Evolvability need not imply learnability [article]

Nisheeth Srivastava
<span title="2009-04-03">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is insufficient to prove the PAC-learnability of monotone Boolean functions, thereby demonstrating a counter-example to a recent claim to the contrary. We further discuss scenarios wherein evolvability and learnability will coincide as well as scenarios under which
more &raquo; ... y differ. The implications of the latter case on the prospects of learning in complex hypothesis spaces is briefly examined.
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