Summary
Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam’s razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse’s thesis of the computer-generated universe.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beeson M (1985) Foundations of Constructive Mathematics. Springer-Verlag, Berlin, New York, Heidelberg.
Bell JS (1966) On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys., 38:447–452.
Bennett CH, DiVicenzo DP Quantum information and computation. Nature, 404(6775):256–259.
Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press.
Brouwer LEJ (1907) Over de Grondslagen der Wiskunde. Dissertation, Doctoral Thesis, University of Amsterdam.
Cajori F (1919) History of mathematics. Macmillan, New York, 2nd edition.
Cantor G (1874) Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen. Crelle’s Journal für Mathematik, 77:258–263.
Chaitin GJ (1975) A theory of program size formally identical to information theory. Journal of the ACM, 22:329–340.
Chaitin GJ (1987) Algorithmic Information Theory. Cambridge University Press, Cambridge, UK.
Deutsch D (1997) The Fabric of Reality. Allen Lane, New York, NY.
Erber T, Putterman S (1985) Randomness in quantum mechanics — nature’s ultimate cryptogram? Nature, 318(7):41–43.
Everett III H (1957) ‘Relative State’ formulation of quantum mechanics. Reviews of Modern Physics, 29:454–462.
Fredkin EF, Toffoli T (1982) Conservative logic. International Journal of Theoretical Physics, 21(3/4):219–253.
Freyvald RV (1977) Functions and functionals computable in the limit. Transactions of Latvijas Vlasts Univ. Zinatn. Raksti, 210:6–19.
Gács P (1983) On the relation between descriptional complexity and algorithmic probability. Theoretical Computer Science, 22:71–93.
Gödel K (1931) Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38:173–198.
Gold EM (1965) Limiting recursion. Journal of Symbolic Logic, 30(1):28–46.
Green MB, Schwarz JH, Witten E (1987) Superstring Theory. Cambridge University Press, Cambridge, UK.
Hochreiter S, Younger AS, Conwell PR (2001) Learning to learn using gradient descent. In Lecture Notes on Comp. Sci. 2130, Proc. Intl. Conf. on Artificial Neural Networks (ICANN-2001), Springer, Berlin, Heidelberg.
Hutter M (2001) Convergence and error bounds of universal prediction for general alphabet. Proceedings of the 12th European Conference on Machine Learning (ECML-2001), Technical Report IDSIA-07-01, cs.AI/0103015), 2001.
Hutter M (2001) General loss bounds for universal sequence prediction. In Brodley CE, Danyluk AP (eds) Proceedings of the 18 th International Conference on Machine Learning (ICML-2001).
Hutter M (2001) Towards a universal theory of artificial intelligence based on algorithmic probability and sequential decisions. Proceedings of the 12 th European Conference on Machine Learning (ECML-2001).
Hutter M (2002) The fastest and shortest algorithm for all well-defined problems. International Journal of Foundations of Computer Science, 13(3):431–443.
Hutter M (2002) Self-optimizing and Pareto-optimal policies in general environments based on Bayes-mixtures. In Proc. 15th Annual Conf. on Computational Learning Theory (COLT 2002), volume 2375 of LNAI, Springer, Berlin.
Hutter M (2005) A gentle introduction to the universal algorithmic agent AIXI. In this volume.
Jordan MI, Rumelhart DE (1990) Supervised learning with a distal teacher. Technical Report Occasional Paper #40, Center for Cog. Sci., MIT.
Kaelbling LP, Littman ML, Moore AW Reinforcement learning: a survey. Journal of AI research, 4:237–285.
Kolmogorov AN (1965) Three approaches to the quantitative definition of information. Problems of Information Transmission, 1:1–11.
Levin LA (1973) Universal sequential search problems. Problems of Information Transmission, 9(3):265–266.
Levin LA (1974) Laws of information (nongrowth) and aspects of the foundation of probability theory. Problems of Information Transmission, 10(3):206–210.
Li M, Vitányi PMB (1997) An Introduction to Kolmogorov Complexity and its Applications. Springer, Berlin, 2nd edition.
Löwenheim L (1915) Über Möglichkeiten im Relativkalkül. Mathematische Annalen, 76:447–470.
Merhav N, Feder M (1998) Universal prediction. IEEE Transactions on Information Theory, 44(6):2124–2147.
Mitchell T (1997) Machine Learning. McGraw Hill.
Moore CH, Leach GC (1970) FORTH: a language for interactive computing, 1970. http://www.ultratechnology.com.
Newell A, Simon H (1963) GPS, a Program that Simulates Human Thought, In: Feigenbaum E, Feldman J (eds), Computers and Thought, MIT Press, Cambridge, MA.
Nguyen, Widrow B (1989) The truck backer-upper: An example of self learning in neural networks. In Proceedings of the International Joint Conference on Neural Networks.
Penrose R The Emperor’s New Mind. Oxford University Press, Oxford.
Popper KR (1934) The Logic of Scientific Discovery. Hutchinson, London.
Putnam H (1965) Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic, 30(1):49–57.
Rissanen J (1986) Stochastic complexity and modeling. The Annals of Statistics, 14(3):1080–1100.
Rogers, Jr. H (1967) Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York.
Rosenbloom PS, Laird JE, and Newell A. The SOAR Papers. MIT Press, 1993.
Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In Rumelhart DE, McClelland JL (eds) Parallel Distributed Processing, volume 1, MIT Press.
Schmidhuber C (2000) Strings from logic. Technical Report CERN-TH/2000-316, CERN, Theory Division. http://xxx.lanl.gov/abs/hep-th/0011065.
Schmidhuber J (1991) Reinforcement learning in Markovian and non-Markovian environments. In Lippman DS, Moody JE, Touretzky DS (eds) Advances in Neural Information Processing Systems 3, Morgan Kaufmann, Los Altos, CA.
Schmidhuber J (1995) Discovering solutions with low Kolmogorov complexity and high generalization capability. In Prieditis A and Russell S (eds) Machine Learning: Proceedings of the Twelfth International Conference. Morgan Kaufmann, San Francisco, CA.
Schmidhuber J (1997) A computer scientist’s view of life, the universe, and everything. In Freksa C, Jantzen M, Valk R (eds) Foundations of Computer Science: Potential — Theory — Cognition, volume 1337 of LLNCS, Springer, Berlin.
Schmidhuber J (1997) Discovering neural nets with low Kolmogorov complexity and high generalization capability. Neural Networks, 10(5):857–873.
Schmidhuber J (2000) Algorithmic theories of everything. Technical Report IDSIA-20-00, quant-ph/0011122, IDSIA. Sections 1–5: see [52]; Section 6: see [54].
Schmidhuber J (2001) Sequential decision making based on direct search. In Sun R, Giles CL (eds) Sequence Learning: Paradigms, Algorithms, and Applications. volume 1828 of LLAI, Springer, Berlin.
Schmidhuber J (2002) Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science, 13(4):587–612.
Schmidhuber J (2004) Optimal ordered problem solver. Machine Learning, 54(3):211–254.
Schmidhuber J (2002) The Speed Prior: a new simplicity measure yielding nearoptimal computable predictions. In Kivinen J, Sloan RH (eds) Proceedings of the 15th Annual Conference on Computational Learning Theory (COLT 2002), Lecture Notes in Artificial Intelligence, Springer, Berlin.
Schmidhuber J (2003) Bias-optimal incremental problem solving. In Becker S, Thrun S, Obermayer K (eds) Advances in Neural Information Processing Systems 15, MIT Press, Cambridge, MA.
Schmidhuber J (2003) Gödel machines: self-referential universal problem solvers making provably optimal self-improvements. Technical Report IDSIA-19-03, arXiv:cs.LO/0309048 v2, IDSIA.
Schmidhuber J (2003) The new AI: General & sound & relevant for physics. Technical Report TR IDSIA-04-03, Version 1.0, cs.AI/0302012 v1, IDSIA.
Schmidhuber J (2003) Towards solving the grand problem of AI. In Quaresma P, Dourado A, Costa E, Costa JF (eds) Soft Computing and complex systems, Centro Internacional de Mathematica, Coimbra, Portugal. Based on [57].
Schmidhuber J and Hutter M (2002) NIPS 2002 workshop on universal learning algorithms and optimal search. Additional speakers: R. Solomonoff, P. M. B. Vitányi, N. Cesa-Bianchi, I. Nemenmann. Whistler, CA.
Schmidhuber J, Zhao J, Wiering M (1997) Shifting inductive bias with success-story algorithm, adaptive Levin search, and incremental self-improvement. Machine Learning, 28:105–130.
Skolem T (1919) Logisch-kombinatorische Untersuchungen über Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theorem üuber dichte Mengen. Skrifter utgit av Videnskapsselskapet in Kristiania, I, Mat.-Nat. Kl., N4:1–36.
Solomonoff R (1964) A formal theory of inductive inference. Part I. Information and Control, 7:1–22.
Solomonoff R (1978) Complexity-based induction systems. IEEE Transactions on Information Theory, IT-24(5):422–432.
Solomonoff R (1986) An application of algorithmic probability to problems in artificial intelligence. In Kanal L, Lemmer J (eds) Uncertainty in Artificial Intelligence, Elsevier Science Publishers/North Holland, Amsterdam.
Solomonoff R (1989) A system for incremental learning based on algorithmic probability. In Proceedings of the Sixth Israeli Conference on Artificial Intelligence, Computer Vision and Pattern Recognition.
’t Hooft G (1999) Quantum gravity as a dissipative deterministic system. Classical and Quantum Gravity (16):3263–3279.
Turing A (1936) On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Series 2, 41:230–267.
Ulam S (1950) Random processes and transformations. In Proceedings of the International Congress on Mathematics, volume 2, pages 264–275.
Vapnik V The Nature of Statistical Learning Theory. Springer, New York, 1995.
von Neumann J (1966) Theory of Self-Reproducing Automata. University of Illionois Press, Champain, IL.
Wallace CS, Boulton DM (1968) An information theoretic measure for classification. Computer Journal, 11(2):185–194.
Werbos PJ (1974) Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. PhD thesis, Harvard University.
Werbos PJ (1987) Learning how the world works: Specifications for predictive networks in robots and brains. In Proceedings of IEEE International Conference on Systems, Man and Cybernetics, N.Y..
Wiering M, Schmidhuber J (1996) Solving POMDPs with Levin search and EIRA. In Saitta L (ed) Machine Learning: Proceedings of the Thirteenth International Conference, Morgan Kaufmann, San Francisco, CA.
Zuse K (1967) Rechnender Raum. Elektronische Datenverarbeitung, 8:336–344.
Zuse K (1969) Rechnender Raum. Friedrich Vieweg & Sohn, Braunschweig. English translation: Calculating Space, MIT Technical Translation AZT-70-164-GEMIT, MIT (Proj. MAC), Cambridge, MA.
Zvonkin AK, Levin LA (1970) The complexity of finite objects and the algorithmic concepts of information and randomness. Russian Math. Surveys, 25(6):83–124.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schmidhuber, J. (2007). The New AI: General & Sound & Relevant for Physics. In: Goertzel, B., Pennachin, C. (eds) Artificial General Intelligence. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68677-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-68677-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23733-4
Online ISBN: 978-3-540-68677-4
eBook Packages: Computer ScienceComputer Science (R0)