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Emulation of dynamical systems by recurrent neural networks

  • Properties of learnable dynamical systems
  • Network capacity
  • Role of single-neuron dynamics and cortical network connectivity

An essential prerequisite for any living being's survival is its ability to predict its environment and to adjust its behaviour according to the outcome of this prediction. From a physicist's point of view, our world constitutes a set of dynamical systems. It has been hypothesized that the mammalian neocortex has evolved towards a flexible dynamical substrate in order to emulate external dynamical systems, similar to a spring emulating the motion of a pendulum. Once a particular dynamical system is learned, trajectories for any (new) initial condition can be predicted. Recent studies have demonstrated that simple recurrent neural networks can indeed be trained to emulate a large number of dynamical systems. Current research in our group is focusing on the properties of the dynamical systems which can be emulated by a given neural network, the network capacity and the role of realistic single-neuron dynamics and cortical network connectivity.

Related publications:

Maass W., Joshi P., Sontag E.D. (2007), Computational aspects of feedback in neural circuits PLOS Comp Biol 3(1):1-20

Legenstein R., Maass W. (2007), Edge of chaos and prediction of computational performance for neural circuit models, Neural Networks 20(3):323-334

Hausler S., Maass, W. (2006), A Statistical Analysis of Information-Processing Properties of Lamina-Specific Cortical Microcircuit Models, Cerebral Cortex 17:149-162

Jaeger H., Haas H. (2004), Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication Science 304(5667):78-80


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