Simple Algorithmic Principles of Discovery, Subjective Beauty, Selective Attention, Curiosity & Creativity

  • Jürgen Schmidhuber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4755)


I postulate that human or other intelligent agents function or should function as follows. They store all sensory observations as they come—the data is ‘holy.’ At any time, given some agent’s current coding capabilities, part of the data is compressible by a short and hopefully fast program / description / explanation / world model. In the agent’s subjective eyes, such data is more regular and more beautiful than other data. It is well-known that knowledge of regularity and repeatability may improve the agent’s ability to plan actions leading to external rewards. In absence of such rewards, however, known beauty is boring. Then interestingness becomes the first derivative of subjective beauty: as the learning agent improves its compression algorithm, formerly apparently random data parts become subjectively more regular and beautiful. Such progress in data compression is measured and maximized by the curiosity drive: create action sequences that extend the observation history and yield previously unknown / unpredictable but quickly learnable algorithmic regularity. I discuss how all of the above can be naturally implemented on computers, through an extension of passive unsupervised learning to the case of active data selection: we reward a general reinforcement learner (with access to the adaptive compressor) for actions that improve the subjective compressibility of the growing data. An unusually large compression breakthrough deserves the name discovery. The creativity of artists, dancers, musicians, pure mathematicians can be viewed as a by-product of this principle. Several qualitative examples support this hypothesis.


Human Observer Kolmogorov Complexity Compression Performance Learning Agent Reinforcement Learning Algorithm 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Balter, M.: Seeking the key to music. Science 306, 1120–1122 (2004)CrossRefGoogle Scholar
  2. 2.
    Barlow, H.B., Kaushal, T.P., Mitchison, G.J.: Finding minimum entropy codes. Neural Computation 1(3), 412–423 (1989)Google Scholar
  3. 3.
    Huffman, D.A.: A method for construction of minimum-redundancy codes. In: Proceedings IRE, vol. 40, pp. 1098–1101 (1952)Google Scholar
  4. 4.
    Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer, Heidelberg (2004) (On J. Schmidhuber’s SNF grant 20-61847)Google Scholar
  5. 5.
    Hutter, M.: On universal prediction and Bayesian confirmation. Theoretical Computer Science (2007)Google Scholar
  6. 6.
    Kaelbling, L.P., Littman, M.L., Moore, A.W.: Reinforcement learning: a survey. Journal of AI research 4, 237–285 (1996)Google Scholar
  7. 7.
    Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Problems of Information Transmission 1, 1–11 (1965)Google Scholar
  8. 8.
    Levin, L.A.: Universal sequential search problems. Problems of Information Transmission 9(3), 265–266 (1973)Google Scholar
  9. 9.
    Li, M., Vitányi, P.M.B.: An Introduction to Kolmogorov Complexity and its Applications, 2nd edn. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  10. 10.
    Pinker, S.: How the mind works (1997)Google Scholar
  11. 11.
    Schmidhuber, J.: Adaptive curiosity and adaptive confidence. Technical Report FKI-149-91, Institut für Informatik, Technische Universität München (April 1991) See also [12]Google Scholar
  12. 12.
    Schmidhuber, J.: Curious model-building control systems. In: Proceedings of the International Joint Conference on Neural Networks, vol. 2, pp. 1458–1463. IEEE, Los Alamitos (1991)CrossRefGoogle Scholar
  13. 13.
    Schmidhuber, J.: Learning complex, extended sequences using the principle of history compression. Neural Computation 4(2), 234–242 (1992)CrossRefGoogle Scholar
  14. 14.
    Schmidhuber, J.: Learning factorial codes by predictability minimization. Neural Computation 4(6), 863–879 (1992)Google Scholar
  15. 15.
    Schmidhuber, J.: Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology 30(2), 97–103 (1997)Google Scholar
  16. 16.
    Schmidhuber, J.: What’s interesting? Technical Report IDSIA-35-97, IDSIA, (1997), (extended abstract in Proc. Snowbird 1998, Utah (1998) see also [16])Google Scholar
  17. 17.
    Schmidhuber, J.: Facial beauty and fractal geometry. Technical Report TR IDSIA-28-98, IDSIA (1998) Published in the Cogprint Archive,
  18. 18.
    Schmidhuber, J.: Exploring the predictable. In: Ghosh, A., Tsuitsui, S. (eds.) Advances in Evolutionary Computing, pp. 579–612. Springer, Heidelberg (2002)Google Scholar
  19. 19.
    Schmidhuber, J.: Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science 13(4), 587–612 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    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)Google Scholar
  21. 21.
    Schmidhuber, J.: Gödel machines: self-referential universal problem solvers making provably optimal self-improvements. Technical Report IDSIA-19-03, arXiv:cs.LO/0309048, IDSIA, Manno-Lugano, Switzerland (2003)Google Scholar
  22. 22.
    Schmidhuber, J.: Optimal ordered problem solver. Machine Learning 54, 211–254 (2004)zbMATHCrossRefGoogle Scholar
  23. 23.
    Schmidhuber, J.: Overview of artificial curiosity and active exploration, with links to publications since 1990 (2004),
  24. 24.
    Schmidhuber, J.: Completely self-referential optimal reinforcement learners. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 223–233. Springer, Heidelberg (2005)Google Scholar
  25. 25.
    Schmidhuber, J.: Gödel machines: Towards a technical justification of consciousness. In: Kudenko, D., Kazakov, D., Alonso, E. (eds.) Adaptive Agents and Multi-Agent Systems III. LNCS (LNAI), vol. 3394, pp. 1–23. Springer, Heidelberg (2005)Google Scholar
  26. 26.
    Schmidhuber, J.: Developmental robotics, optimal artificial curiosity, creativity, music, and the fine arts. Connection Science 18(2), 173–187 (2006)CrossRefGoogle Scholar
  27. 27.
    Schmidhuber, J.: Gödel machines: fully self-referential optimal universal problem solvers. In: Goertzel, B., Pennachin, C. (eds.) Artificial General Intelligence, pp. 199–226. Springer, Heidelberg (2006)Google Scholar
  28. 28.
    Schmidhuber, J., Heil, S.: Sequential neural text compression. IEEE Transactions on Neural Networks 7(1), 142–146 (1996)CrossRefGoogle Scholar
  29. 29.
    Schmidhuber, J., Huber, R.: Learning to generate artificial fovea trajectories for target detection. International Journal of Neural Systems 2(1 & 2), 135–141 (1991)CrossRefGoogle Scholar
  30. 30.
    Shannon, C.E.: A mathematical theory of communication (parts I and II). Bell System Technical Journal XXVII, 379–423 (1948)MathSciNetGoogle Scholar
  31. 31.
    Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and Control 7, 1–22 (1964)CrossRefMathSciNetzbMATHGoogle Scholar
  32. 32.
    Solomonoff, R.J.: Complexity-based induction systems. IEEE Transactions on Information Theory IT-24(5), 422–432 (1978)CrossRefMathSciNetGoogle Scholar
  33. 33.
    Storck, J., Hochreiter, S., Schmidhuber, J.: Reinforcement driven information acquisition in non-deterministic environments. In: Proceedings of the International Conference on Artificial Neural Networks, Paris, vol. 2, pp. 159–164. EC2 & Cie (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jürgen Schmidhuber
    • 1
  1. 1.TU Munich, Boltzmannstr. 3, 85748 Garching bei München, Germany & IDSIA, Galleria 2, 6928 Manno (Lugano)Switzerland

Personalised recommendations