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A Theory of the Learnable

Valiant, L. G.·2026·Foundations of Computation and Machine Learning
DOI 10.1145/3749740.3749746
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Abstract

Humans appear to be able to learn new concepts without needing to be programmed explicitly in any conventional sense. In this paper we regard learning as the phenomenon of knowledge acquisition in the absence of explicit programming. We give a precise methodology for studying this phenomenon from a computational viewpoint. It consists of choosing an appropriate information gathering mechanism, the learning protocol, and exploring the class of concepts that can be learned using it in a reasonable (polynomial) number of steps. Although inherent algorithmic complexity appears to set serious limits to the range of concepts that can be learned, we show that there are some important nontrivial classes of propositional concepts that can be learned in a realistic sense.

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Research works printed but not linked: 9

  1. 10.1145/356914.356918 · DOI
  2. [2] Barr, A., and Feigenbaum, E.A. The Handbook of Artificial Intelligence. Vol. 2. William Kaufmann, Los Altos, Calif., 1982.
  3. 10.1145/800157.805047 · DOI · Paper page
  4. [4] Duda, R.O., and Hart, P.F. Pattern Classification and Scene Analysis. Wiley, New York, 1973.
  5. [5] Erdös, P., and Spencer, J. Probabilistic Methods in Combinatorics. Academic Press, New York, 1974.
  6. 10.1109/SFCS.1984.715949 · DOI
  7. 10.1007/978-3-662-12405-5 · DOI
  8. 10.1109/SFCS.1981.3 · DOI
  9. [9] Valiant, L.G. Deductive learning. Philosophical Transactions of the Royal Society of London (1984). To be published.

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Metadata

Authors
Valiant, L. G.
Venue
Foundations of Computation and Machine Learning
Publisher
ACM
Published
2026-08-11
Pages
69-94
DOI
10.1145/3749740.3749746
Cited by
0
References
0
Language
en

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CoChat. (2026). Citation check: A Theory of the Learnable. https://app.cochat.ai/papers/10.1145/3749740.3749746
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Valiant, L. G. (2026). A Theory of the Learnable. Foundations of Computation and Machine Learning. https://doi.org/10.1145/3749740.3749746