What is U-shaped learning

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U-shaped-learning concerns the development of distinguishing the application of the inflectional past-tense morpheme of -ed to regular and irregular words – those which require an -ed (e. g. ‘waste’ –> ‘wasted’) and those which are expressed with a completely different word (e. g. ‘run’ –> ‘ran’), respectively. It is the learning pattern of initial overregularisation of past-tense plural application, whereby children treat irregular words as regular, representing the culmination of an increase in irregular word vocabulary, knowledge of the regular rules, and an absence of the knowledge of its exceptions.

It is learning these exceptions and subsequent correct past-tense application to lexical words and subsequent new ones that represents the sudden increase and then levelling out, completing the U-shape pattern. However, to truly define U-shaped-learning, a model must efficiently characterise its underlying mechanisms in a way that corresponds as accurately as possible with the pattern unique errors that the literature has established.

The dual-route model (Pinker 1991; Pinker & Prince 1988; Prasada & Pinker 1993) argues that U-shaped-learning in correct past-tense acquisition is governed by one route which is rule-governed and enables the forming of the past-tense of regular verbs, while another involves a memory store of irregular past-tense forms. U-shaped-learning occurs when the irregular route is insufficiently strong to prevent the rule-governed regular route from overriding it (Pinker 1985). Evidence has been found for the model (e. g. Clahsen et al. , 1992; Pinker 1997; Pinker and Prince, 1994), with the most concrete being Jaeger et al. 1996) who found that regular and irregular inflections are processed by different brain areas, which has also been supported by Ullman et al (1997) and Gopnik & Crago (1991). Prasada, Pinker and Snyder (1990) found frequency effects for irregular English past-tense forms, but no frequency effects for regular forms. Finally, Marcus et al (1992), in analysing 83 children’s spontaneous speech for irregularities, found that they typically exhibited a pattern that generally fit the documented pattern of U-shaped-learning but also found that there was no correlation between the vocabulary of the children and the onset of overregularisation.

A formulated blocking hypothesis argued that the results demonstrates that overregularisation of irregular verbs is relatively rare in children’s speech, which is contrary to connectionist predictions, and is ultimately compatible with the mechanics of the dual-route model. Rumelhart & McClelland’s (1986) (R&M) connectionist model assumes that U-shaped-learning demonstrates a difficulty in relating the verb stem to it’s past-tense form. For irregular verbs, the network activates the verb root in the output units but the -ed form is inactive because the network would have only seen regular verbs.

Accordingly, the -ed connection is initially strong and the network has an initial tendency to activate the -ed connection. The network identifies this difference and the network’s weights are adjusted to turn the suffix units off. Thus, when the network re-experiences a regular verb, the prior experience of the no-change word will have forced the network to express the correct verb unit. The model was tested on 420 regular and irregular verbs. The first training epochs exhibited both verb types as dramatically increasing but after ten epochs, a decrease in accurate application occurred, despite earlier demonstrating correct applications. Read The Boarding House questions and answers

Further training removed these errors in the way that the original network conception had predicted and after several hundred epochs, almost all verbs had been mastered. This finding largely represented the U-shaped-learning pattern in children, thereby supporting the model’s assertion that a singular-function network can recreate U-shaped-learning. However, as Pinker & Prince (1988) argued, the network could not deal with the representation of forms where syllables are repeated, whereby its configuration allows it to reverse transformations (e. g. it –> tih), which is something not found in any language. As Plunkett (1999) found, the model also produced past-tense errors which are not exhibited by children (e. g. ‘membled’ being the past-tense of ‘mail’). Plunkett & Marchman (1991) (P&M) modelled how hidden units can reproduce U-shaped-learning but with keeping the input at about the same level real children experience at the typical onset age, which the R&M model failed to account for. No error-free periods in the network’s initial epochs of learning resembled the established pattern in the literature.

The network also corresponded to a period of Marcus et al’s (1992) account that showed micro-U-shaped-learning (small periods of overregularisation prior to the main onset) over a protracted period of development, as did finding that the network made irregularisations of regular and irregular verbs, which was also consistent with the empirically established pattern. However, a discovered ‘leaking’ of words from irregular into regular classes has never been documented.

Also, the absence of an initial error-free period counters Marcus et al’s (1992) analysis which found there to be this period in almost all of the analysed children. Therefore, the model “fails to account for a part of inflectional morphological development that has been used to argue that language acquisition is a process of learning a system of rules, as in, the transition from a period of entirely correct behaviour to a subsequent period where errors are observed” (Plunkett 1998).

Plunkett & Marchman’s (1993) revised network was initially trained on a small verb set until it reached an optimum level of performance. Then, the set was expanded by one verb at a time, whereby as each one was added, there was an 80% chance that it would be regular. These verbs were added at regular intervals, regardless of whether the network had correctly learned the previous one, and this pattern followed until the network’s vocabulary reached 500 verbs. A pattern of overregularisation errors resembled the same pattern observed in Marcus et al (1992).

Similarly, the low rate of errors produced by the network resembled a typical pattern of past-tense acquisition in Marcus et al (1992), whereby it made less than 10% overregularisation, as did the finding of micro-U-shaped patterns prior to the main decrease. Also, consistent with U-shaped-learning literature, the network experienced an initial period where it does not produce any overregularisation on irregular verbs until the vocabulary size has significantly expanded, in this case, until the network had been fed about 120 verbs into it’s vocabulary.

As the vocabulary expanded from 50 verbs to 120 verbs, the probability of adding a suffix to new verbs increased from 2% to 70%, indicating that the network has constructed a generalisation of the way in how past-tense forms are generated from stems in the training set. The neurological evidence supporting the dual-route model has been convincingly demonstrated to be explained within a single-route model (Seidenberg and Hoeffner 1998), as has Prasada, Pinker and Snyder (1990)’s findings by Daugherty and Seidenberg (1992, 1994).

To be a strong model, it would have to explain U-shaped-learning in the context of children’s natural uninhibited speech because the prior research which has established the U-shaped-learning phenomenon is largely based on words chosen by the experimenter in a controlled environment. This prevents them from talking in a way that reflects their own true linguistic abilities, thereby reducing the credibility of the phenomenon. Though Marcus et al (1992) satisfies this criteria, its “failure to find a relationship between the size of verb vocabulary and the onset of overregularisation errors appear to be an artefact of data sampling i. . they did not analyse data from children with very small vocabularies” (Plunkett 1996) who undergo the U-shaped-learning pattern. Marcus et al (1992) so largely corresponds with the documented U-shaped pattern that it’s discovery of micro-U-shape patterns acts as a refinement of the established pattern, rather than a rejection, and therefore signifies the importance that future research uses spontaneous speech rather than designating a subjective set of words.

The material used in prior research still closely resembles the state of a child’s vocabulary and so it maintains the validity of the establishing studies, and therefore also the validity of the models that correspond with it. Ultimately, those that correspond with the refined pattern that Marcus et al (1992; 1995) established will be more efficient than those that correspond with the unrefined pattern will because it is closer in keeping with spontaneous and unrestricted speech.

Marcus et al’s (1992) flaw of an absence of a correlation is a separate issue that does not affect the pattern it has found and, therefore, the essence of what it necessitates in future research. All of the dual-route model’s pillars of support are undermined and it does not fulfil any of the criteria for an efficient model. The connectionist R&M model is minimally efficient in that it produces the familiar U-shaped-learning pattern.

However, it lacks the exhibition of micro-U-shaped periods, which is possibly the result of its other flaw of not introducing vocabulary into the network at an approximate rate that children develop their own, as well as processing undocumented errors. The first P&M network eliminates the undocumented errors made by the R&M model and exhibits the micro-U-shaped errors evident in spontaneous speech errors (Marcus et al 1992), but it makes other undocumented errors and still fails to introduce the vocabulary at a realistic rate. The latest P&M network is the most efficient model of U-shaped-learning mechanisms.

However, though it introduced vocabulary at a typical rate for a child, accounted for U-shaped-learning errors as well as not making other undocumented ones, and exhibited the pattern consistent with spontaneous speech, the network is still a reflection, like its preceding models, of the experimental subjective vocabulary that merely corresponds with the spontaneous speech pattern observed by Marcus et al (1992). Being as the P&M nevertheless represents the most accurate correspondence with U-shaped-learning, the underlying mechanism could be conceived as a multilayered network.

The hidden unit layer ensures that the -ed suffix connection remains completely inactive in processing irregular verbs once the differences that input stem-word nodes and output equivalent past-tense nodes have established, via repeated backpropogated experience, the correct weights that they are adjusted to, to turn the suffix units off in response to an irregular verb. Essentially, the hidden units ensure that no “residual error remains even after training” (Elman et al 2001) of the input and output units.

Ultimately however, to truly understand the underlying mechanism of the U-shaped-learning pattern, a model such as P&M’s needs to be tested in conjunction with transcribed recordings of children’s spontaneous speech rather than a subjectively devised vocabulary, the impact of which Marcus et al’s (1992) significant findings clearly highlight. Only then can the best current definition that P&M contributes to inflectional morphological development research be realistically tested and the nature of U-shaped-learning be comprehensively explained.

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