MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Generic steady and dynamic tuning properties in neural field models with rectifying rate functions

Thomas Wennekers


Neural field models have been used widely to explain tuning properties of cortical neurons. This paper shows that such models generically reveal tuning independent of input intensity, i.e. contrast in the visual domain, if they only have semilinear rate functions with threshold zero. Other model details are unimportant as long as spatially localized rate profiles representing receptive fields still exist. Those details concern the number and dimension of layers, and the precise form of the spatial input profiles and connectivity kernels. Arbitrary feature maps can further be imposed onto the model, and the cells in some of the model layers may reveal cell-adaptation (or facilitation) described by a passive linear kinetics. In any case, do all spatio-temporal solutions of the model scale linearly with input strength, but are otherwise form invariant. As a consequence the tuning of simple cells for orientation and spatial frequency as well as direction tuning indexes are contrast independent in these models. It is demonstrated that the results shown in the present paper apply - at least in approximation - to most models for contrast independent tuning of V1 simple cells proposed in the literature. The assumption of rectifying rate functions is discussed in the context of previous theoretical and experimental results concerning the approximate linearization of neuronal rate functions by noise.

cortex, v1, contrast independent tuning, neural field models

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2001 Repository Open Access
Thomas Wennekers

Generic steady and dynamic tuning properties in neural field models with rectifying rate functions