On the Necessity of U‐Shaped Learning

Abstract

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.

Unimodal Versus Bimodal EEG-fMRI Neurofeedback of a Motor Imagery Task

“…Interestingly, this decrease of performance on NF features was also observed in related works (Zotev et al, 2014) though both on EEG and fMRI features. This decrease of performance can also be explained as being part of the U-shaped learning curve (Carlucci and Case, 2013; Gaume et al, 2016): by trying new regulation strategies, the cognitive load of the subject suddenly increases and results in a temporary loss of performance. However, it is not yet known how this applies to bimodal NF.…”

A psychoengineering paradigm for the neurocognitive mechanisms of biofeedback and neurofeedback

“…(A neuroscience perspective regarding schemata formation and integration is presented in sections 4 and 4.2.) A common observation in developmental skill acquisition is the U-shaped learning curve, representing a three-step process: good performance, followed by bad performance, followed by good performance once again (Carlucci & Case, 2013). The adoption of novel processing strategies leads to an increased cognitive load and to temporary losses of processing efficiency (Pauls, Macha, & Petermann, 2013;Siegler, 2004).…”

“…The adoption of novel processing strategies leads to an increased cognitive load and to temporary losses of processing efficiency (Pauls, Macha, & Petermann, 2013;Siegler, 2004). Language acquisition models confirm that U-shaped behavior is unavoidable since human learners are limited by cognitive constraints (Carlucci & Case, 2013). If the cognitive load of a task is too high, performance will decline.…”

Language Learning From Positive Evidence, Reconsidered: A Simplicity‐Based Approach

“… Recovery from overgeneralization can be explored in a number of frameworks, for example, Carlucci and Case (). …”