Learnability can be undecidable

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00500071" target="_blank" >RIV/67985840:_____/19:00500071 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1038/s42256-018-0002-3" target="_blank" >http://dx.doi.org/10.1038/s42256-018-0002-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1038/s42256-018-0002-3" target="_blank" >10.1038/s42256-018-0002-3</a>

Result language
angličtina
Original language name
Learnability can be undecidable
Original language description
The mathematical foundations of machine learning play a key role in the development of the field. They improve our understanding and provide tools for designing new learning paradigms. The advantages of mathematics, however, sometimes come with a cost. Gödel and Cohen showed, in a nutshell, that not everything is provable. Here we show that machine learning shares this fate. We describe simple scenarios where learnability cannot be proved nor refuted using the standard axioms of mathematics. Our proof is based on the fact the continuum hypothesis cannot be proved nor refuted. We show that, in some cases, a solution to the ‘estimating the maximum’ problem is equivalent to the continuum hypothesis. The main idea is to prove an equivalence between learnability and compression.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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