1. The Neuronal Replicator Hypothesis • Chrisantha Fernando & Eors Szathmary • CUNY, December 2009 • 1Collegium Budapest (Institute for Advanced Study), Budapest, Hungary • 2Centre for Computational Neuroscience and Robotics, Sussex University, UK • 3MRC National Institute for Medical Research, Mill Hill, London, UK • 4Parmenides Foundation, Kardinal-Faulhaber-Strase 14a, D-80333 Munich, Germany • 5Institute of Biology, Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary

2. Visiting Fellow MRC National Institute for Medical Research London Post-Doc Center for Computational Neuroscience and Robotics Sussex University Marie Curie Fellow Collegium Budapest (Institute for Advanced Study) Hungary

3. The Hypothesis • Evolution by natural selection takes place in the brain at rapid timescales and contributes to solving cognitive/behavioural search problems. • Our background is in evolutionary biology/the origin of non-enzymatic template replication/evolutionary robotics/computational neuroscience.

4. Outline • Limitations of some proposed search algorithms, e.g. • Reward biased stochastic search • Reinforcement Learning • How copying/replication of neuronal data structures can alleviate these limitations.

5. Mechanisms of neuronal replication • Applications and future work

6. Simple Search Tasks • Behavioural and neuropsychological learning tasks can be solved by stochastic-hill climbing • Stroop Task • Wisconsin Card Sorting Task (WCST) • Instrumental Conditioning in Spiking Neural Networks • Simple inverse kinematics problem

7. Stochastic Hill-Climbing • Initially P(xi = 1) = 0.5, Initial reward = 0 • Make random change to P • Generate M examples of binary strings • Calculate reward • If r(t) > r(t-1), keep changes of P, else revert to previous P values. • One solution, change solution, keep good changes, loose bad changes.

8. Can get stuck on local optima

9. Stroop Task GreenRedBlue PurpleBluePurple BluePurpleRedGreenPurpleGreen Name the colour of the words.

10. dW = Reward x pre x post • Decreased reward -> Instability in workspace Dehaene et al, 1998

11. WCST • Each card has several “features”. Subjects must sort cards according to a feature (color, number, shape, size).

12. Rougier et al 2005. PFC weights stabilised if expected reward obtained, destabilised if expected reward not obtained, i.e. TD learning

13. Instrumental Conditioning

14. In a spiking neural net • Simple spiking model • Random connections • STDP • Delayed reward • Eligibility traces • Synapse selected Izhikevich 2007

15. Simple spiking model

16. STDP

19. Time tpre

20. Time tpost

21. Interval = Tpost - Tpre

22. Time tpost

26. Time tpre

27. Interval = Tpost - Tpre

29. A simple 2D inverse kinematics problem

30. Reinforcement Learning • For large problems a tabular representation of state-action pairs is not possible. • How does compression of state representation occur? Function approximation • Domain-specific knowledge provided by the designer, e.g. TD-Gammon was dependent on Tesauro’s skillful design of a non-linear multilayered neural network, used for value function approximation in the Backgammon domain consisting of approximately 1020 states” p20 [51].

31. So far… • SHC works on simple problems • RL is a sophisticated kind of SHC • In order for RL/SHC to work, action/value representations must fit the problem domain. • RL doesn’t explain how appropriate data-structures/representations arise.

32. Large search space so random search or exhaustive search not possible. Representation critical local optima. Requires internal sub-goals, no explicit reward. • What neural mechanisms underlie complex search?

33. What is natural selection? • multiplication • heredity • variability Some hereditary traits affect survival and/or fertility

34. Natural selection reinvented itself

35. Evolutionary Computation • Solving problems by EC also requires decisions about genetic representations • And about fitness functions • For example, we use EC to solve the 10 coins problem

37. Fitness function • Convolution of desired inverted triangle over grid • Instant fitness = number of coins occupying he inverted triangle template • An important question is how such fitness functions (subgoals/goals) could themselves be bootstrapped in cognition.

39. Michael Ollinger, Parmenides Foundation, Munich

40. Structuring Phenotypic Variation • Natural Selection can act on • genetic representations • variability properties (genetic operators, e.g mutation rates)

41. Variation in Variability A Improvement of representations for free…

42. B

43. Non-trivial Neutrality g1 ed 1 ed 2 p g2 Adapted from Toussaint 2003

44. Population Search • Natural selection allows redistribution of search resources between multiple solutions. • We propose that multiple (possibly interacting) solutions to a search problem exist at the same time in the neuronal substrate.

45. A B C D B A A D C A B C D B A A D C

46. A B C D B D B A D A A A B C D C C Waste A B C D D’ D’’ D A D’’’ D’ D’’ D’’’ D

47. Can units of selection exist in the brain? • We propose 3 possible mechanisms • Copying of connectivity patterns • Copying of bistable activity patterns • Copying of spatio-temporal spike patterns & explicit rules

48. Copying of connectivity patterns

49. How to copy small neuronal circuits DNA neuronal network

50. STDP and causal inference