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17
The Power of Vacillation in Language Learning
, 1992
"... Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are ..."
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Cited by 44 (11 self)
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Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are classes of languages that can be learned if convergence in the limit to up to (n+1) exactly correct grammars is allowed but which cannot be learned if convergence in the limit is to no more than n grammars, where the no more than n grammars can each make finitely many mistakes. This contrasts sharply with results of Barzdin and Podnieks and, later, Case and Smith, for learnability from both positive and negative data. A subset principle from a 1980 paper of Angluin is extended to the vacillatory and other criteria of this paper. This principle, provides a necessary condition for circumventing overgeneralization in learning from positive data. It is applied to prove another theorem to the eff...
Infinitary Self Reference in Learning Theory
, 1994
"... Kleene's Second Recursion Theorem provides a means for transforming any program p into a program e(p) which first creates a quiescent self copy and then runs p on that self copy together with any externally given input. e(p), in effect, has complete (low level) self knowledge, and p represents how ..."
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Cited by 18 (6 self)
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Kleene's Second Recursion Theorem provides a means for transforming any program p into a program e(p) which first creates a quiescent self copy and then runs p on that self copy together with any externally given input. e(p), in effect, has complete (low level) self knowledge, and p represents how e(p) uses its self knowledge (and its knowledge of the external world). Infinite regress is not required since e(p) creates its self copy outside of itself. One mechanism to achieve this creation is a self replication trick isomorphic to that employed by singlecelled organisms. Another is for e(p) to look in a mirror to see which program it is. In 1974 the author published an infinitary generalization of Kleene's theorem which he called the Operator Recursion Theorem. It provides a means for obtaining an (algorithmically) growing collection of programs which, in effect, share a common (also growing) mirror from which they can obtain complete low level models of themselves and the other prog...
Synthesizing Enumeration Techniques For Language Learning
 In Proceedings of the Ninth Annual Conference on Computational Learning Theory
, 1996
"... this paper we assume, without loss of generality, that for all oe ` ø , [M(oe) 6=?] ) [M(ø) 6=?]. ..."
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Cited by 16 (7 self)
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this paper we assume, without loss of generality, that for all oe ` ø , [M(oe) 6=?] ) [M(ø) 6=?].
Complexity issues for vacillatory function identification
 Information and Computation
, 1995
"... 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, ..."
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Cited by 12 (9 self)
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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. CR Classification Number: I.2.6 (Learning – Induction). 1
On learning limiting programs
 International Journal of Foundations of Computer Science
, 1992
"... Machine learning of limit programs (i.e., programs allowed finitely many mind changes about their legitimate outputs) for computable functions is studied. Learning of iterated limit programs is also studied. To partially motivate these studies, it is shown that, in some cases, interesting global pr ..."
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Cited by 11 (5 self)
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Machine learning of limit programs (i.e., programs allowed finitely many mind changes about their legitimate outputs) for computable functions is studied. Learning of iterated limit programs is also studied. To partially motivate these studies, it is shown that, in some cases, interesting global properties of computable functions can be proved from suitable (n + 1)iterated limit programs for them which can not be proved from any niterated limit programs for them. It is shown that learning power is increased when (n + 1)iterated limit programs rather than niterated limit programs are to be learned. Many tradeoff results are obtained regarding learning power, number (possibly zero) of limits taken, program size constraints and information, and number of errors tolerated in final programs learned.
Robust Learning Aided by Context
 In Proceedings of the Eleventh Annual Conference on Computational Learning Theory
, 1998
"... Empirical studies of multitask learning provide some evidence that the performance of a learning system on its intended targets improves by presenting to the learning system related tasks, also called contexts, as additional input. Angluin, Gasarch, and Smith, as well as Kinber, Smith, Velauthapilla ..."
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Cited by 10 (6 self)
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Empirical studies of multitask learning provide some evidence that the performance of a learning system on its intended targets improves by presenting to the learning system related tasks, also called contexts, as additional input. Angluin, Gasarch, and Smith, as well as Kinber, Smith, Velauthapillai, and Wiehagen have provided mathematical justification for this phenomenon in the inductive inference framework. However, their proofs rely heavily on selfreferential coding tricks, that is, they directly code the solution of the learning problem into the context. Fulk has shown that for the Ex and Bcanomaly hierarchies, such results, which rely on selfreferential coding tricks, may not hold robustly. In this work we analyze robust versions of learning aided by context and show that  in contrast to Fulk's result above  the robust versions of This work was carried out while J. Case, S. Jain, M. Ott, and F. Stephan were visiting the School of Computer Science and Engineering at ...
Looking for an analogue of Rice's Theorem in circuit complexity theory
 Mathematical Logic Quarterly
, 1989
"... Abstract. Rice’s Theorem says that every nontrivial semantic property of programs is undecidable. In this spirit we show the following: Every nontrivial absolute (gap, relative) counting property of circuits is UPhard with respect to polynomialtime Turing reductions. For generators [31] we show a ..."
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Cited by 5 (1 self)
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Abstract. Rice’s Theorem says that every nontrivial semantic property of programs is undecidable. In this spirit we show the following: Every nontrivial absolute (gap, relative) counting property of circuits is UPhard with respect to polynomialtime Turing reductions. For generators [31] we show a perfect analogue of Rice’s Theorem. Mathematics Subject Classification: 03D15, 68Q15. Keywords: Rice’s Theorem, Counting problems, Promise classes, UPhard, NPhard, generators.
Spatial/Kinematic Domain and Lattice Computers
 JOURNAL OF EXPERIMENTAL AND THEORETICAL ARTIFICIAL INTELLIGENCE
, 1994
"... An approach to analogical representation for objects and their motions in space is proposed. This approach involves lattice computer architectures and associated algorithms and is shown to be abstracted from the behavior of human beings mentally solving spatial /kinematic puzzles. There is also dis ..."
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Cited by 4 (4 self)
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An approach to analogical representation for objects and their motions in space is proposed. This approach involves lattice computer architectures and associated algorithms and is shown to be abstracted from the behavior of human beings mentally solving spatial /kinematic puzzles. There is also discussion of where in this approach the modeling of human cognition leaves off and the engineering begins. The possible relevance of the approach to a number of issues in Artificial Intelligence is discussed. These issues include efficiency of sentential versus analogical representations, common sense reasoning, update propagation, learning performance tasks, diagrammatic representations, spatial reasoning, metaphor, human categorization, and pattern recognition. Lastly there is a discussion of the somewhat related approach involving cellular automata applied to computational physics.
Machine induction without revolutionary changes in hypothesis size
 Information and Computation
, 1996
"... This paper provides a beginning study of the effects on inductive inference of paradigm shifts whose absence is approximately modeled by various formal approaches to forbidding large changes in the size of programs conjectured. One approach, called severely parsimonious, requires all the programs co ..."
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Cited by 3 (2 self)
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This paper provides a beginning study of the effects on inductive inference of paradigm shifts whose absence is approximately modeled by various formal approaches to forbidding large changes in the size of programs conjectured. One approach, called severely parsimonious, requires all the programs conjectured on the way to success to be nearly (i.e., within a recursive function of) minimal size. It is shown that this very conservative constraint allows learning infinite classes of functions, but not infinite r.e. classes of functions. Another approach, called nonrevolutionary, requires all conjectures to be nearly the same size as one another. This quite conservative constraint is, nonetheless, shown to permit learning some infinite r.e. classes of functions. Allowing up to one extra bounded size mind change towards a final program learned certainly doesn’t appear revolutionary. However, somewhat surprisingly for scientific (inductive) inference, it is shown that there are classes learnable with the nonrevolutionary constraint (respectively, with severe parsimony), up to (i + 1) mind changes, and no anomalies, which classes cannot be learned with no size constraint, an unbounded, finite number of anomalies in the final program, but with no more than i mind changes. Hence, in some cases, the possibility of one extra mind change is considerably more liberating than removal of very conservative size shift constraints. The proofs of these results are also combinatorially interesting. 1
Control Structures in Hypothesis Spaces: The Influence on Learning
"... . In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the effects 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 ..."
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Cited by 3 (1 self)
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. In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the effects 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. Then presented are the main theorems. Each of these characterizes the invariance of a learning class over hypothesis space V (and a little more about V ) as: V has suitable instances of all denotational control structures. 1 Introduction In any learnability setting, hypotheses are conjectured from some hypothesis space, for example, in [OSW86] from general purpose programming systems, in [ZL95, Wie78] from subrecursive systems, and in [Qui92] from very simple classes of classificatory decision trees. 3 Much is known theoretically about the restrictions on learning power resulting from restricted hypothesis spaces [ZL95]. In the present paper we begin to...