Skip to main content
SpringerLink
Log in

Ultimate Intelligence Part II: Physical Complexity and Limits of Inductive Inference Systems

  • Conference paper
  • First Online:
Artificial General Intelligence (AGI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9782))

Included in the following conference series:

Abstract

We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that involve volume and energy. We introduce a graphical model of computational complexity that we believe to be appropriate for intelligent machines. We show several asymptotic relations between energy, logical depth and volume of computation for inductive inference. In particular, we arrive at a “black-hole equation” of inductive inference, which relates energy, volume, space, and algorithmic information for an optimal inductive inference solution. We introduce energy-bounded algorithmic entropy. We briefly apply our ideas to the physical limits of intelligent computation in our universe.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A prefix-free code is a set of codes in which no code is a prefix of another. A computer file uses a prefix-free code, ending with an EOF symbol, thus, most reasonable programming languages are prefix-free.

  2. 2.

    We used the regular expression notation in language theory.

  3. 3.

    Time as discrete timestamps, as opposed to duration.

  4. 4.

    If the derivation is \(A \rightarrow AA \rightarrow AAA\), it has \(1+2+3 = 6\) volume.

  5. 5.

    Although the assumption that it takes only 1 unit of space-time volume to simulate the minimal program that reproduces the pdf \(\mu \) is not realistic, we are only considering this for the sake of simplicity, and because 1 \(m^3\) is close to the volume of a personal computer, or a brain. For many pdfs, it could be much larger in practice.

References

  1. Bennett, C.H.: Logical depth and physical complexity. In: Herkin, R. (ed.) The Universal Turing Machine: A Half-Century Survey, pp. 227–257 (1988). citeseer.ist.psu.edu/bennet88logical.html

  2. Bremermann, H.J.: Minimum energy requirements of information transfer and computing. Int. J. Theor. Phy. 21(3), 203–217 (1982). http://dx.doi.org/10.1007/BF01857726

    Article  MathSciNet  MATH  Google Scholar 

  3. Chaitin, G.J.: Algorithmic Information Theory. Cambridge University Press, New York (2004)

    Book  MATH  Google Scholar 

  4. Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5(3), 183–191 (1961). http://dx.doi.org/10.1147/rd.53.0183

    Article  MathSciNet  MATH  Google Scholar 

  5. Levin, L.A.: Some theorems on the algorithmic approach to probability theory and information theory. CoRR abs/1009.5894 (2010)

    Google Scholar 

  6. Lloyd, S.: Ultimate physical limits to computation. Nature 406, 1047–1054 (2000)

    Article  Google Scholar 

  7. Lloyd, S.: Computational capacity of the universe. Phys. Rev. Lett. 88(23), 237901 (2002)

    Article  Google Scholar 

  8. Margolus, N., Levitin, L.B.: The maximum speed of dynamical evolution. Physica D Nonlinear Phenomena 120, 188–195 (1998)

    Article  Google Scholar 

  9. Miller, D.B., Fredkin, E.: Two-state, reversible, universal cellular automata in three dimensions. In: Proceedings of the 2nd Conference on Computing Frontiers, CF 2005, pp. 45–51 (2005). http://doi.acm.org/10.1145/1062261.1062271

  10. Neary, T., Woods, D.: The complexity of small universal turing machines: a survey. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 385–405. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Özkural, E.: Towards heuristic algorithmic memory. In: Schmidhuber, J., Thórisson, K.R., Looks, M. (eds.) AGI 2011. LNCS, vol. 6830, pp. 382–387. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Özkural, E.: Diverse consequences of algorithmic probability. In: Dowe, D.L. (ed.) Solomonoff Festschrift. LNCS, vol. 7070, pp. 285–298. Springer, Heidelberg (2013)

    Google Scholar 

  13. Özkural, E.: Ultimate Intelligence part I: physical completeness and objectivity of induction. In: Bieger, J., Goertzel, B., Potapov, A. (eds.) AGI 2015. LNCS, vol. 9205, pp. 131–141. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  14. Schmidhuber, J.: Optimal ordered problem solver. Mach. Learn. 54, 211–256 (2004)

    Article  MATH  Google Scholar 

  15. Schmidhuber, J.: The Speed Prior: a new simplicity measure yielding near-optimal computable predictions. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 216–228. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  16. Solomonoff, R.: Perfect training sequences and the costs of corruption - a progress report on inductive inference research. Technical report, Oxbridge Research (Aug 1982)

    Google Scholar 

  17. Solomonoff, R.J.: A formal theory of inductive inference, part i. Inform. Control 7(1), 1–22 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  18. Solomonoff, R.J.: A formal theory of inductive inference, part ii. Inform. Control 7(2), 224–254 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  19. Solomonoff, R.J.: Complexity-based induction systems: comparisons and convergence theorems. IEEE Trans. Inform. Theor. IT 24(4), 422–432 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  20. Solomonoff, R.J.: A system for incremental learning based on algorithmic probability. In: Proceedings of the Sixth Israeli Conference on Artificial Intelligence, pp. 515–527. Tel Aviv, Israel., December 1989

    Google Scholar 

  21. Solomonoff, R.J.: Progress in incremental machine learning. Technical report IDSIA-16-03, IDSIA, Lugano, Switzerland (2003)

    Google Scholar 

  22. Solomonoff, R.J.: Three kinds of probabilistic induction: universal distributions and convergence theorems. Comput. J. 51(5), 566–570 (2008)

    Article  Google Scholar 

  23. Solomonoff, R.J.: Algorithmic probability, heuristic programming and AGI. In: Third Conference on Artificial General Intelligence, pp. 251–157 (2010)

    Google Scholar 

Download references

Acknowledgements

Thanks to anonymous reviewers whose comments substantially improved the presentation. Thanks to Gregory Chaitin and Juergen Schmidhuber for inspiring the mathematical philosophy/digital physics angle in the paper. I am forever indebted for the high-quality research coming out of IDSIA which revitalized interest in human-level AI research.

Author information

Authors and Affiliations

  1. Gök Us Sibernetik Ar&Ge Ltd. Şti, Istanbul, Turkey

    Eray Özkural

Authors
  1. Eray Özkural
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eray Özkural .

Editor information

Editors and Affiliations

  1. Galleria 1, IDSIA, Manno, Switzerland

    Bas Steunebrink

  2. Temple University, Phoenixville, Pennsylvania, USA

    Pei Wang

  3. Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Ben Goertzel

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Özkural, E. (2016). Ultimate Intelligence Part II: Physical Complexity and Limits of Inductive Inference Systems. In: Steunebrink, B., Wang, P., Goertzel, B. (eds) Artificial General Intelligence. AGI 2016. Lecture Notes in Computer Science(), vol 9782. Springer, Cham. https://doi.org/10.1007/978-3-319-41649-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-41649-6_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41648-9

  • Online ISBN: 978-3-319-41649-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation