1. Lior Segev Ranit Aharonov Alon Keinan Isaac Meilijson www.math.tau.ac.il/~ruppin Localization of Function in Neurocontrollers

2. Localization of Function –How does one ``understand’’ neural information processing? –A classical, good point to start with is localization of function(s) in neurocontrollers –A good model to start with is Evolutionary Autonomous Agents (EAAs) –Scope of analysis method may be more general

3. Evolved neurocontrollers

4. Talk Overview The basic Functional Contribution Analysis (FCA) Localization of Subtasks Synaptic Analysis High-dimensional FCA Informational Lesioning Playing games in the brain, or “My fair lady”.

5. The basic FCA A multi-lesion approach: learning about normal, intact functioning via lesion ``perturbations’’ Given are a set of neurocontroller lesions and the agent’s corresponding performance levels Assign ``importance’’ levels to the different units of the neurocontroller? The FCA: Find such assginments that maximize performance prediction of unseen lesions

6. Lesioning C1C1 C2C2 C3C3 C4C4 C5C5 C6C6 p = f(c 1 +c 3 +c 4 +c 6 ) ~ argmin = Σ (p-p) 2 {f,c}{f,c} 1 2N2N ~

7. The Functional Contribution Algorithm (FCA) f module c module optimal f and c training set min(p-p) 2 ~

9. The performance prediction function (m. c) P

10. Single Lesions vs. FCA

11. Generalization – an Adaptive Lesion Selection algorithm

12. Task Comparison

13. The Contribution Matrix – Localization and Specification Task Neuron 12  P 1C 11 C 12  C1PC1P 2C 21 C 22  C2PC2P 3C 31 C 32  C3PC3P.............................. NCN1CN1 CN2CN2  C NP

14. Synaptic Analysis

16. Network Backbone By weights By contributions

17. High-dimensional FCA The inherent limitations of basic FCA (e.g., paradoxical lesioning) Compound Elements Order (dimension) of compound elements An efficient High-D algorithm for compound element selection

18. Complexity of Task Localization

19. Types of 2D Interactions Paradoxical Interactions – element 1 is advantageous only if element 2 is intact Inverse Paradoxical interactions – element 1 is advantageous only if element 2 is lesioned All significant 2D compound elements belong to either type (there can be others..)

20. Informational Lesioning Method (ILM) The paradox of the lesioning paradigm The dependence on the lesioning method Controlled lesioning – approaching the limit of intact behavior Implement a lesion as a channel whose input is the firing of the intact element and output is the firing of the lesioned element (given an input). Quantify the lesioning level as an inverse function of the Mutual Information between the input and output of the channel

26. ILM – In summary: Increased localization precision Portraying a spectrum of short-to-long term functional effects of system units Approaching the limit CVs of the intact state, in the ILM lesioning family Does such a limit exist more generally? Is the beauty inherently in the of the beholder?

27. Where Game Theory meets Brain Research.. “George said: You know, we are on a wrong track altogether. We must not think of the things we could do with, but only of the things that we can’t do without.” [Three men in a boat: to say nothing of the dog!, by Jerome K. Jerome, chapter 3]

28. FCA and the Shapley Value The Shapley value (SH): A famed, unique solution of cost allocation in a game theory axiomatic system Many functioning networks (including our EAA neurocontrollers) can be addressed within this framework An alternative formulation of the FCA is equivalent to the SH (even though the starting standpoints and motivations are different).

29. Ongoing FCA Research Optimal Lesioning ? Relation to SH and more efficient algorithms (sampling, high-D..). Generalization to PPR Application to neuroscience data (reverse inactivation, TMS, fMRI). Application to gene networks?

30. The contribution values can be efficiently determined using the simple FCA. More complex networks require higher dimensional FCA descriptions. The minimal dimension of the FCA may provide an interesting measure of functional complexity. The importance of being lesioned (in the “right” way..) – ILM and beyond. Even if the brain is not “a society of minds”, it can be analyzed with the aids of fundamental tools from game theory. www.math.tau.ac.il/~ruppin – papers (and code)www.math.tau.ac.il/~ruppin Summary

33. Network backbone: 2D interactions