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

1. TNI: Computational Neuroscience Instructors: Peter Latham Maneesh Sahani Peter Dayan TA: Phillipp Hehrmann, hehrmann@gatsby.ucl.ac.uk Website: http://www.gatsby.ucl.ac.uk/~hehrmann/TN1/ (slides will be on website) Lectures: Tuesday/Friday, 11:00-1:00. Review: Friday, 1:00-3:00. Homework: Assigned Friday, due Friday (1 week later). first homework: 2 weeks later (no class Oct. 12).

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

6. Example #1: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. house sun tree bad artist

7. x1 x2 x3 r1 r2 r3 r4 ^ ^ ^ x1 x2 x3 Example #1: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. the algorithm: graphical models. latent variables peripheral spikes estimate of latent variables

8. Example #1: vision. the problem (modern version): 2-D image on retina → reconstruction of latent variables. the algorithm: graphical models. implementation in networks of neurons: no clue.

9. Example #2: memory. the problem: recall events, typically based on partial information.

10. r3 r2 r1 activity space Example #2: memory. the problem: recall events, typically based on partial information. associative or content-addressable memory. the algorithm: dynamical systems with fixed points.

11. Example #2: memory. the problem: recall events, typically based on partial information. associative or content-addressable memory. the algorithm: dynamical systems with fixed points. neural implementation: Hopfield networks. xi = sign( ∑j Jij xj)

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

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

14. Comment #1: the problem: easier the algorithm: harder neural implementation: harder My favorite example: CPGs (central pattern generators) rate rate

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

16. Comment #3: the problem: easier the algorithm: harder neural implementation: harder This is a good goal, but it’s hard to do in practice. We shouldn’t be afraid to just mess around with experimental observations and equations.

17. dendrites soma axon +40 mV 1 ms voltage -50 mV 100 ms time A classic example: Hodgkin and Huxley.

18. A classic example: Hodgkin and Huxley. CdV/dt = –gL(V-VL) – gNam3h(V-VNa) – … dm/dt = … …

19. the problem: easier the algorithm: harder neural implementation: harder A lot of what we do as computational neuroscientists is turn experimental observations into equations. The goal here is to understand how networks or single neurons work. We should always keep in mind that: a) this is less than ideal, b) we’re really after the big picture: how the brain works.

20. Basic facts about the brain

21. Your brain

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

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

24. 1 mm3 of cortex: 50,000 neurons 10000 connections/neuron (=> 500 million connections) 4 km of axons

25. 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

26. 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

27. 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

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

30. synapse current flow

31. synapse current flow

32. +40 mV voltage -50 mV 100 ms time

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

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

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

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

37. synapse current flow

38. A bigger picture view of the brain

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

40. r

41. r

42. r

43. r

44. you are the cutest stick figure ever! r

45. x r emotions cognition memory ^ r action selection brain ^ r' r' x' • Questions: • How does the brain re-represent latent variables? • How does it manipulate re-represented variables? • How does it learn to do both? • Ask at three levels: • What are the properties of task x? • What are the algorithms? • How are they implemented in neural circuits?

46. Knowing the algorithms is a critical, but often neglected, step!!! We know the algorithms that the vestibular system uses. We know (sort of) how it’s implemented at the neural level. We know the algorithm for echolocation. We know (mainly) how it’s implemented at the neural level. We know the algorithm for computing x+y. We know (mainly) how it might be implemented in the brain.

47. Knowing the algorithms is a critical, but often neglected, step!!! We don’t know the algorithms for anything else. We don’t know how anything else is implemented at the neural level. This is not a coincidence!!!!!!!!

48. Highly biased What we know about the brain

49. 1. Anatomy. We know a lot about what is where. But be careful about labels: neurons in motor cortex sometimes respond to color. Connectivity. We know (more or less) which area is connected to which. We don’t know the wiring diagram at the microscopic level. wij

50. 2. Single neurons. We know very well how point neurons work (think Hodgkin Huxley). Dendrites. Lots of potential for incredibly complex processing. My guess: they make neurons bigger and reduce wiring length.