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Cognition, Information and Subjective Computation

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One of the most important contending theories deeply connects consciousness to information theory. We keep connecting mind properties to computation. Turing did it with human intelligence and computation. John Searle (unintended I will claim) connected understanding (and consciousness) to program complexity (and soft AI). And more recently, Guilio Tononi formally connected internal experience and consciousness to computation and information. Therefore, can understanding computation shed light on intelligence and consciousness? I claim it does. So what is computation?. I aim at finding a grading (such as Tononi's phi) metric of computation, weakly observer dependent (following some ideas of Searle) and with considerations to resources complexity to give it sense to the Turing test (as Scott Aaronson would agree with).

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Cognition, Information and Subjective Computation

  1. 1. Cognition, Information & Subjective Computation Hector Zenil hector.zenil@ki.se Unit of Computational Medicine, KI Invited Talk Representation of Reality: Humans, Animals and Machines @ AISB50 Study of Artificial Intelligence and Simulation of Behaviour Goldsmiths, University of London, 1-4 April, London, UK Hector Zenil Cognition, Information & Subjective Computation 1 / 28
  2. 2. Introduction Outline Outline Intelligence, understanding and internal experience The information network approach to consciousness A measure of subjective computation and programmability Clinical application and Information Biology Hector Zenil Cognition, Information & Subjective Computation 2 / 28
  3. 3. Intelligence vs. conscience tests A behavioural approach to machine intelligence A behavioural approach to intelligence The Turing test (TT) is a reformulation of a question of non-factual character into a measurable one: something is intelligent if it behaves in an intelligent fashion. Figure : The classic Turing-test to decide intelligent behaviour Hector Zenil Cognition, Information & Subjective Computation 3 / 28
  4. 4. Intelligence vs. conscience tests A behavioural approach to machine intelligence Turing test-like approaches are far from death (Cronin, Krasnogor, et al, Nature Biotechnology 2006) (Maier et al., A Turing test for artificial expression data, Bioinformatics (2013) 29 (20): 2603-2609, 2013). [Zenil in Computing Nature, & SAPERE Series, Springer (2013)] Hector Zenil Cognition, Information & Subjective Computation 4 / 28
  5. 5. Intelligence vs. conscience tests A behavioural approach to machine intelligence intelligence consciousness Figure : Searle’s Chinese room argument (CRA): The person inside the room understands nothing but replies in an “intelligent” fashion (meaning it would pass the Turing test under optimal conditions). Hector Zenil Cognition, Information & Subjective Computation 5 / 28
  6. 6. Intelligence vs. conscience tests A behavioural approach to machine intelligence Passing the Turing test is trivially achievable (in principle) By a CRA-type thought experiment! Number of (comprehensible) sentences is finite Time of conversations is finite Write a lookup table with all possible conversations. Passing the TT is trivially attainable in finite amount of time and space by brute force: just a combinatorial problem. Lookup tables run in O(1) time! (by exchange of time for space) but the size of the lookup table for a machine to pass the TT would grow exponentially for linearly growing conversations. Hector Zenil Cognition, Information & Subjective Computation 6 / 28
  7. 7. Intelligence vs. conscience tests A behavioural approach to machine intelligence Program efficiency and program size matters Scott Aaronson rightly points out that, in light of the theoretical triviality of passing the Turing test, one has to ask about resources. Personally, I find this response to Searle extremely interesting [his attack to rule based systems] since if correct, it suggests that the distinction between polynomial and exponential complexity has metaphysical significance. According to this response, an exponential-sized [computer program] lookup table that passed the Turing Test would not be sentient (or conscious, intelligent, self-aware, etc.), but a polynomially-bounded program with exactly the same input/output behavior would be sentient. Furthermore, the latter program would be sentient because it was polynomially-bounded. –S Aaronson (emphasis and brackets added) [S. Aaronson, Why Philosophers Should Care About Computational Complexity, 2011. arXiv:1108.1791 [cs.CC]] Hector Zenil Cognition, Information & Subjective Computation 7 / 28
  8. 8. Intelligence vs. conscience tests A behavioural approach to machine intelligence Constraints or metaphysics Machine (or human) understanding for Searle cannot be achieved by lookup table brute force. TT objections can be: of metaphysical type or adhere to Searle and introduce resource constraints or some other option not covered here Either: the mind has some metaphysical properties that cannot be represented and reproduced by science, or the TT can only make sense if resources are taken into account. That is, passing TT with certain amount of space and in certain amount of time, or the question of machine intelligence is independent of the TT (and of computing) understanding is a form of rule/data compression and decompression time (answer efficiency)? Searle is right in that the brain is unlikely to have such an enormous lookup table (although one cannot completely rule it out, i.e. the mind is like a Chinese room!) Compression is comprehension [G. Chaitin]. Hector Zenil Cognition, Information & Subjective Computation 8 / 28
  9. 9. Intelligence vs. conscience tests A behavioural approach to machine intelligence Lookup tables, rules and computer programs In summary: Searle’s CRA and soft AI seem to suggest that a program that does not grow with the size of the input is not subject to CRA-type objections (perhaps because we don’t longer understand those programs? at the lowest level they are not different to pure rule-based). The TT test, Searle’s CRA and Aaronson argument, seem to imply a role for program-size and efficiency in the concept of intelligence `a la Searle (i.e. understanding, internal experience, consciousness!) This is compatible with the fact that Searle does not oppose himself to the idea that human minds may be soft AI, he opposes lookup table type of programs epitomized by the CRA, but CRA is not an instance of all computer programs, hence Searle is not metaphysical (he agrees on this). This is again deeply related to computation, more precisely questions of computational and algorithmic (program-size) complexity! Hector Zenil Cognition, Information & Subjective Computation 9 / 28
  10. 10. Intelligence vs. conscience tests A behavioural approach to machine intelligence Integrated Information Theory The phenomenology of internal experience, the unity and integration of the notion of consciousness have been taken as axioms for a integrated information theory (Tononi). The higher the φ, the more conscious the entity. Panpsychism can prevented by a threshold. [From FQXi Tononi’s presentation] Hector Zenil Cognition, Information & Subjective Computation 10 / 28
  11. 11. Intelligence vs. conscience tests A behavioural approach to machine intelligence Dreams, Zombies and Anesthesia [From FQXi Tononi’s presentation] Hector Zenil Cognition, Information & Subjective Computation 11 / 28
  12. 12. Intelligence vs. conscience tests A behavioural approach to machine intelligence A feedforward network A feedforward network resembles a lookup table (modulo the encoding of the interconnections) Figure : Highly hierarchical, layers are disconnected beyond distance 1. φ = 0 network (no consciousness). [From FQXi Tononi’s presentation] Hector Zenil Cognition, Information & Subjective Computation 12 / 28
  13. 13. Intelligence vs. conscience tests A behavioural approach to machine intelligence What is Computation? One of the most important contending theories deeply connects consciousness to information theory. We keep connecting mind properties to computation: Turing connected human intelligence to computation Searle indirectly connects understanding (and consciousness) to program complexity (soft AI). Tononi’s connects consciousness to computation and information Can understanding computation shed light on intelligence and consciousness? What is computation? I aim at finding a (grading and weakly observer dependent) metric of computation. Hector Zenil Cognition, Information & Subjective Computation 13 / 28
  14. 14. Intelligence vs. conscience tests A behavioural approach to machine intelligence Cellular automata as case study [Wolfram, (1994)] Hector Zenil Cognition, Information & Subjective Computation 14 / 28
  15. 15. Intelligence vs. conscience tests A behavioural approach to machine intelligence Long run of rule 30 [Wolfram, (1994)] Hector Zenil Cognition, Information & Subjective Computation 15 / 28
  16. 16. Intelligence vs. conscience tests A behavioural approach to machine intelligence Behavioural richness (sorted by K complexity) Hector Zenil Cognition, Information & Subjective Computation 16 / 28
  17. 17. Intelligence vs. conscience tests A behavioural approach to machine intelligence Towards a metric based on uncompressibility Which string looks more random? (a) 1111111111111111111111111111111111111111 (b) 0011010011010010110111010010100010111010 (c) 0101010101010101010101010101010101010101 Definition KU(s) = min{|p|, U(p) = s} (1) Compressibility A string with low Kolmogorov complexity is c-compressible if |p| + c = |s|. A string is random if K(s) ≈ |s|. K takes advantage of any patterns and compress the object. [Kolmogorov (1965); Chaitin (1966)] Hector Zenil Cognition, Information & Subjective Computation 17 / 28
  18. 18. Intelligence vs. conscience tests A behavioural approach to machine intelligence Rule 22 dual behaviour [Zenil and Villarreal, Bifurcation and Chaos, (2013)] Hector Zenil Cognition, Information & Subjective Computation 18 / 28
  19. 19. Intelligence vs. conscience tests A behavioural approach to machine intelligence Rule 22 dual behaviour detection [Zenil and Villarreal, Bifurcation and Chaos, (2013)] Hector Zenil Cognition, Information & Subjective Computation 19 / 28
  20. 20. Intelligence vs. conscience tests A behavioural approach to machine intelligence Measuring asymptotic qualitative behaviour Compressed evolutions over time: [Zenil, Complex Systems (2010)] Hector Zenil Cognition, Information & Subjective Computation 20 / 28
  21. 21. Intelligence vs. conscience tests A behavioural approach to machine intelligence Capturing behaviour (sensitivity, variability and efficiency) Histograms of asymptotic behaviour of compression ratios (space saving) of ECAs evolutions over time for different initial conditions (see rules 22, 30, 54): Hector Zenil Cognition, Information & Subjective Computation 21 / 28
  22. 22. Intelligence vs. conscience tests A behavioural approach to machine intelligence A behavioural approach to computation A Turing-test like test strategy to the question of life (instead of Turing’s original question of artificial intelligence): [Zenil, Philosophy & Technology and SAPERE, (2013)] Hector Zenil Cognition, Information & Subjective Computation 22 / 28
  23. 23. Intelligence vs. conscience tests A behavioural approach to machine intelligence Programmability measure Let the characteristic exponent ct n be defined as the mean of the absolute values of the differences between the compressed lengths of the outputs of a system M running over the initial segment of initial conditions ij with j = {1, . . . , n} following a Gray-code, and running for t steps in intervals of n. Formally, ct n = |C(Mt(i1)) − C(Mt(i2))| + . . . + |C(Mt(in−1)) − C(Mt(in))| t(n − 1) (2) Let C denote the transition coefficient defined as C(U) = f (Sc), the derivative of the line that fits the sequence Sc by finding the least-squares with Sc = S(cn t ) for a chosen sample frequency n and running time t. The value Ct n(U) (simply C until the discussion of definitions in the next section), based on the phase transition coefficient, will be an indicator of the degree of programmability of a system U relative to its external stimuli (input). The larger the derivative, the greater the change. Hector Zenil Cognition, Information & Subjective Computation 23 / 28
  24. 24. Intelligence vs. conscience tests A behavioural approach to machine intelligence Chalmer’s rock multirealizability objection to functionalism Figure : Sieve-like behaviour of ECA R4 has a low Ct n value for any n and t (it doesn’t react to external stimuli) hence behaviourally this is not a computer. [Zenil, Philosophy & Technology, (2013)] Hector Zenil Cognition, Information & Subjective Computation 24 / 28
  25. 25. Intelligence vs. conscience tests A behavioural approach to machine intelligence Turing universality Figure : ECA R110 has large asymptotic coefficient Ct n value for large enough choices of t and n, which is compatible with the fact that it is Turing universal (for particular semi-periodic initial configurations). Hector Zenil Cognition, Information & Subjective Computation 25 / 28
  26. 26. Intelligence vs. conscience tests A behavioural approach to machine intelligence A hierarchical view of computing by programmability Programmability of physical and biological entities sorted by variability versus controllability: The diagonal determines the degree of programmability (there is a correspondence to intelligence). [Zenil, Ball, Tegn´er, ECAL MIT Press Proceedings, (2013)] Hector Zenil Cognition, Information & Subjective Computation 26 / 28
  27. 27. Intelligence vs. conscience tests A behavioural approach to machine intelligence Properties of C C is: Similar to the Turing test in that it is behavioral in nature (Turing) Observer relative (Searle) Is a graded numerical metric of computation (as Tononi’s φ) Sensitive to resources complexity (Aaronson) Strength sources: uncomputability introduces inevitable subjectivity (what you see with the resources you are given) links to Kolmogorov complexity, the theory of mathematical randomness, towards optimal pattern detection. Possible caveats: It is likely not a distance (no triangle inequality holds, not yet proven) A related, independent, idea to mine was recently pointed out to me: J. Hern´andez-Orallo, and D.L. Dowe. Measuring Universal Intelligence: Towards an Anytime Intelligence Test Artificial Intelligence, 2010. [Zenil, Philosophy & Technology, Springer (2013)] Hector Zenil Cognition, Information & Subjective Computation 27 / 28
  28. 28. Intelligence vs. conscience tests A behavioural approach to machine intelligence Algorithmic information theory in the clinic! Hector Zenil Cognition, Information & Subjective Computation 28 / 28
  29. 29. Intelligence vs. conscience tests A behavioural approach to machine intelligence H. Zenil, Compression-based Investigation of the Dynamical Properties of Cellular Automata and Other Systems, Complex Systems, Vol. 19, No. 1, pages 1-28, 2010. H. Zenil, What is Nature-like Computation? A Behavioural Approach and a Notion of Programmability, Philosophy & Technology (special issue on History and Philosophy of Computing), 2013. H. Zenil, On the Dynamic Qualitative Behavior of Universal Computation Complex Systems, vol. 20, No. 3, pp. 265-278, 2012. G. Terrazas, H. Zenil and N. Krasnogor, Exploring Programmable Self-Assembly in Non DNA-based Computing, Natural Computing, vol 12(4): 499–515, 2013. DOI: 10.1007/s11047-013-9397-2. H. Zenil and E. Villarreal-Zapata, Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces, Journal of Bifurcation and Chaos (in press). H. Zenil, G. Ball and J. Tegn´er, Testing Biological Models for Non-linear Sensitivity with a Programmability Test. In P. Li`o, O. Miglino, G. Nicosia, S. Nolfi and M. Pavone (eds), Advances in Artificial Intelligence, ECAL 2013, pp. 1222-1223, MIT Press, 2013. H. Zenil, A Turing Test-Inspired Approach to Natural Computation. In G. Primiero and L. De Mol (eds.), Turing in Context II (Brussels, 10-12 October 2012), Hector Zenil Cognition, Information & Subjective Computation 28 / 28
  30. 30. Intelligence vs. conscience tests A behavioural approach to machine intelligence Historical and Contemporary Research in Logic, Computing Machinery and Artificial Intelligence, Proceedings published by the Royal Flemish Academy of Belgium for Science and Arts, 2013. A Behavioural Foundation for Natural Computing and a Programmability Test. In G. Dodig-Crnkovic and R. Giovagnoli (eds), Computing Nature: Turing Centenary Perspective, SAPERE Series vol. 7, Springer, 2013. H. Zenil, Turing Patterns with Turing Machines: Emergence and Low-level Structure Formation, Natural Computing, 12(2): 291-303 (2013), 2013. J.-P. Delahaye and H. Zenil, Numerical Evaluation of the Complexity of Short Strings: A Glance Into the Innermost Structure of Algorithmic Randomness, Applied Mathematics and Computation 219, pp. 63-77, 2012. Hector Zenil Cognition, Information & Subjective Computation 28 / 28

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