Experimenting the variational definition of neural map computation
© Rochel et al; licensee BioMed Central Ltd. 2007
Published: 6 July 2007
Variational formulation to spiking neural networks: A top-down approach
We bring new insights to better understand the link between spiking neural networks and variational approaches. To do so, we consider two simple visual tasks formulated as variational approaches, related to linear/non-linear filtering  and input selection: Image denoising via edge-preserving smoothing, and focus of attention via a winner-take-all mechanism. Variational approaches, which refer to an energy minimization formulation, are defined in a continuous setting. Our goal is to show how spiking neural networks can be used to minimize those energies. Based on some recent advances [2, 3], including spiking neurons , the key point is to understand the relation between smoothness constraints and cortical activity diffusion (as observed with extrinsic optical imaging). In particular, we will focus on the two following issues:
Depending on the task, and given the underlying neural circuitry and computational power, how far, and how fast should local information be transmitted (e.g., intensity, local gradient, local movement)?
How can different information pathways, associated with different processing tasks, interact?
Results and discussion
This work was partially supported by the EC IP project FP6-015879, FACETS.
- Aubert G, Kornprobst P: Mathematical problems in image processing: partial differential equations and the calculus of variations. Applied Mathematical Sciences. 2006, Springer-Verlag, 147:Google Scholar
- Cottet G-H, El Ayyadi M: Volterra type model for image processing. IEEE transactions on image processing. 1998, 7-Google Scholar
- Viéville T, Kornprobst P: Modeling cortical maps with feed-backs. Int Joint Conf on Neural Networks. 2006Google Scholar
- Kornprobst P, Chemla S, Rochel O, Vieville T: A 1st step towards an abstract view of computation in spiking neural networks. in Proc NeuroComp. 2006Google Scholar
- Singer W: Neuronal synchrony: a versatile code for the definition of relations?. Neuron. 1998, 24: 49-65. 10.1016/S0896-6273(00)80821-1.View ArticleGoogle Scholar
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