Bibliographische Detailangaben

Beteilige Person:	Kharitonov, Michael (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Stanford, Calif. 1992
Schriftenreihe:	Stanford University / Computer Science Department: Report STAN CS 1445
Schlagwörter:	Cryptography Machine learning
Abstract:	Abstract: "We investigate cryptographic lower bounds on the learnability of Boolean formulas and constant depth circuits on the uniform distribution and other specific distributions. We first show that weakly learning Boolean formulas and constant depth threshold circuits with membership queries on the uniform distribution in polynomial time is as hard as factoring Blum integers (or inverting RSA, or deciding quadratic residuosity). We formalize the notion of a trivially learnable distribution and extend these hardness results to all non-trivial distributions Moreover, we show that under appropriate assumptions on the hardness of factoring, the learnability of Boolean formulas and constant depth threshold circuits on any distribution is characterized by the distribution's Renyi entropy. Furthermore, we show that a sub-exponential lower bound for factoring implies a [formula] lower bound (for some constant [beta]) for learning Boolean circuits of depth d on the uniform distribution (with membership queries), which matches the upper bound of Linial, Mansour, and Nisan [19]. From this we conclude that, assuming such a lower bound for factoring, there is no O(n[superscript poly log n]) algorithm to learn all of AC p0 s on the uniform distribution We observe that, under cryptographic assumptions, all our bounds can be used to establish tradeoffs between the running time and the number of samples necessary to learn.
Umfang:	24 S.