Generality's price: Inescapable deficiencies in machine-learned programs

John Case, Keh Jiann Chen, Sanjay Jain, Wolfgang Merkle, James S. Royer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device and the quality of the programs it learns successfully. There are results to the effect that, thanks to small increases in generality of a learning device, the computational complexity of some successfully learned programs is provably unalterably suboptimal. There are also results in which the complexity of successfully learned programs is asymptotically optimal and the learning device is general, but, still thanks to the generality, some of those optimal, learned programs are provably unalterably information deficient-in some cases, deficient as to safe, algorithmic extractability/provability of the fact that they are even approximately optimal. For these results, the safe, algorithmic methods of information extraction will be by proofs in arbitrary, true, computably axiomatizable extensions of Peano Arithmetic.

Original languageEnglish (US)
Pages (from-to)303-326
Number of pages24
JournalAnnals of Pure and Applied Logic
Issue number1-3
StatePublished - May 2006


  • Applications of computability theory
  • Computational learning theory

ASJC Scopus subject areas

  • Logic


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