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From brain activities to mathematical models

From brain activities to mathematical models. The TempUnit model, a study case for GPU computing in scientific computation. What part of the brain?. How to study it ?. First attempt: use of a MLP. What is a MLP?. First Attempt: MLP (2). Results (1). Results (2). Crack the code !!.

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From brain activities to mathematical models

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  1. From brain activities to mathematical models The TempUnit model, a study case for GPU computing in scientific computation.

  2. What part of the brain?

  3. How to study it ?

  4. First attempt: use of a MLP • What is a MLP?

  5. First Attempt: MLP (2)

  6. Results (1)

  7. Results (2)

  8. Crack the code !! • Frequency code (Number of spikes in a time lap) ? • Spatial coding (distributed trough the network) ? • Temporal code (Precise binary pattern) ? • Spatio-temporal code (Synchronies) ? • Something else ?

  9. The model Xt x

  10. Learn the parameters vi • Solving a system of linear equation oversized. • Much faster and straightforward than backpropagation for the MLP Example of a learned basis function

  11. Performances compared to MLP

  12. Check Chap. 12

  13. Graph of Neuronal Activity • The output activity of a TempUnit neural network can be described by a graph directly related to its connectivity • You determine the topology of your graph easily • Allow to determine the input activity for a particular desired output

  14. Can a real biological neuron do that ?

  15. Pattern recognition

  16. learning rules for unsupervised learning

  17. EPSP from the integrate-and-fire model • From the integrate and fire, the α function: time (Gerstner & Kistler, 2002) To find the position of the maximum (peak), one has to resolve the following equation:

  18. The new equation of the TempUnit model: p=0 p=6 p : position of the synapse time With μ, the maximum value:

  19. From equations to a simulation software

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