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Neural Networks

Neural Networks. 1m. CNS. 10cm. Sub-Systems. 1cm. Areas / „Maps“. 1mm. Local Networks. Levels of Information Processing in the Nervous System. 100 m m. Neurons. 1 m m. Synapses. 0.01 m m. Molecules. 3) determine motion and sound perceptions. Interaural Time Difference (ITD):.

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Neural Networks

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  1. Neural Networks

  2. 1m CNS 10cm Sub-Systems 1cm Areas / „Maps“ 1mm Local Networks Levels of Information Processing in the Nervous System 100mm Neurons 1mm Synapses 0.01mm Molecules

  3. 3) determine motion and sound perceptions

  4. Interaural Time Difference (ITD): Sound coming from a particular location in space reaches the two ears at different times. From the interaural time difference the azimuth of the sound direction can be estimated. Example:

  5. Delay line correlator: Each neuron receives input from both ears. Due to the lengths of the two axons, the inputs arrive at different times. The neuron acts as a „coincidence detector“ and only fires if two spikes arrive at the same time. => Each neuron encodes a specific interaural time difference.

  6. Delay lines in the owl brain: Input Coincidence detector Ear -> Auditory nerve -> NM -> NL -> LS -> ICx

  7. Back to an old problem

  8. But the basic problem is not solved (A=0 -> A’=1)

  9. What else can we do with networks of neurons? But… so far we only considered excitatory and inhibitory synapses with the same strength (+1, -1). different EPSP amplitudes Are other values possible? What determines the synaptic strength?

  10. Schematic Diagram of a Synapse: Receptor ≈ Channel Transmitter Axon Vesicle Dendrite

  11. Release Probability of Neurotransmitters Receptors Second messengers In a network we have maaany synapses… too complicated!!! Senn, Markram, and Tsodyks, 2000

  12. Schematic Diagram of a Synapse: Receptor ≈ Channel Transmitter Axon Vesicle Dendrite Transmitter, Receptors, Vesicles, Channels, etc. synaptic weight:

  13. Schaffer collaterals mossy fiber perforant pathway

  14. in the CA3

  15. How does an associative memory work? Input Output Recurrent Activity2 Recurrent Activity1 Recurrent Activity3 Recurrent Activityn=n-1 … Input Output time

  16. Associative Memory: Simple Example firing threshold The input yields following initial recurrent activity: synaptic weight spike no spike another example

  17. Associative Memory: Simple Example Energy: The stable state is determined by the connections in A. Thus, a certain pattern can be learned by changing A accordingly. Associative memory of this network → Learning

  18. Associative Memory: statistical physics How many patterns can we store? unstable region (pattern states are unstable) noise stable region (and energy of patterns is lower than energy of spurious states) stable region (but energy of patterns is higher than energy of spurious states) storage capacity number of neurons number of patterns A network of 1000 neurons can store 138 patterns.

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