CFT Duals for Extreme Black Holes

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.Comment: 18 pages; v2 minor change

An almost sure limit theorem for super-Brownian motion

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this case, the spectral theoretical assumptions that required in Chen et al (2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in $\mathbb{R}^d$.Comment: 14 page

Towards heuristic algorithmic memory

We propose a long-term memory design for artificial general intelligence based on Solomonoff's incremental machine learning methods. We introduce four synergistic update algorithms that use a Stochastic Context-Free Grammar as a guiding probability distribution of programs. The update algorithms accomplish adjusting production probabilities, re-using previous solutions, learning programming idioms and discovery of frequent subprograms. A controlled experiment with a long training sequence shows that our incremental learning approach is effective. © 2011 Springer-Verlag Berlin Heidelberg

Dark Energy Content of Nonlinear Electromagnetism

Quasi-constant external fields in nonlinear electromagnetism generate a contribution to the energy-momentum tensor with the form of dark energy. To provide a thorough understanding of the origin and strength of the effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor $T^{\mu\nu}$ for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We also address modifications of charged particle kinematics by strong background fields.Comment: 16 pages, 12 figures; reorganized introduction and sections 4 and 5, added further numerical results and discussion, updated references, fixed typo

Diverse consequences of algorithmic probability

We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline. We also relate to our own work in incremental machine learning and philosophy of complexity. © 2013 Springer-Verlag Berlin Heidelberg

Offline to Online Conversion

We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing's famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.Comment: 20 LaTeX page

Evaluating a reinforcement learning algorithm with a general intelligence test

In this paper we apply the recent notion of anytime universal intelligence tests to the evaluation of a popular reinforcement learning algorithm, Q-learning. We show that a general approach to intelligence evaluation of AI algorithms is feasible. This top-down (theory-derived) approach is based on a generation of environments under a Solomonoff universal distribution instead of using a pre-defined set of specific tasks, such as mazes, problem repositories, etc. This first application of a general intelligence test to a reinforcement learning algorithm brings us to the issue of task-specific vs. general AI agents. This, in turn, suggests new avenues for AI agent evaluation and AI competitions, and also conveys some further insights about the performance of specific algorithms. © 2011 Springer-Verlag.We are grateful for the funding from the Spanish MEC and MICINN for projects TIN2009-06078-E/TIN, Consolider-Ingenio CSD2007-00022 and TIN2010-21062-C02, for MEC FPU grant AP2006-02323, and Generalitat Valenciana for Prometeo/2008/051.Insa Cabrera, J.; Dowe, DL.; Hernández Orallo, J. (2011). Evaluating a reinforcement learning algorithm with a general intelligence test. En Advances in Artificial Intelligence. Springer Verlag (Germany). 7023:1-11. https://doi.org/10.1007/978-3-642-25274-7_1S1117023Dowe, D.L., Hajek, A.R.: A non-behavioural, computational extension to the Turing Test. In: Intl. Conf. on Computational Intelligence & multimedia applications (ICCIMA 1998), Gippsland, Australia, pp. 101–106 (1998)Genesereth, M., Love, N., Pell, B.: General game playing: Overview of the AAAI competition. AI Magazine 26(2), 62 (2005)Hernández-Orallo, J.: Beyond the Turing Test. J. Logic, Language & Information 9(4), 447–466 (2000)Hernández-Orallo, J.: A (hopefully) non-biased universal environment class for measuring intelligence of biological and artificial systems. In: Hutter, M., et al. (eds.) 3rd Intl. Conf. on Artificial General Intelligence, Atlantis, pp. 182–183 (2010)Hernández-Orallo, J.: On evaluating agent performance in a fixed period of time. In: Hutter, M., et al. (eds.) 3rd Intl. Conf. on Artificial General Intelligence, pp. 25–30. Atlantis Press (2010)Hernández-Orallo, J., Dowe, D.L.: Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence 174(18), 1508–1539 (2010)Legg, S., Hutter, M.: A universal measure of intelligence for artificial agents. Intl. Joint Conf. on Artificial Intelligence, IJCAI 19, 1509 (2005)Legg, S., Hutter, M.: Universal intelligence: A definition of machine intelligence. Minds and Machines 17(4), 391–444 (2007)Levin, L.A.: Universal sequential search problems. Problems of Information Transmission 9(3), 265–266 (1973)Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer-Verlag New York, Inc. (2008)Sanghi, P., Dowe, D.L.: A computer program capable of passing IQ tests. In: Proc. 4th ICCS International Conference on Cognitive Science (ICCS 2003), Sydney, Australia, pp. 570–575 (2003)Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and Control 7(1), 1–22 (1964)Strehl, A.L., Li, L., Wiewiora, E., Langford, J., Littman, M.L.: PAC model-free reinforcement learning. In: Proc. of the 23rd Intl. Conf. on Machine Learning, ICML 2006, New York, pp. 881–888 (2006)Sutton, R.S., Barto, A.G.: Reinforcement learning: An introduction. The MIT press (1998)Turing, A.M.: Computing machinery and intelligence. Mind 59, 433–460 (1950)Veness, J., Ng, K.S., Hutter, M., Silver, D.: Reinforcement learning via AIXI approximation. In: Proc. 24th Conf. on Artificial Intelligence (AAAI 2010), pp. 605–611 (2010)Watkins, C.J.C.H., Dayan, P.: Q-learning. Machine learning 8(3), 279–292 (1992)Weyns, D., Parunak, H.V.D., Michel, F., Holvoet, T., Ferber, J.: Environments for multiagent systems state-of-the-art and research challenges. In: Weyns, D., Van Dyke Parunak, H., Michel, F. (eds.) E4MAS 2004. LNCS (LNAI), vol. 3374, pp. 1–47. Springer, Heidelberg (2005)Whiteson, S., Tanner, B., White, A.: The Reinforcement Learning Competitions. The AI magazine 31(2), 81–94 (2010)Woergoetter, F., Porr, B.: Reinforcement learning. Scholarpedia 3(3), 1448 (2008)Zatuchna, Z., Bagnall, A.: Learning mazes with aliasing states: An LCS algorithm with associative perception. Adaptive Behavior 17(1), 28–57 (2009

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

Comparing humans and AI agents

Comparing humans and machines is one important source of information about both machine and human strengths and limitations. Most of these comparisons and competitions are performed in rather specific tasks such as calculus, speech recognition, translation, games, etc. The information conveyed by these experiments is limited, since it portrays that machines are much better than humans at some domains and worse at others. In fact, CAPTCHAs exploit this fact. However, there have only been a few proposals of general intelligence tests in the last two decades, and, to our knowledge, just a couple of implementations and evaluations. In this paper, we implement one of the most recent test proposals, devise an interface for humans and use it to compare the intelligence of humans and Q-learning, a popular reinforcement learning algorithm. The results are highly informative in many ways, raising many questions on the use of a (universal) distribution of environments, on the role of measuring knowledge acquisition, and other issues, such as speed, duration of the test, scalability, etc.We thank the anonymous reviewers for their helpful comments. We also thank José Antonio Martín H. for helping us with several issues about the RL competition, RL-Glue and reinforcement learning in general. We are also grateful to all the subjects who took the test. We also thank the funding from the Spanish MEC and MICINN for projects TIN2009-06078- E/TIN, Consolider-Ingenio CSD2007-00022 and TIN2010-21062-C02, for MEC FPU grant AP2006-02323, and Generalitat Valenciana for Prometeo/2008/051Insa Cabrera, J.; Dowe, DL.; España Cubillo, S.; Henánez-Lloreda, MV.; Hernández Orallo, J. (2011). Comparing humans and AI agents. En Artificial General Intelligence. Springer Verlag (Germany). 6830:122-132. https://doi.org/10.1007/978-3-642-22887-2_13S1221326830Dowe, D.L., Hajek, A.R.: A non-behavioural, computational extension to the Turing Test. In: Intl. Conf. on Computational Intelligence & multimedia applications (ICCIMA 1998), Gippsland, Australia, pp. 101–106 (1998)Gordon, D., Subramanian, D.: A cognitive model of learning to navigate. In: Proc. 19th Conf. of the Cognitive Science Society, 1997, vol. 25, p. 271. Lawrence Erlbaum, Mahwah (1997)Hernández-Orallo, J.: Beyond the Turing Test. J. Logic, Language & Information 9(4), 447–466 (2000)Hernández-Orallo, J.: A (hopefully) non-biased universal environment class for measuring intelligence of biological and artificial systems. In: Hutter, M., et al. (eds.) 3rd Intl. Conf. on Artificial General Intelligence, pp. 182–183. Atlantis Press, London (2010) Extended report at, http://users.dsic.upv.es/proy/anynt/unbiased.pdfHernández-Orallo, J., Dowe, D.L.: Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence 174(18), 1508–1539 (2010)Hernández-Orallo, J., Dowe, D.L., España-Cubillo, S., Hernández-Lloreda, M.V., Insa-Cabrera, J.: On more realistic environment distributions for defining, evaluating and developing intelligence. In: Schmidhuber, J., Thórisson, K.R., Looks, M. (eds.) AGI 2011. LNCS(LNAI), pp. 81–90. Springer, Heidelberg (2011)Legg, S., Hutter, M.: A universal measure of intelligence for artificial agents. In: Intl Joint Conf on Artificial Intelligence, IJCAI, vol. 19, p. 1509 (2005)Legg, S., Hutter, M.: Universal intelligence: A definition of machine intelligence. Minds and Machines 17(4), 391–444 (2007)Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer-Verlag New York, Inc., Heidelberg (2008)Oppy, G., Dowe, D.L.: The Turing Test. In: Zalta, E.N. (ed.) Stanford Encyclopedia of Philosophy, Stanford University, Stanford (2011), http://plato.stanford.edu/entries/turing-test/Sanghi, P., Dowe, D.L.: A computer program capable of passing IQ tests. In: 4th Intl. Conf. on Cognitive Science (ICCS 2003), Sydney, pp. 570–575 (2003)Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and control 7(1), 1–22 (1964)Strehl, A.L., Li, L., Wiewiora, E., Langford, J., Littman, M.L.: PAC model-free reinforcement learning. In: ICML 2006, pp. 881–888. New York (2006)Sutton, R.S., Barto, A.G.: Reinforcement learning: An introduction. The MIT press, Cambridge (1998)Turing, A.M.: Computing machinery and intelligence. Mind 59, 433–460 (1950)Veness, J., Ng, K.S., Hutter, M., Silver, D.: A Monte Carlo AIXI Approximation. Journal of Artificial Intelligence Research, JAIR 40, 95–142 (2011)von Ahn, L., Blum, M., Langford, J.: Telling humans and computers apart automatically. Communications of the ACM 47(2), 56–60 (2004)Watkins, C.J.C.H., Dayan, P.: Q-learning. Mach. learning 8(3), 279–292 (1992

Compression and intelligence: social environments and communication

Compression has been advocated as one of the principles which pervades inductive inference and prediction - and, from there, it has also been recurrent in definitions and tests of intelligence. However, this connection is less explicit in new approaches to intelligence. In this paper, we advocate that the notion of compression can appear again in definitions and tests of intelligence through the concepts of `mind-reading¿ and `communication¿ in the context of multi-agent systems and social environments. Our main position is that two-part Minimum Message Length (MML) compression is not only more natural and effective for agents with limited resources, but it is also much more appropriate for agents in (co-operative) social environments than one-part compression schemes - particularly those using a posterior-weighted mixture of all available models following Solomonoff¿s theory of prediction. We think that the realisation of these differences is important to avoid a naive view of `intelligence as compression¿ in favour of a better understanding of how, why and where (one-part or two-part, lossless or lossy) compression is needed.We thank the anonymous reviewers for their helpful comments, and we thank Kurt Kleiner for some challenging and ultimately very helpful questions in the broad area of this work. We also acknowledge the funding from the Spanish MEC and MICINN for projects TIN2009-06078-E/TIN, Consolider-Ingenio CSD2007-00022 and TIN2010-21062-C02, and Generalitat Valenciana for Prometeo/2008/051.Dowe, DL.; Hernández Orallo, J.; Das, PK. (2011). Compression and intelligence: social environments and communication. En Artificial General Intelligence. Springer Verlag (Germany). 6830:204-211. https://doi.org/10.1007/978-3-642-22887-2_21S2042116830Chaitin, G.J.: Godel’s theorem and information. International Journal of Theoretical Physics 21(12), 941–954 (1982)Dowe, D.L.: Foreword re C. S. Wallace. Computer Journal 51(5), 523–560 (2008); Christopher Stewart WALLACE (1933-2004) memorial special issueDowe, D.L.: Minimum Message Length and statistically consistent invariant (objective?) Bayesian probabilistic inference - from (medical) “evidence”. Social Epistemology 22(4), 433–460 (2008)Dowe, D.L.: MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness. In: Bandyopadhyay, P.S., Forster, M.R. (eds.) Handbook of the Philosophy of Science. Philosophy of Statistics, vol. 7, pp. 901–982. Elsevier, Amsterdam (2011)Dowe, D.L., Hajek, A.R.: A computational extension to the Turing Test. Technical Report #97/322, Dept Computer Science, Monash University, Melbourne, Australia, 9 pp (1997)Dowe, D.L., Hajek, A.R.: A non-behavioural, computational extension to the Turing Test. In: Intl. Conf. on Computational Intelligence & multimedia applications (ICCIMA 1998), Gippsland, Australia, pp. 101–106 (February 1998)Hernández-Orallo, J.: Beyond the Turing Test. J. Logic, Language & Information 9(4), 447–466 (2000)Hernández-Orallo, J.: Constructive reinforcement learning. International Journal of Intelligent Systems 15(3), 241–264 (2000)Hernández-Orallo, J.: On the computational measurement of intelligence factors. In: Meystel, A. (ed.) Performance metrics for intelligent systems workshop, pp. 1–8. National Institute of Standards and Technology, Gaithersburg, MD, U.S.A (2000)Hernández-Orallo, J., Dowe, D.L.: Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence 174(18), 1508–1539 (2010)Hernández-Orallo, J., Minaya-Collado, N.: A formal definition of intelligence based on an intensional variant of Kolmogorov complexity. In: Proc. Intl Symposium of Engineering of Intelligent Systems (EIS 1998), pp. 146–163. ICSC Press (1998)Legg, S., Hutter, M.: Universal intelligence: A definition of machine intelligence. Minds and Machines 17(4), 391–444 (2007)Lewis, D.K., Shelby-Richardson, J.: Scriven on human unpredictability. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 17(5), 69–74 (1966)Oppy, G., Dowe, D.L.: The Turing Test. In: Zalta, E.N. (ed.) Stanford Encyclopedia of Philosophy, Stanford University, Stanford (2011), http://plato.stanford.edu/entries/turing-test/Salomon, D., Motta, G., Bryant, D.C.O.N.: Handbook of data compression. Springer-Verlag New York Inc., Heidelberg (2009)Sanghi, P., Dowe, D.L.: A computer program capable of passing I.Q. tests. In: 4th International Conference on Cognitive Science (and 7th Australasian Society for Cognitive Science Conference), vol. 2, pp. 570–575. Univ. of NSW, Sydney, Australia (July 2003)Sayood, K.: Introduction to data compression. Morgan Kaufmann, San Francisco (2006)Scriven, M.: An essential unpredictability in human behavior. In: Wolman, B.B., Nagel, E. (eds.) Scientific Psychology: Principles and Approaches, pp. 411–425. Basic Books (Perseus Books), New York (1965)Searle, J.R.: Minds, brains and programs. Behavioural and Brain Sciences 3, 417–457 (1980)Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and control 7(1), 1–22 (1964)Sutton, R.S.: Generalization in reinforcement learning: Successful examples using sparse coarse coding. Advances in neural information processing systems, 1038–1044 (1996)Sutton, R.S., Barto, A.G.: Reinforcement learning: An introduction. The MIT Press, Cambridge (1998)Turing, A.M.: Computing machinery and intelligence. Mind 59, 433–460 (1950)Veness, J., Ng, K.S., Hutter, M., Silver, D.: A Monte Carlo AIXI Approximation. Journal of Artificial Intelligence Research, JAIR 40, 95–142 (2011)Wallace, C.S.: Statistical and Inductive Inference by Minimum Message Length. Springer, Heidelberg (2005)Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11(2), 185–194 (1968)Wallace, C.S., Dowe, D.L.: Intrinsic classification by MML - the Snob program. In: Proc. 7th Australian Joint Conf. on Artificial Intelligence, pp. 37–44. World Scientific, Singapore (November 1994)Wallace, C.S., Dowe, D.L.: Minimum message length and Kolmogorov complexity. Computer Journal 42(4), 270–283 (1999); Special issue on Kolmogorov complexityWallace, C.S., Dowe, D.L.: MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions. Statistics and Computing 10, 73–83 (2000