Perceptual grouping through competition in coupled oscillator networks

Abstract

Abstract. In this paper we present a novel approach to model perceptual grouping based on phase and frequency synchronization in a network of coupled Kuramoto oscillators. Transferring the grouping concept from the Competitive Layer Model (CLM) to a network of Kuramoto oscillators, we preserve the excellent grouping capabilities of the CLM, while dramatically improving the convergence rate, robustness to noise, and computational performance, which is verified in a series of artificial grouping experiments.

Using Collective Behavior of Coupled Oscillators for Solving DCOP

“…Classical synchronization models maintain a static coupling strength among oscillators. Nevertheless, some studies (Skardal & Restrepo, 2012;Meier, Haschke, & Ritter, 2014;Gushchin, Mallada, & Tang, 2015) have addressed variations of the Kuramoto model by introducing coupling strength as symmetric functions. Such models represent couplings between pairs of oscillators in which coupling strengths can vary according to the current state of the oscillators.…”

“…Therefore, the synchronization dynamics in a DCOP must lead the agents to a coherence of their actions, even if there are conflicting local actions. In this sense, some studies on clustering detection in oscillator networks (Arenas, Daz-Guilera, & Prez-Vicente, 2006;Hong & Strogatz, 2011;Wu, Jiao, Li, & Chen, 2011;Meier et al, 2014) are candidates for addressing such consensus problems, which naturally require coordination of the agents for group formation. Arenas et al (2006) demonstrated that mean-field-based synchronization models are inefficient for identifying the effects of the local dynamics of the oscillators.…”

“…where the cosine of the phases difference is a similarity measure for detecting functional groups or communities of oscillators at a given t time. Meier et al (2014) introduced an alternative synchronization model for perceptual grouping in coupled oscillator networks. This model uses discrete frequencies ω α = αω 0 from a discrete and finite N (α) = {1, ..., L} set of possible α states arranged in a L-layered architecture, where α ∈ N (α) and ω 0 is the initial frequency.…”

Oscillations in working memory and neural binding: a mechanism for multiple memories and their interactions

“…Evidence of relationships between oscillations and the maintenance of working memory in humans has been obtained in numerous neurophysiological, imaging, and computational studies [6, 23-25, 27, 36, 48-54]. Oscillatory models have been developed both in the context of working memory [35,[55][56][57] and of binding [37,[58][59][60], and models -often with an eye towards image processing -have employed the distinction between bound and distinct objects as synchronous or asynchronous oscillations [37,[60][61][62][63][64]. These models tend to be spiking networks, appeal to cross-frequency coupling (e.g., theta-gamma codings), provide unrealistic connections (e.g., delayed self-inhibition for excitatory elements), use delays or constant inputs to produce persistent oscillatory activity, or employ structured architectures (e.g., using Hopfield networks, Hebbian rules, or pre-wired assemblies).…”

“…We also note that, while we have explored these networks within the context of the persistent activity observed in working memory dynamics, the presented behaviors would persist if we did not include NMDA dynamics, instead providing sustained drive to the excitatory and inhibitory populations (e.g., we show the same qualitative dynamics for such a reduced system with one population in Appendix A). Object differentiation and feature binding, as required in image segmentation, for example, may thus be modeled in our network using the same mechanisms described in the present results without consideration for persistent activity, so that simply removing the stimulus immediately quenches the activity of the selected populations, as in other work dealing with image analysis [61][62][63][64].…”