TNI: Computational Neuroscience Instructors: Peter Latham Maneesh Sahani Peter Dayan

1. TNI: Computational Neuroscience Instructors: Peter Latham Maneesh Sahani Peter Dayan TAs: David Barrett, barrett@gatsby.ucl.ac.uk Ross Williamson, rossw@gatsby.ucl.ac.uk Website: www.gatsby.ucl.ac.uk/~rossw/teaching/TN1 (slides will be on website) Lectures: Tuesday/Friday, 11:00-1:00. Review: Friday, 1:30-3:30. Homework: Assigned Friday, due Friday (1 week later). first homework: assigned Oct. 16, due Oct. 23.

2. What is computational neuroscience? Our goal: figure out how the brain works.

3. There are about 10 billion cubes of this size in your brain! 10 microns

4. How do we go about making sense of this mess? David Marr (1945-1980) proposed three levels of analysis: 1. the problem (computational level) 2. the strategy (algorithmic level) 3. how it’s actually done by networks of neurons (implementational level)

5. Example #1: memory. the problem: recall events, typically based on partial information.

6. r3 r2 r1 activity space Example #1: memory. the problem: recall events, typically based on partial information. associative or content-addressable memory. an algorithm: dynamical systems with fixed points.

7. Example #1: memory. the problem: recall events, typically based on partial information. associative or content-addressable memory. an algorithm: dynamical systems with fixed points. neural implementation: Hopfield networks. xi = sign(∑j Jij xj)

8. Example #2: vision. the problem (Marr): 2-D image on retina → 3-D reconstruction of a visual scene.

9. Example #2: vision. the problem (modern version): 2-D image on retina → recover the latent variables. house sun tree bad artist

10. Example #2: vision. the problem (modern version): 2-D image on retina → recover the latent variables. house sun tree bad artist cloud

11. Example #2: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. an algorithm: graphical models. x1 x2 x3 latent variables r1 r2 r3 r4 low level representation

12. Example #2: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. an algorithm: graphical models. x1 x2 x3 latent variables inference r1 r2 r3 r4 low level representation

13. Example #2: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. an algorithm: graphical models. implementation in networks of neurons: no clue.

14. Comment #1: the problem: the algorithm: neural implementation:

15. Comment #1: the problem: easier the algorithm: harder neural implementation: harder often ignored!!!

16. Comment #1: the problem: easier the algorithm: harder neural implementation: harder A common approach: Experimental observation → model Usually very underconstrained!!!!

17. Comment #1: the problem: easier the algorithm: harder neural implementation: harder Example i: CPGs (central pattern generators) rate rate Too easy!!!

18. Comment #1: the problem: easier the algorithm: harder neural implementation: harder Example ii: single cell modeling CdV/dt = -gL(V – VL) – n4(V – VK) … dn/dt = … … lots and lots of parameters … which ones should you use?

19. Comment #1: the problem: easier the algorithm: harder neural implementation: harder Example iii: network modeling lots and lots of parameters × thousands

20. r3 x1 x2 x3 r2 r1 r2 r3 r4 r1 activity space Comment #2: the problem: easier the algorithm: harder neural implementation: harder You need to know a lot of math!!!!!

21. Comment #3: the problem: easier the algorithm: harder neural implementation: harder This is a good goal, but it’s hard to do in practice. Our actual bread and butter: 1. Explaining observations (mathematically) 2. Using sophisticated analysis to design simple experiments that test hypotheses.

22. Comment #3: Two experiments I have been closely involved with: - record, using loose patch, from a bunch of cells in culture - add blockers - record again - found quantitative support for the balanced regime. J. Neurophys., 83:808-827, 828-835, 2000

23. Comment #3: Two experiments I have been closely involved with: - perform whole cell recordings in vivo - stimulate cells with a current pulse every couple hundred ms - build current-triggered PSTH - showed that the brain is intrinsically very noisy, and is likely to be using a rate code. Not published yet (not that I’m bitter)

24. Comment #4: the problem: easier the algorithm: harder neural implementation: harder some algorithms are easy to implement on a computer but hard in a brain, and vice-versa. these are linked!!!

25. Comment #4: hard for a brain, easy for a computer: A-1 z=x+y ∫dx ... easy for a brain, hard for a computer: associative memory

26. Comment #4: the problem: easier the algorithm: harder neural implementation: harder some algorithms are easy to implement on a computer but hard in a brain, and vice-versa. we should be looking for the vice-versa ones. it can be hard to tell which is which. these are linked!!!

27. Basic facts about the brain

28. Your brain

29. Your cortex unfolded neocortex (cognition) 6 layers ~30 cm ~0.5 cm subcortical structures (emotions, reward, homeostasis, much much more)

30. Your cortex unfolded 1 cubic millimeter, ~3*10-5 oz

31. 1 mm3 of cortex: 50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons

32. 1 mm3 of cortex: 50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons 1 mm2 of a CPU: 1 million transistors 2 connections/transistor (=> 2 million connections) .002 km of wire

33. 1 mm3 of cortex: 50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons whole brain (2 kg): 1011 neurons 1015 connections 8 million km of axons 1 mm2 of a CPU: 1 million transistors 2 connections/transistor (=> 2 million connections) .002 km of wire whole CPU: 109 transistors 2*109 connections 2 km of wire

34. 1 mm3 of cortex: 50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons whole brain (2 kg): 1011 neurons 1015 connections 8 million km of axons 1 mm2 of a CPU: 1 million transistors 2 connections/transistor (=> 2 million connections) .002 km of wire whole CPU: 109 transistors 2*109 connections 2 km of wire

35. dendrites (input) soma (spike generation) axon (output) +40 mV 1 ms voltage -50 mV 100 ms time

37. synapse current flow

38. synapse current flow

39. +40 mV voltage -50 mV 100 ms time

40. neuron i neuron j neuron j emits a spike: EPSP V on neuron i t 10 ms

41. neuron i neuron j neuron j emits a spike: IPSP V on neuron i t 10 ms

42. neuron i neuron j neuron j emits a spike: IPSP V on neuron i t amplitude = wij 10 ms

43. neuron i neuron j neuron j emits a spike: changes with learning IPSP V on neuron i t amplitude = wij 10 ms

44. wij current flow

45. A bigger picture view of the brain

46. x latent variables peripheral spikes r sensory processing ^ r “direct” code for latent variables cognition memory action selection brain ^ r' “direct” code for motor actions motor processing r' peripheral spikes x' motor actions

47. r

48. r

49. r

50. r