On the inference of sequences of functions

  • William I. Gasarch
  • Carl H. Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 265)


We have shown that, in some sense, computers can be taught how to learn how to learn. The mathematical result constructed sequences of functions that were easy to learn, provided they were learned one at a time in a specific order. Furthermore, the sequences of functions constructed above are impossible to learn, by an algorithmic device, if the functions are not presented in the specified order.

As with any mathematical model, there is some question as to whether or not our result accurately captures the intuitive notion that it was intended to. Independently of how close our proof paradigm is to the intuitive notion of learning how to learn, if it were no were no formal analogue to the concept of machines that learn how to learn, then our result could not possibly be true. Our proof indicates not only that it is not impossible to program computers that learn based, in part, on their previous experiences, but that it is sometimes impossible to succeed without doing so.


Recursive Function Inductive Inference Finite Variant Previous Function Intuitive Notion 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • William I. Gasarch
    • 1
  • Carl H. Smith
    • 2
  1. 1.Department of Computer ScienceUniversity of MarylandCollege Park
  2. 2.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandCollege Park

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