Oscillatory Networks: Pattern Recognition Without a Superposition Catastrophe

Burwick, Thomas

doi:10.1162/089976606775093864

Cited by 18 publications

(9 citation statements)

References 48 publications

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“…Burwick [13], [14] has developed a model for oscillatory networks with objectives similar to ours, in being able to perform separation and segmentation of inputs. His approach differs in that the units employ different frequency regimes, with on and off states corresponding to high and low frequency.…”

Section: ) Itmentioning

confidence: 99%

Efficient segmentation in multi-layer oscillatory networks

Rao¹,

Cecchi²,

Peck³

et al. 2008

2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence)

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In earlier work, we derived the dynamical behavior of a network of oscillatory units described by the amplitude and phase of oscillations. The dynamics were derived from an objective function that rewards both the faithfulness and the sparseness of representation. After unsupervised learning, the network is capable of separating mixtures of inputs, and also segmenting the inputs into components that most contribute to the classification of a given input object.In the current paper, we extend our analysis to multi-layer networks, and demonstrate that the dynamical equations derived earlier can be successfully applied to multi-layer networks. The topological connectivity between the different layers are derived from biological observations in primate visual cortex, and consist of receptive fields that are topographically mapped between layers. We explore the role of feedback connections, and show that increasing the diffusivity of feedback connections significantly improves segmentation performance, but does not affect separation performance.

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Section: ) Itmentioning

confidence: 99%

Efficient segmentation in multi-layer oscillatory networks

Rao¹,

Cecchi²,

Peck³

et al. 2008

2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence)

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“…The CGH model (Cohen & Grossberg, 1983;Hopfield, 1984) may be extended to an oscillatory network model that allows implementing features of temporal coding (Burwick, 2005); see also (Burwick, 2006). Given a network with N units, where each unit k is described in terms of the real-valued u k and phase θ k , k = 1, .…”

Section: Thementioning

confidence: 99%

“…For reviews of its growing biological evidence, see Engel, Fries, & Singer, 2001. And for references to models of temporal coding based on oscillatory networks, see Burwick, 2005Burwick, , 2006 In this letter, we present a new approach of dealing with this problem. The approach is a consequence of including an effect that we denote as acceleration.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Neural Networks with Self-Organized Segmentation of Overlapping Patterns

Burwick

2007

Neural Computation

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Temporal coding is considered with an oscillatory network model that generalizes the Cohen-Grossberg-Hopfield model. It is assumed that the frequency of oscillating units increases with stronger and more coherent input. We refer to this mechanism as acceleration. In the context of Hebbian memory, synchronization and acceleration take complementary roles, and their combined effect on the storage of patterns is profound. Acceleration implies the desynchronization that is needed for self-organized segmention of two overlapping patterns. The superposition problem is thereby solved even without including competition couplings. With respect to brain dynamics, we point to analogies with oscillation spindles in the gamma range and responses to perceptual rivalries.

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“…Topologies of networks of coupled Stuart-Landau oscillators such as all-to-all networks [Matthews & Strogatz, 1990;Ermentrout, 1990;Hakim & Rappel, 1992;Nakagawa & Kuramoto, 1993] and arrays of Stuart-Landau oscillators [Mirollo & Strogatz, 1990] have been studied in several works. Networks of Stuart-Landau oscillators are also often used as models of oscillator neural networks [Aoyagi, 1995;Kawaguchi, 2000;Hoppensteadt & Izhikevich, 2001;Burwick, 2006;Uchiyama, 2012]. In this work, we investigate a specific motif, namely a star network formed by nonidentical Stuart-Landau units.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations in a Star-Like Network of Stuart–landau Oscillators

Frasca

Bergner

Kurths

et al. 2012

Int. J. Bifurcation Chaos

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In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.

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Oscillatory Networks: Pattern Recognition Without a Superposition Catastrophe

Cited by 18 publications

References 48 publications

Efficient segmentation in multi-layer oscillatory networks

Efficient segmentation in multi-layer oscillatory networks

Oscillatory Neural Networks with Self-Organized Segmentation of Overlapping Patterns

Bifurcations in a Star-Like Network of Stuart–landau Oscillators

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