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Lior Segev Ranit Aharonov Alon Keinan Isaac Meilijson math.tau.ac.il/~ruppin

Localization of Function in Neurocontrollers. Lior Segev Ranit Aharonov Alon Keinan Isaac Meilijson www.math.tau.ac.il/~ruppin. Localization of Function. How does one ``understand’’ neural information processing?

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Lior Segev Ranit Aharonov Alon Keinan Isaac Meilijson math.tau.ac.il/~ruppin

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

  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. C3 C5 C1 C4 C2 C6 ~ p = f(c1+c3+c4+c6) argmin = Σ(p-p)2 1 ~ 2N {f,c} Lesioning

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

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

  9. Single Lesions vs. FCA

  10. Generalization – an Adaptive Lesion Selection algorithm

  11. Task Comparison

  12. The Contribution Matrix – Localization and Specification

  13. Synaptic Analysis

  14. Network Backbone By weights By contributions

  15. 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

  16. Complexity of Task Localization

  17. 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..)

  18. 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

  19. 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?

  20. 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]

  21. 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).

  22. 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?

  23. Summary • 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)

  24. Network backbone: 2D interactions

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