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"... this paper initiates a study in which it is demonstrated that certain concepts (represented by functions) can be learned, but only in the event that certain relevant subconcepts (also represented by functions) have been previously learned. In other words, the Soar project presents empirical evidence ..."
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this paper initiates a study in which it is demonstrated that certain concepts (represented by functions) can be learned, but only in the event that certain relevant subconcepts (also represented by functions) have been previously learned. In other words, the Soar project presents empirical evidence that learning how to learn is viable for computers and this paper proves that doing so is the only way possible for computers to make certain inferences.
Parsimony hierarchies for inductive inference
 Journal of Symbolic Logic
"... Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and “nearly” minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requ ..."
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Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and “nearly” minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A limcomputable function is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be “notsonearly ” minimal size, e.g., to be within a limcomputable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are limcomputable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of limcomputability, the power of
Abstract
"... Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on at most a bits? Let 0 ≤ a ≤ n − 1. We show that any deterministic protocol, as well as any errorfree quantum protocol (C ∗ version), for this problem requires at least n − 2 bits of communication. We ..."
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Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on at most a bits? Let 0 ≤ a ≤ n − 1. We show that any deterministic protocol, as well as any errorfree quantum protocol (C ∗ version), for this problem requires at least n − 2 bits of communication. We show the same bounds for the problem of determining if two strings differ in exactly a bits. We also prove a lower bound of n/2 − 1 for errorfree Q ∗ quantum protocols. Our results are obtained by lowerbounding the ranks of the appropriate matrices. 1
InputDependence in FunctionLearning
"... Abstract. In the standard literature on inductive inference, a learner sees as input the course of values of the function to be learned. In the present work, it is investigated how reasonable this choice is and how sensitive the model is with respect to variations like the overgraph or undergraph of ..."
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Abstract. In the standard literature on inductive inference, a learner sees as input the course of values of the function to be learned. In the present work, it is investigated how reasonable this choice is and how sensitive the model is with respect to variations like the overgraph or undergraph of the function. Several implications and separations are shown and for the basic notions, a complete picture is obtained. Furthermore, relations to oracles, additional information and teams are explored.