to our study of computation using competitive networks. Figure 1 shows the simultaneously recorded activity of three different projection neurons (PNs) in the locust antennal lobe (AL) evoked by two different odors: despite similar PN activities before the stimulus onset (the result of the action of noise) each odor evokes a specific spatiotemporal activity pattern that results from interactions between these and other neurons in the network [2,8].Using this experimental data and knowledge about the anatomy and physiology of the AL we hypothesize that such olfactory networks form, store, and recognize patterns using a WLC strategy. The experiments on which our ideas are based indicate the following features of neural encoding: the representation of input (sensory) information (i) uses both identity (or "space") and time, (ii) sensitively depends on the stimulus, (iii) is deterministic and reproducible, and (iv) is robust against noise. These observations suggest (a) that a dynamical system which possesses FIG. 1. The temporal patterns produced by three simultaneously sampled PNs...

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