1. Bump attractors and the homogeneity assumption Kevin Rio NEUR 1680 28 April 2011

2. Bump attractors Can explain sustained (but bounded) activity in populations of neurons. A useful description of working memory by combining self-sustained activity with sensitivity to external inputs.

5. Firing-Rate Model τ r time constant r i (t) firing rate of neuron i I i (t) input current for neuron i J ij synaptic strength between neurons i,j Θcurrent bias

6. Firing-Rate Model 0 x if x > 0 0 if x < 0 J ij = -J 0 + J 2 cos (2π(i-j)/N)

7. Homogeneity Homogeneity is required to create a continuum of bump attractors. –Even a small amount of heterogeneity destroys continuum, leaving only a few discrete attractors. Biologically implausible: number and strength of synaptic connections is variable.

8. Solutions Fine tuning properties of each neuron. Network learns to tune itself through an activity-dependent mechanism. –“Activity-dependent scaling of synaptic weights, which up- or downregulates excitatory inputs so that the long term average firing rate is similar for each neuron” (Renart, Song, Wang 2003).

9. Synaptic Scaling (Renart, Song, Wang 2003) τ g time constant [large] g(θ) factor that multiplies excitatory synaptic conductances to neuron θ r(θ) instantaneous firing rate of neuron θ r tg (θ) target firing rate of neuron θ

10. Project Outline 1.Simulate network of firing-rate neurons. 2.Observe bump attractors. 3.Show how loss of symmetry destroys continuum of bump attractors. 4.Restore symmetry by activity-dependent scaling of synaptic weights.

11. Sequential Modeling in the Auditory System By Rohan Ramesh and Srihari Sritharan

12. Recurrent Networks Three layer network with feedback: input layer, intermediate layer, and output layer Intermediate layer in this instance are SAM cells

13. Spike Accumulation Model (SAM) Variable of importance – the accumulated potential of SAM cells in intermediate layer –The accumulated potential = a constantly- updating characterization of a constant stream of sensory input

14. Membrane Time Constant Sequential memory dependent on membrane time constant (τ) of SAM cells –Different response to stimuli 1  2 than 2  1 due to difference in neuronal response –Activity of the entire population of SAM cells important

15. Output Sequential learning decoded due to input from SAM cells AND efferent copy of activity of output layer to intermediate layer –How do we decode this? How does the efferent feedback loop aid decoding? –Activation of output cell:

16. Learning How will the network learn a series of tones? The input to the SAM cells are determined by a comparison of the output of the output cells to the output of the input cells

17. Encode Specificity and Timing Specificity – tone 1 vs. tone 2 –Auditory tuning within SAM cells could determine the frequency of the input Timing - tone 1  tone 2 OR tone 2  tone 1 –The membrane time constant and the efferent copy of the output will help determine the order of the tones

18. Auditory Input

19. Auditory Tuning Curves

20. Supervised learning with lateral interaction and back propagation within a neural network 4/27/11 Sunmee Park, Jing Wang, Rizwan Huq Computational neuroscience 2011

21. Motivation Natural vision can differentiate various handwritten digits Can we mimic the vision system? (Of course, in a simpler way) Supervised learning: given input/output –Traditional backpropagation neural network(NN) –Biophysically appropriate inter-layer communications

22. Network diagram

23. Methods … -Hand-written digits set from 0~ 9, collected by USPS/NIST database - 8 bit grayscale images (1100 examples of each class) Input dataset

24. Preprocessing Applying Gabor filter

26. Deliverables A simulated neural system capable of decoding handwritten image data and identifying the input digit. System performance curves, for which we will reserve training examples. Analysis of the impact inter-layer communications.

27. Kuhn, et al. 2004: Neuronal Integration of Synaptic Input in the Fluctuation-Driven Regime Project Team: Tommy Tea and Christina Hahn

28. Paper Recap Visual synaptic bombardment leads to changes in conductance. This in turn increases fluctuations in membrane potential and these fluctuations modify the firing rate. Firing rate decreases because of shunted membrane potential fluctuations, and increases because of shorter membrane time constants, allowing for faster membrane potential fluctuations.

29. Methods Transient current-based model: Transient conductance-based model: Firing Rate model:

30. Figures of model with current input increasing monotonically

31. Figures of model with non-monotonic conductance input:

32. Physiological Significance In the conductance-based model, the fluctuations are expected to reach a maximum standard deviation of ~3 mV, which is within the range of values observed in vivo