Abstract
U-shaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether U-shaped learning behaviour may be necessary in the abstract mathematical setting of inductive inference, that is, in the computational learning theory following the framework of Gold. All notions considered are learning from text, that is, from positive data. Previous work showed that U-shaped learning behaviour is necessary for behaviourally correct learning but not for syntactically convergent, learning in the limit (= explanatory learning). The present paper establishes the necessity for the whole hierarchy of classes of vacillatory learning where a behaviourally correct learner has to satisfy the additional constraint that it vacillates in the limit between at most k grammars, where k ≥ 1. Non U-shaped vacillatory learning is shown to be restrictive: Every non U-shaped vacillatorily learnable class is already learnable in the limit. Furthermore, if vacillatory learning with the parameter k=2 is possible then non U-shaped behaviourally correct learning is also possible. But for k=3, surprisingly, there is a class witnessing that this implication fails.
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References
Baliga, G., Case, J., Merkle, W., Stephan, F., Wiehagen, R.: When unlearning helps Manuscript (2005), http://www.cis.udel.edu/~case/papers/decisive.ps , Preliminary version of the paper appeared at ICALP 2000. LNCS, vol. 1853, pp. 844–855. Springer, Heidelberg (2000)
Bārzdiņš, J.: Two theorems on the limiting synthesis of functions. In: Theory of Algorithms and Programs, vol. 1, pp. 82–88. Latvian State University (1974) (in Russian)
Blum, L., Blum, M.: Towards a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)
Blum, M.: A machine independent theory of the complexity of the recursive functions. Journal of the Association for Computing Machinery 14, 322–336 (1967)
Bower, T.G.R.: Concepts of development. In: Proceedings of the 21st International Congress of Psychology, pp. 79–97. Presses Universitaires de France (1978)
Bowerman, M.: Starting to talk worse: Clues to language acquisition from children’s late speech errors. In: Strauss, S., Stavy, R. (eds.) U-Shaped Behavioral Growth. Academic Press, New York (1982)
Carey, S.: Face perception: Anomalies of development. In: Strauss, S., Stavy, R. (eds.) U-Shaped Behavioral Growth. Developmental Psychology Series, pp. 169–190. Academic Press, London (1982)
Case, J.: The power of vacillation in language learning. SIAM Journal on Computing 28(6), 1941–1969 (1999)
Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982)
Case, J., Smith, C.H.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)
Fulk, M.: Prudence and other conditions on formal language learning. Information and Computation 85, 1–11 (1990)
Fulk, M., Jain, S., Osherson, D.: Open problems in “Systems That Learn”. Journal of Computer and System Sciences 49, 589–604 (1994)
Mark Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)
Kirsh, D.: PDP learnability and innate knowledge of language. In: Davis, S. (ed.) Connectionism: Theory and Practice, pp. 297–322. Oxford University Press, Oxford (1992)
Marcus, G., Pinker, S., Ullman, M., Hollander, M., Rosen, T.J., Xu, F.: Overregularization in Language Acquisition. Monographs of the Society for Research in Child Development, vol. 57(4), University of Chicago Press (1992); Includes commentary by Harold Clahsen
Odifreddi, P.: Classical Recursion Theory. North Holland, Amsterdam (1989)
Osherson, D., Weinstein, S.: Criteria of language learning. Information and Control 52, 123–138 (1982)
Pinker, S.: Formal models of language learning. Cognition 7, 217–283 (1979)
Plunkett, K., Marchman, V.: U-shaped learning and frequency effects in a multi-layered perceptron: implications for child language acquisition. Cognition 38(1), 43–102 (1991)
Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); Reprinted, MIT Press, 1987
Smith, C.H.: The power of pluralism for automatic program synthesis. Journal of the Association of Computing Machinery 29, 1144–1165 (1982)
Strauss, S., Stavy, R. (eds.): U-Shaped Behavioral Growth. Developmental Psychology Series. Academic Press, London (1982)
Taatgen, N.A., Anderson, J.R.: Why do children learn to say broke? A model of learning the past tense without feedback. Cognition 86(2), 123–155 (2002)
Wexler, K.: On extensional learnability. Cognition 11, 89–95 (1982)
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Carlucci, L., Case, J., Jain, S., Stephan, F. (2005). Non U-Shaped Vacillatory and Team Learning. In: Jain, S., Simon, H.U., Tomita, E. (eds) Algorithmic Learning Theory. ALT 2005. Lecture Notes in Computer Science(), vol 3734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564089_20
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DOI: https://doi.org/10.1007/11564089_20
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