Linsker-type Hebbian Learning: A Qualitative Analysis on the Parameter Space

Feng, Jianfeng; Pan, Hong; Roychowdhury, Vwani P.

doi:10.1016/s0893-6080(97)00020-8

Cited by 6 publications

(3 citation statements)

References 45 publications

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“…It seems that the power of extreme value theory in neural computation has not yet been fully realized. In previous papers [8][9][10]7] we developed a theory related to extreme values in other classes of neurodynamics. In [6], we applied extreme value theory to some challenging problems in neural computation, such as the capacity of the Hopfield model, learning curves of perceptron learning etc.…”

Section: Discussionmentioning

confidence: 99%

Spike output jitter, mean firing time and coefficient of variation

Feng¹,

Brown²

1998

J. Phys. A: Math. Gen.

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To understand how a single neurone processes information, it is critical to examine the relationship between input and output. Marsalek, Koch and Maunsell's study focused on output jitter (standard deviation of output interpike interval) found that for the integrate-and-fire (I&F) model this response measure converges towards zero as the number of inputs increases indefinitely when interarrival times of excitatory inputs (EPSPs) are normally or uniformly distributed. In this work we present a complete, theoretical investigation, corroborated by numerical simulation, of output jitter in the I&F model with a variety of input distributions and a range of values of number of inputs, N. Our main results are: the exponential distribution input is a critical case and its output jitter is independent of N. For input distributions with tails which decrease faster than the exponential distribution, output jitter converges to zero as discovered by Marsalek, Koch and Maunsell; whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter. Exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation. The I&F model with leakage is also briefly considered.

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Section: Discussionmentioning

confidence: 99%

Spike output jitter, mean firing time and coefficient of variation

Feng¹,

Brown²

1998

J. Phys. A: Math. Gen.

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“…The effect on these coefficients is such that if the magnitude of CI is large, then it gives a significant head start to the all-excitatory (all-inhibitory) profiles. Feng, Pan, and Roychowdhury (1995) analyzed how this head start would affect the outcome of the evolution of equation 2.1 if the synaptic weights were constrained to lie between fixed minimum and maximum values. These authors reached the conclusion that the stable fixed-point solutions to the equation would lie in four domains where receptive-field profiles are (1) all excitatory, (2) all inhibitory, (3) all excitatory or all inhibitory, or (4) of various shapes, including anisotropic ones.…”

Section: ~mentioning

confidence: 99%

Possible Roles of Spontaneous Waves and Dendritic Growth for Retinal Receptive Field Development

Bürgi

Grzywacz

1997

Neural Computation

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Several models of cortical development postulate that a Hebbian process fed by spontaneous activity amplifies orientation biases occurring randomly in early wiring, to form orientation selectivity. These models are not applicable to the development of retinal orientation selectivity, since they neglect the polarization of the retina's poorly branched early dendritic trees and the wavelike organization of the retina's early noise. There is now evidence that dendritic polarization and spontaneous waves are key in the development of retinal receptive fields. When models of cortical development are modified to take these factors into account, one obtains a mod.el of retinal development in which early dendritic polarization is the seed of orientation selectivity, while the spatial extent of spontaneous waves controls the spatial profile of receptive fields and their tendency to be isotropic.

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“…While most attention has been given in theoretical analysis to the emergence of center-surrounded or oriented receptive fields [6], [7], little is known about the underlying nonlinear dynamics of this multi-layer neural network. In this paper, we formulate this network as a coupled nonlinear differential system operating at different time-scales under vanishing perturbations.…”

Section: Introductionmentioning

confidence: 99%

Robust stability analysis of Linsker-Type Hebbian learning multi-time scale neural networks under parametric uncertainties

Meyer‐Baese

Lespinats²,

Keck

et al. 2010

The 2010 International Joint Conference on Neural Networks (IJCNN)

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Ahstract-A novel network based on Linsker-type Hebbian learning is analyzed in its dynamical behavior. The network combines a coupled dynamics of fast and slow states and is prone to internal parametrical fluctuations as well as external noises. Robustness represents a crucial property of the network to attenuate the effects of internal fluctuation and external noise.In this study, we formulate this novel neural network as a cou pled nonlinear differential systems operating at different time scales under vanishing perturbations. We determine conditions for the existence of a global uniform attractor of the perturbed biological system. By using a Lyapunov function for the coupled system, we derive a maximal upper bound for the fast time scale associated with the fast state. Finally, two examples are given to confirm the applicability of the developed theoretical framework. Index Terms-Linsker-type Hebbian learning, multi-time scale neural network, parametric uncertainties, robust stability I. INTRODUC TION Linsker [5] proposed a neural network relevant to the phenomena observed in the visual cortex. It combines a unsupervised nonlinear learning scheme with a temporal activity evolution.While most attention has been given in theoretical analysis to the emergence of center-surrounded or oriented receptive fields [6], [7], little is known about the underlying nonlinear dynamics of this multi-layer neural network. In this paper, we formulate this network as a coupled nonlinear differential system operating at different time-scales under vanishing perturbations. Differently from previous work [1] viewing parametric uncertain systems as perturbations to a known nominal linear system [2], [3], in this paper the perturbed neural system is modeled as nonlinear perturbations to a known nonlinear idealized system and is represented by two time-scale subsystems. These perturbations can lead to location errors of equilibria, to instabilities, and even to spurious states. Therefore, a rigorous understanding of the qualitative robustness properties of neural systems with respect to parameter variations on both a fast or slow time scale becomes imperative.The goal of the present paper is to study stability and robustness properties of Linsker-type Hebbian learning modAnke Meyer-Baese is with the eled by a system of competitive differential equations, from a rigorous analytic standpoint and to apply results of the theory of nonlinear uncertain singularly perturbed systems [4]. The networks under study model the nonlinear dynamics of both fast and slow states under consideration of nonlinear uncertainties.In the following, we present the underlying nonlinear dynamics for the Linsker-type Hebbian learning network. The equations are adopted from the original dynamical mechanism of Linsker's network [5].The general neural network equations describing the tem poral evolution of the unperturbed STM and LTM states for the jth neuron of aN-neuron network are:

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Linsker-type Hebbian Learning: A Qualitative Analysis on the Parameter Space

Cited by 6 publications

References 45 publications

Spike output jitter, mean firing time and coefficient of variation

Spike output jitter, mean firing time and coefficient of variation

Possible Roles of Spontaneous Waves and Dendritic Growth for Retinal Receptive Field Development

Robust stability analysis of Linsker-Type Hebbian learning multi-time scale neural networks under parametric uncertainties

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