2 research outputs found
Divisive Normalization from Wilson-Cowan Dynamics
Divisive Normalization and the Wilson-Cowan equations are influential models
of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci.
2012; Wilson and Cowan Kybernetik 1973]. However, they have not been
analytically related yet. In this work we show that Divisive Normalization can
be obtained from the Wilson-Cowan model. Specifically, assuming that Divisive
Normalization is the steady state solution of the Wilson-Cowan differential
equation, we find that the kernel that controls neural interactions in Divisive
Normalization depends on the Wilson-Cowan kernel but also has a
signal-dependent contribution. A standard stability analysis of a Wilson-Cowan
model with the parameters obtained from our relation shows that the Divisive
Normalization solution is a stable node. This stability demonstrates the
consistency of our steady state assumption, and is in line with the
straightforward use of Divisive Normalization with time-varying stimuli.
The proposed theory provides a physiological foundation (a relation to a
dynamical network with fixed wiring among neurons) for the functional
suggestions that have been done on the need of signal-dependent Divisive
Normalization [e.g. in Coen-Cagli et al., PLoS Comp.Biol. 2012]. Moreover, this
theory explains the modifications that had to be introduced ad-hoc in Gaussian
kernels of Divisive Normalization in [Martinez et al. Front. Neurosci. 2019] to
reproduce contrast responses. The proposed relation implies that the
Wilson-Cowan dynamics also reproduces visual masking and subjective image
distortion metrics, which up to now had been mainly explained via Divisive
Normalization. Finally, this relation allows to apply to Divisive Normalization
the methods which up to now had been developed for dynamical systems such as
Wilson-Cowan networks