Skip to main content
SpringerLink
Log in

The new AI is general and mathematically rigorous

  • Research Article
  • Published:
Frontiers of Electrical and Electronic Engineering in China

Abstract

Most traditional artificial intelligence (AI) systems of the past decades 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. We first briefly review the history of AI since Gödel’s 1931 paper, then discuss recent post-2000 approaches that are currently transforming general AI research into a formal science.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Solomonoff R J. A formal theory of inductive inference. Part I. Information and Control, 1964, 7(1): 1–22

    Article  MATH  MathSciNet  Google Scholar 

  2. Kolmogorov A N. Three approaches to the quantitative definition of information. Problems of Information Transmission, 1965, 1(1): 1–11

    MathSciNet  Google Scholar 

  3. Newell A, Simon H. GPS, a program that simulates human thought. In: Feigenbaum E, Feldman J, eds. Computers and Thought. New York: McGraw-Hill, 1963, 279–293

    Google Scholar 

  4. Rosenbloom P S, Laird J E, Newell A. The Soar Papers: Research on Integrated Intelligence. MIT Press, 1993

  5. Mitchell T. Machine Learning. New York: McGraw Hill, 1997

    MATH  Google Scholar 

  6. Kaelbling L P, Littman M L, Moore A W. Reinforcement learning: A survey. Journal of Artificial Intelligence Research, 1996, 4: 237–285

    Google Scholar 

  7. Schmidhuber J. Ultimate cognition à la Gödel. Cognitive Computation, 2009, 1(2): 177–193

    Article  Google Scholar 

  8. Schmidhuber J. Towards solving the grand problem of AI. In: Quaresma P, Dourado A, Costa E, Costa J F, eds. Soft Computing and Complex Systems. Coimbra: Centro Internacional de Mathematica, 2003, 77–97

    Google Scholar 

  9. Gödel K. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter. Systeme I. Monatshefte für Mathematik und Physik, 1931, 38: 173–198

    Article  Google Scholar 

  10. Schmidhuber J. New millennium AI and the convergence of history. In: Duch W, Mandziuk J, eds. Challenges to Computational Intelligence. Studies in Computational Intelligence. Berlin: Springer, 2007, 63: 15–36

    Chapter  Google Scholar 

  11. Schmidhuber J. 2006: Celebrating 75 years of AI - history and outlook: The next 25 years. In: Lungarella M, Iida F, Bongard J, Pfeifer R, eds. 50 Years of Artificial Intelligence. Lecture Notes in Artificial Intelligence, 2007, 4850: 29–41

  12. Turing A M. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Series 2, 1936, 42: 230–265

    Article  MATH  Google Scholar 

  13. Shannon C E. A mathematical theory of communication (Parts I and II). Bell System Technical Journal, 1948, 27(3&4): 379–423, 623–656

    MATH  MathSciNet  Google Scholar 

  14. Solomonoff R J. Complexity-based induction systems. IEEE Transactions on Information Theory, 1978, IT-24(4): 422–432

    Article  MathSciNet  Google Scholar 

  15. Hutter M. Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability. Berlin: Springer, 2004

    Google Scholar 

  16. Rechenberg I. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart Fromman-Holzboog, 1973

  17. Holland J H. Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press, 1975

    Google Scholar 

  18. Minsky M, Papert S. Perceptrons. Cambridge: MIT Press, 1969

    MATH  Google Scholar 

  19. Kohonen T. Self-Organization and Associative Memory. 2nd ed. Berlin: Springer, 1988

    MATH  Google Scholar 

  20. Werbos P J. Beyond regression: New tools for prediction and analysis in the behavioral sciences. Dissertation for the Doctoral Degree. Cambridge: Harvard University, 1974

    Google Scholar 

  21. Rissanen J. Modeling by shortest data description. Automatica, 1978, 14(5): 465–471

    Article  MATH  Google Scholar 

  22. Brooks R A. Intelligence without reason. In: Proceedings of the Twelfth International Joint Conference on Artificial Intelligence. 1991, 569–595

  23. Dorigo M, Di Caro G, Gambardella L M. Ant algorithms for discrete optimization. Artificial Life, 1999, 5(2): 137–172

    Article  Google Scholar 

  24. Vapnik V. The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995

    MATH  Google Scholar 

  25. Dickmanns E D, Behringer R, Dickmanns D, Hildebrandt T, Maurer M, Thomanek F, Schiehlen J. The seeing passenger car ‘VaMoRs-P’. In: Proceedings of the International Symposium on Intelligent Vehicles 1994. 1994, 68–73

  26. Nilsson N J. Principles of Artificial Intelligence. San Francisco: Morgan Kaufmann, 1980

    MATH  Google Scholar 

  27. Pfeifer R, Scheier C. Understanding Intelligence. Cambridge: MIT Press, 2001

    Google Scholar 

  28. Zvonkin A K, Levin L A. The complexity of finite objects and the algorithmic concepts of information and randomness. Russian Mathematical Surveys, 1970, 25(6): 83–124

    Article  MATH  MathSciNet  Google Scholar 

  29. Gács P. On the relation between descriptional complexity and algorithmic probability. Theoretical Computer Science, 1983, 22(1–2): 71–93

    Article  MATH  MathSciNet  Google Scholar 

  30. Li M, Vitányi P M B. An Introduction to Kolmogorov Complexity and Its Applications. 2nd ed. Berlin: Springer-Verlag, 1997

    MATH  Google Scholar 

  31. Merhav N, Feder M. Universal prediction. IEEE Transactions on Information Theory, 1998, 44(6): 2124–2147

    Article  MATH  MathSciNet  Google Scholar 

  32. Schmidhuber J. Algorithmic theories of everything. Technical Report IDSIA-20-00, quant-ph/0011122, 2000

  33. Schmidhuber J. Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science, 2002, 13(4): 587–612

    Article  MATH  MathSciNet  Google Scholar 

  34. Brouwer L E J. Over de Grondslagen der Wiskunde. Dissertation for the Doctoral Degree. Amsterdam: University of Amsterdam, 1907

    Google Scholar 

  35. Beeson M. Foundations of Constructive Mathematics. Heidelberg: Springer-Verlag, 1985

    MATH  Google Scholar 

  36. Gold E M. Limiting recursion. Journal of Symbolic Logic, 1965, 30(1): 28–48

    Article  MATH  MathSciNet  Google Scholar 

  37. Putnam H. Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic, 1965, 30(1): 49–57

    Article  MATH  MathSciNet  Google Scholar 

  38. Freyvald R V. Functions and functionals computable in the limit. Transactions of Latvijas Vlasts Univ. Zinatn. Raksti, 1977, 210: 6–19

    Google Scholar 

  39. Rogers H Jr. Theory of Recursive Functions and Effective Computability. New York: McGraw-Hill, 1967

    MATH  Google Scholar 

  40. Chaitin G J. Algorithmic Information Theory. Cambridge: Cambridge University Press, 1987

    Book  Google Scholar 

  41. Löwenheim L. Über Möglichkeiten im Relativkalkül. Mathematische Annalen, 1915, 76: 447–470

    Article  MathSciNet  Google Scholar 

  42. Skolem T. Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theorem über dichte Mengen. Skrifter utgit av Videnskapsselskapet in Kristiania I, Matematicsk-Naturvidenskabelig, 1920, 4: 1–36

    Google Scholar 

  43. Cajori F. History of Mathematics. 2nd ed. New York: Macmillan, 1919

    Google Scholar 

  44. Cantor G. Ü ber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen. Crelle’s Journal für Mathematik, 1874, 77: 258–262

    Google Scholar 

  45. Wallace C S, Boulton D M. An information theoretic measure for classification. The Computer Journal, 1968, 11(2): 185–194

    MATH  Google Scholar 

  46. Schmidhuber J. The Speed Prior: A new simplicity measure yielding near-optimal computable predictions. In: Kivinen J, Sloan R H, eds. Proceedings of the 15th Annual Conference on Computational Learning Theory. Lecture Notes in Artificial Intelligence, 2002, 2375: 216–228

  47. Levin L A. Laws of information (nongrowth) and aspects of the foundation of probability theory. Problems of Information Transmission, 1974, 10(3): 206–210

    Google Scholar 

  48. Schmidhuber J. Discovering solutions with low Kolmogorov complexity and high generalization capability. In: Prieditis A, Russell S, eds. Proceedings of Machine Learning: Proceedings of the Twelfth International Conference. 1995, 488–496

  49. Schmidhuber J. Discovering neural nets with low Kolmogorov complexity and high generalization capability. Neural Networks, 1997, 10(5): 857–873

    Article  Google Scholar 

  50. Popper K R. The Logic of Scientific Discovery. London: Hutchinson, 1934

    Google Scholar 

  51. Green M B, Schwarz J H, Witten E. Superstring Theory. Cambridge: Cambridge University Press, 1987

    MATH  Google Scholar 

  52. Everett H III. ’Relative State’ formulation of quantum mechanics. Reviews of Modern Physics, 1957, 29(3): 454–462

    Article  MathSciNet  Google Scholar 

  53. Zuse K. Rechnender raum. Elektronische Datenverarbeitung, 1967, 8: 336–344

    Google Scholar 

  54. Zuse K. Rechnender Raum. Braunschweig: Friedrich Vieweg & Sohn, 1969. English translation: Calculating Space. MIT Technical Translation AZT-70-164-GEMIT. Cambridge: Massachusetts Institute of Technology (Proj. MAC), 1970

    MATH  Google Scholar 

  55. Schmidhuber J. Randomness in physics. Nature, 2006, 439(7075): 392

    Article  Google Scholar 

  56. Ulam S. Random processes and transformations. In: Proceedings of the International Congress on Mathematics. 1950, 2: 264–275

    Google Scholar 

  57. von Neumann J. Theory of Self-Reproducing Automata. Champaign: University of Illinois Press, 1966

    Google Scholar 

  58. Bennett C H, DiVicenzo D P. Quantum information and computation. Nature, 2000, 404(6775): 256–259

    Article  Google Scholar 

  59. Deutsch D. The Fabric of Reality. New York: Allen Lane, 1997

    Google Scholar 

  60. Penrose R. The Emperor’s New Mind. Oxford: Oxford University Press, 1989

    Google Scholar 

  61. Bell J S. On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 1966, 38(3): 447–452

    Article  MATH  MathSciNet  Google Scholar 

  62. ’t Hooft G. Quantum gravity as a dissipative deterministic system. Technical Report SPIN-1999/07/gr-gc/9903084, 1999. http://xxx.lanl.gov/abs/gr-qc/9903084

  63. Schmidhuber J. A computer scientist’s view of life, the universe, and everything. In: 5Freksa C, Jantzen M, Valk R, eds. Foundations of Computer Science: Potential-Theory-Cognition. Lecture Notes in Computer Science, 1997, 1337: 201–208

  64. Erber T, Putterman S. Randomness in quantum mechanics - nature’s ultimate cryptogram? Nature, 1985, 318(6041): 41–43

    Article  Google Scholar 

  65. Fredkin E F, Toffoli T. Conservative logic. International Journal of Theoretical Physics, 1982, 21(3/4): 219–253

    Article  MATH  MathSciNet  Google Scholar 

  66. Levin L A. Universal sequential search problems. Problems of Information Transmission, 1973, 9(3): 265–266

    Google Scholar 

  67. Hutter M. The fastest and shortest algorithm for all well-defined problems. International Journal of Foundations of Computer Science, 2002, 13(3): 431–443

    Article  MATH  MathSciNet  Google Scholar 

  68. Schmidhuber J, Zhao J, Wiering M. Shifting inductive bias with success-story algorithm, adaptive Levin search, and incremental self-improvement. Machine Learning, 1997, 28(1): 105–130

    Article  Google Scholar 

  69. Solomonoff R J. An application of algorithmic probability to problems in artificial intelligence. In: Kanal L N, Lemmer J F, eds. Uncertainty in Artificial Intelligence. Amsterdam: Elsevier Science Publishers, 1986, 473–491

    Google Scholar 

  70. Solomonoff R J. A system for incremental learning based on algorithmic probability. In: Proceedings of the Sixth Israeli Conference on Artificial Intelligence, Computer Vision and Pattern Recognition. 1989, 515–527

  71. Wiering M A, Schmidhuber J. Solving POMDPs with Levin search and EIRA. In: Saitta L, ed. Machine Learning: Proceedings of the Thirteenth International Conference. San Francisco: Morgan Kaufmann Publishers, 1996, 534–542

    Google Scholar 

  72. Schmidhuber J. Optimal ordered problem solver. Machine Learning, 2004, 54(3): 211–254

    Article  MATH  Google Scholar 

  73. Schmidhuber J. Bias-optimal incremental problem solving. In: Becker S, Thrun S, Obermayer K, eds. Advances in Neural Information Processing Systems 15. Cambridge: MIT Press, 2003, 1571–1578

    Google Scholar 

  74. Chaitin G J. A theory of program size formally identical to information theory. Journal of the Association for Computing Machinery, 1975, 22(3): 329–340

    MATH  MathSciNet  Google Scholar 

  75. Moore C H, Leach G C. FORTH - A Language for Interactive Computing. Amsterdam: Mohasco Industries Inc, 1970

    Google Scholar 

  76. Rumelhart D E, Hinton G E, Williams R J. Learning internal representations by error propagation. In: Rumelhart D E, McClelland J L, eds. Parallel Distributed Processing. Camridge: MIT Press, 1986, 1: 318–362

    Google Scholar 

  77. Bishop C M. Neural Networks for Pattern Recognition. Oxford: Oxford University Press, 1995

    Google Scholar 

  78. Hochreiter S, Younger A S, Conwell P R. Learning to learn using gradient descent. In: Proceedings of the International Conference on Artificial Neural Networks. 2001, 87–94

  79. Schmidhuber J. Gödel machines: Fully self-referential optimal universal self-improvers. In: Goertzel B, Pennachin C, eds. Artificial General Intelligence. Berlin: Springer-Verlag, 2006, 199–226

    Google Scholar 

  80. Schmidhuber J. Completely self-referential optimal reinforcement learners. In: Duch W, Kacprzyk J, Oja E, Zadrozny S, eds. Proceedings of the International Conference on Artificial Neural Networks. 2005, 223–233

  81. Schmidhuber J. Dynamische neuronale Netze und das fundamentale raumzeitliche Lernproblem. Dissertation for the Doctoral Degree. München: Institut für Informatik, Technische Universität München, 1990

    Google Scholar 

  82. Schmidhuber J. A possibility for implementing curiosity and boredom in model-building neural controllers. In: Meyer J A, Wilson S W, eds. Proceedings of the International Conference on Simulation of Adaptive Behavior: From Animals to Animats. 1991, 222–227

  83. Schmidhuber J. Adaptive curiosity and adaptive confidence. Technical Report FKI-149-91, Institut für Informatik, Technische Universität München, 1991

  84. Schmidhuber J. Curious model-building control systems. In: Proceedings of the International Joint Conference on Neural Networks. 1991, 2: 1458–1463

    Google Scholar 

  85. Storck J, Hochreiter S, Schmidhuber J. Reinforcement driven information acquisition in non-deterministic environments. In: Proceedings of the International Conference on Artificial Neural Networks. 1995, 2: 159–164

    Google Scholar 

  86. Schmidhuber J. What’s interesting? Technical Report IDSIA-35-97, 1997. ftp://ftp.idsia.ch/pub/juergen/interest.ps.gz

  87. Schmidhuber J. Exploring the predictable. In: Ghosh A, Tsuitsui S, eds. Advances in Evolutionary Computing. Berlin: Springer, 2002, 579–612

    Google Scholar 

  88. Schmidhuber J. Developmental robotics, optimal artificial curiosity, creativity, music, and the fine arts. Connection Science, 2006, 18(2): 173–187

    Article  Google Scholar 

  89. Schmidhuber J. Simple algorithmic principles of discovery, subjective beauty, selective attention, curiosity & creativity. In: Proceedings of the 10th International Conference on Discovery Science. Lecture Notes in Computer Science, 2007, 4755: 26–38

    Article  Google Scholar 

  90. Schmidhuber J. Driven by compression progress. In: Lovrek I, Howlett R J, Jain L C, eds. Proceedings of the 12th International Conference on Knowledge-Based Intelligent Information and Engineering Systems. Lecture Notes in Computer Science, 2008, 5177: 11

  91. Schmidhuber J. Simple algorithmic theory of subjective beauty, novelty, surprise, interestingness, attention, curiosity, creativity, art, science, music, jokes. SICE Journal of the Society of Instrument and Control Engineers, 2009, 48(1): 21–32

    Google Scholar 

  92. Schmidhuber J. Driven by compression progress: A simple principle explains essential aspects of subjective beauty, novelty, surprise, interestingness, attention, curiosity, creativity, art, science, music, jokes. In: Pezzulo G, Butz M V, Sigaud O, Baldassarre G, eds. Anticipatory Behavior in Adaptive Learning Systems. From Psychological Theories to Artificial Cognitive Systems. Lecture Notes in Computer Science, 2009, 5499: 48–76

  93. Schmidhuber J. Art & science as by-products of the search for novel patterns, or data compressible in unknown yet learnable ways. In: Botta M, ed. Multiple Ways to Design Research. Research Cases That Reshape the Design Discipline. Swiss Design Network - Et al. Edizioni, 2009, 98–112

  94. Schmidhuber J. Artificial scientists & artists based on the formal theory of creativity. In: Hutter M, Servedio R A, Takimoto E, eds. Proceedings of the Third Conference on Artificial General Intelligence. 2010

  95. Schmidhuber J. An on-line algorithm for dynamic reinforcement learning and planning in reactive environments. In: Proceedings of IEEE/INNS International Joint Conference on Neural Networks. 1990, 2: 253–258

    Article  Google Scholar 

  96. Sutton R S, Barto A G. Reinforcement Learning: An Introduction. Cambridge: MIT Press, 1998

    Google Scholar 

  97. Schmidhuber J. Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology, 1997, 30(2): 97–103

    Google Scholar 

  98. Kolmogorov A N. Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer-Verlag, 1933

    Google Scholar 

  99. Utgoff P. Shift of bias for inductive concept learning. In: Michalski R, Carbonell J, Mitchell T, eds. Machine Learning. Los Altos: Morgan Kaufmann, 1986, 2: 163–190

    Google Scholar 

  100. Schmidhuber J. The new AI: General & sound & relevant for physics. In: Goertzel B, Pennachin C, eds. Artificial General Intelligence. Berlin: Springer-Verlag, 2006, 175–198

    Google Scholar 

  101. Schmidhuber C. Strings from logic. Technical Report CERN-TH/2000-316, CERN, Theory Division, 2000. http://xxx.lanl.gov/abs/hep-th/0011065

Download references

Author information

Authors and Affiliations

  1. IDSIA, University of Lugano and SUPSI, Galleria 2, 6928, Manno-Lugano, Switzerland

    Jürgen Schmidhuber

Authors
  1. Jürgen Schmidhuber
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jürgen Schmidhuber.

Additional information

Part of this work is reprinted from Refs. [11] and [100] with friendly permission by Springer-Verlag.

Jürgen Schmidhuber wants to build an optimal scientist, then retire. He is Director of the Swiss Artificial Intelligence Lab IDSIA (since 1995), Professor of Artificial Intelligence at the University of Lugano, Switzerland (since 2009), Head of the CogBotLab at TU Munich, Germany (since 2004, as Professor Extraordinarius until 2009), and Professor SUPSI, Switzerland (since 2003). He obtained his doctoral degree in computer science from TUM in 1991 and his Habilitation degree in 1993, after a postdoctoral stay at the University of Colorado at Boulder. He helped to transform IDSIA into one of the world’s top ten AI labs (the smallest!), according to the ranking of Business Week Magazine. In 2008 he was elected member of the European Academy of Sciences and Arts. He has published more than 200 peer-reviewed scientific papers (some won best paper awards) on topics such as machine learning, mathematically optimal universal AI, artificial curiosity and creativity, artificial recurrent neural networks (which won several recent handwriting recognition contests), adaptive robotics, algorithmic information and complexity theory, digital physics, theory of beauty, and the fine arts.

About this article

Cite this article

Schmidhuber, J. The new AI is general and mathematically rigorous. Front. Electr. Electron. Eng. China 5, 347–362 (2010). https://doi.org/10.1007/s11460-010-0105-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11460-010-0105-z

Keywords

Search

Navigation