Inverse Problems in Neural Field Theory

Potthast, Roland; Graben, Peter beim

doi:10.1137/080731220

Cited by 43 publications

(42 citation statements)

References 37 publications

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“…Finally, we apply the inverse methods and its theory to problems of Dynamic Cognitive Modeling as suggested in [4,5,75]. The basic task here is to gain a better understanding of cognitive processes by mapping them into a dynamic field environment.…”

Section: Cognitive Modellingmentioning

confidence: 99%

“…We also refer to [75] for an interpretation of the above approach in terms of bi-orthogonal basis functions, which are numerically realized by the Moore-Penrose pseudoinverse given by K WD .K T K/ 1 K T and which is stabilized by Tikhonov regularization (1.155) when K is an ill-posed operator as for the inverse neural field problem.…”

Section: Inverse Problemsmentioning

confidence: 99%

“…12), and Dynamic Causal Modelling [28] (Chap. 17), as well as being studied from an inverse problems perspective [5,75]. As well as an increase in the applications of models like (1.1) and (1.2) in neuroscience, there has been a push to develop a deeper mathematical understanding of their behaviour.…”

Section: Introductionmentioning

confidence: 99%

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Tutorial on Neural Field Theory

2014

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The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this tutorial chapter we describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integrodifferential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of spatiotemporal patterns, based around natural extensions of those used for local differential equation models. We present an overview of these techniques, covering Turing instability analysis, amplitude equations, and travelling waves. Finally we address inverse problems for neural fields to train synaptic weight kernels from prescribed field dynamics.

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Section: Cognitive Modellingmentioning

confidence: 99%

Section: Inverse Problemsmentioning

confidence: 99%

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Tutorial on Neural Field Theory

2014

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“…More recent work that tackles heterogeneity (primarily using simulations) can be found in Brackley and Turner (2007), Bressloff (2001), Schmidt et al (2009), andCoombes et al (2012) and functional analytic results in Faugeras et al (2008), and Potthast and beim Graben (2010). The inverse problems perspective for either homogeneous or nonhomogeneous kernels has been investigated by Potthast and beim Graben (2009) and beim . More recently, stochastic neural field equations have become very popular; compare the review by Bressloff (2012).…”

Section: Delay Neural Field Equation and Homogeneous Kernelsmentioning

confidence: 96%

Amari Model

Potthast

2014

Encyclopedia of Computational Neuroscience

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DefinitionThe Amari neural field model (cf. (Amari 1975(cf. (Amari , 1977) provides a simple field-theoretic approach to the dynamics of neural activity in the brain. The model uses excitations and inhibitions over some distance as an effective model of mixed inhibitory and excitatory neurons with typical cortical connectivities. The model is a scalar dynamical equation for the voltage or activity u(x, t) of the form

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“…The state descriptions of the parser are mapped onto ICS neural network architectures by employing filler/role decomposition and a new, hierarchical tensor product representation, which we shall refer to as the fractal tensor product representation. The networks are trained using generalized Hebbian learning Potthast and beim Graben 2009). For visualizing network dynamics through activation state space, an appropriate observable model in terms of principal component analysis is constructed (beim Graben et al 2008a) that allows for comparison of different parsing processes.…”

Section: Introductionmentioning

confidence: 99%

Unifying syntactic theory and sentence processing difficulty through a connectionist minimalist parser

Gerth

Graben

2009

Cogn Neurodyn

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Syntactic theory provides a rich array of representational assumptions about linguistic knowledge and processes. Such detailed and independently motivated constraints on grammatical knowledge ought to play a role in sentence comprehension. However most grammar-based explanations of processing difficulty in the literature have attempted to use grammatical representations and processes per se to explain processing difficulty. They did not take into account that the description of higher cognition in mind and brain encompasses two levels: on the one hand, at the macrolevel, symbolic computation is performed, and on the other hand, at the microlevel, computation is achieved through processes within a dynamical system. One critical question is therefore how linguistic theory and dynamical systems can be unified to provide an explanation for processing effects. Here, we present such a unification for a particular account to syntactic theory: namely a parser for Stabler's Minimalist Grammars, in the framework of Smolensky's Integrated Connectionist/Symbolic architectures. In simulations we demonstrate that the connectionist minimalist parser produces predictions which mirror global empirical findings from psycholinguistic research.

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Inverse Problems in Neural Field Theory

Cited by 43 publications

References 37 publications

Tutorial on Neural Field Theory

Tutorial on Neural Field Theory

Amari Model

Unifying syntactic theory and sentence processing difficulty through a connectionist minimalist parser

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