Parallelism increases iterative learning power

Case, John; Moelius, Samuel E.

doi:10.1016/j.tcs.2009.01.015

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…The results of this query reveal 1. the importance of order in LDP and the relative unimportance of distance, 2. that a debate about the nature of locality in phonology is also a debate about computational complexity in phonology, and 3. that long-distance dissimilation fundamentally differs from long-distance assimilation with respect to the kinds of phonotactic patterns they derive. 1 This resembles what formal learning theorists call parallel learning (Case and Moelius 2007). 2 Within OT, there are particular learning proposals that fail to learn the factorial typology and in this way constrain the predicted possible languages (Tesar andSmolensky 2000, Boersma 2003).…”

Section: Outlinementioning

confidence: 88%

Learning Long-Distance Phonotactics

2010

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This article shows that specific properties of long-distance phonotactic patterns derived from consonantal harmony patterns (Hansson 2001, Rose andWalker 2004) follow from a learner that generalizes only on the basis of the order of sounds, not the distance between them. The proposed learner is simple, efficient, and provably correct, and does not require an a priori notion of tier or projection (contra the model in Hayes and Wilson 2008); nor does it rely on the additional structure provided by Optimality Theory grammars (Prince and Smolensky 1993Smolensky , 2004 or grammars in the principles-and-parameters framework (Chomsky 1981, Dresher and Kaye 1990, Gibson and Wexler 1994. Not only does the noncounting nature of nonlocal dependencies automatically follow from the way the learner generalizes, it also explains the absence of blocking patterns from the typology. Finally, the learner lends support to the idea that long-distance phonotactic patterns are phenomenologically distinct from spreading patterns, contra the hypothesis of Strict Locality (Gafos 1999, et seq.).

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Section: Outlinementioning

confidence: 88%

Learning Long-Distance Phonotactics

2010

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“…rRInf Exs " rInf Exs and rRTxtExs " rTxtExs. On the other hand [CM09] showed rRItTxtExs Ĺ rItTxtExs.…”

Section: Iterative Learning From Informantmentioning

confidence: 94%

“…For understanding iterative learners we analyze what normal forms can be assumed about such learners in Section 2.2. First we show that, analogously to the case of learning from text (as analyzed in [CM09]), we cannot assume learners to be total (i.e. always giving an output).…”

Section: Introductionmentioning

confidence: 98%

Learning Half-Spaces and other Concept Classes in the Limit with Iterative Learners

Khazraei,

Kötzing,

Seidel

2020

Preprint

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In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important additional requirements and their impact on iterative learners.In this paper, our results are twofold. First, we analyze the relative learning power of various settings of iterative learning, including learning from text and from informant, as well as various further restrictions, for example we show that strongly non-U-shaped learning is restrictive for iterative learning from informant.Second, we investigate the learnability of the concept class of half-spaces and provide a constructive iterative algorithm to learn the set of half-spaces from informant.

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“…An iterative learner computes its guesses about the target language based on its own most recent conjecture and on the current data item only . Iterative Learning is a well‐studied model (Becerra‐Bonache, Case, Jain, & Stephan, ; Case & Moelius, ; Case, Jain, Lange, & Zeugmann, ; Jain & Kinber, ; Jain, Lange, & Zilles, ; Lange & Grieser, ). Most interestingly, in the perspective of the present study, Iterative Learning is the base case of a hierarchy of stronger and stronger memory‐limited models.…”

Section: U‐shaped Learning With Memory Limitationsmentioning

confidence: 99%

On the Necessity of U‐Shaped Learning

Carlucci

Case

2013

Topics in Cognitive Science

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A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research.

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Parallelism increases iterative learning power

Cited by 6 publications

References 15 publications

Learning Long-Distance Phonotactics

Learning Long-Distance Phonotactics

Learning Half-Spaces and other Concept Classes in the Limit with Iterative Learners

On the Necessity of U‐Shaped Learning

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