Composition is almost as good as s-1-1

Chen²,

Analogical and Inductive Inference

1992

Suppose LC 1 and LC 2 are two machine learning classes each based on a criterion of success. Suppose, for every machine which learns a class of functions according to the LC 1 criterion of success, there is a machine which learns this class according to the LC 2 criterion. In the case where the converse does not hold LC 1 is said to be separated from LC 2 . It is shown that for many such separated learning classes from the literature a much stronger separation holds:It is also shown that there is a pair of separated learning classes from the literature for which the stronger separation just above does not hold. A philosophical heuristic toward the design of artificially intelligent learning programs is presented with each strong separation result.

Section: Notationmentioning

confidence: 99%

Strong separation of learning classes

Chen²,

Analogical and Inductive Inference

1992

“…(Case showed the acceptable systems are characterized as those in which every control structure can be constructed; Royer and later Marcoux examined complexity analogs of this characterization ( Riccardi (1980), Riccardi (1981), Royer (1987), Marcoux (1989).) ϕ i denotes the partial computable function computed by program i in the ϕ-system.…”

Section: Preliminariesmentioning

confidence: 99%

Complexity issues for vacillatory function identification

Lecture Notes in Computer Science

Sharma

1991

It was previously shown by Barzdin and Podnieks that one does not increase the power of learning programs for functions by allowing learning algorithms to converge to a finite set of correct programs instead of requiring them to converge to a single correct program. In this paper we define some new, subtle, but natural concepts of mind change complexity for function learning and show that, if one bounds this complexity for learning algorithms, then, by contrast with Barzdin and Podnieks result, there are interesting and sometimes complicated tradeoffs between these complexity bounds, bounds on the number of final correct programs, and learning power.

“…W , one has, of course, computable instances of union and intersect. Similarly, in typical, practical programming languages, one has instances of while-loop and if-then-else which are not only computable, but, since they can be realized by simple substitution of the constituent programs into some fixed template, they are computable in linear-time [27,20].…”

Section: Definition 11mentioning

confidence: 99%

Control structures in hypothesis spaces: the influence on learning

Theoretical Computer Science

Suraj

2002

In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the influence on learnability of the presence or absence of certain control structures in the hypothesis space. First presented are control structure characterizations of some rather specific but illustrative learnability results. The presence of these control structures is thereby shown essential to maintain full learning power. Then presented are the main theorems. Each of these non-trivially characterizes the invariance of a learning class over hypothesis space V and the presence of a particular projection control structure, called proj, in V as: V has suitable instances of all denotational control structures. In a sense, then, proj epitomizes the control structures whose presence needn't help and whose absence needn't hinder learning power.