This paper explores the simplicity of learned neural networks under various settings: learned on real vs random data, varying size/architecture and using large minibatch size vs small minibatch size. The notion of simplicity used here is that of learnability i.e., how accurately can the prediction function of a neural network be learned from labeled samples from it. While learnability is differ...

Bohannon and Stanowicz (1988) have claimed that contrary to popular belief, children do receive negative evidence about the ungrammaticality of their utterances in the form of recasts, expansions, and repetitions. Bohannon and Stanowicz argue that given such negative evidence, learnability theory shows that natural languages can be learned and that there is no need to postulate innate knowledge...

Pattern languages seem to suit case-based reasoning particularly well. Therefore, the problem of inductively learning pattern languages is paraphrased in a case-based manner. A careful investigation requires a formal semantics for case bases together with similarity measures in terms of formal languages. Two basic semantics are introduced and investigated. It turns out that representabil-ity pr...

The present study addresses whether linguistic experience affects the learnability of non-speech categories and in turn whether learning non-speech categories affects speech perception. Speakers of English and Spanish, languages that have different mappings between voice-onset-time (VOT) and their voicing categories, were trained to categorize a series of analogous non-speech (tone-onset-time) ...

This paper explores the simplicity of learned neural networks under various settings: learned on real vs random data, varying size/architecture and using large minibatch size vs small minibatch size. The notion of simplicity used here is that of learnability i.e., how accurately can the prediction function of a neural network be learned from labeled samples from it. While learnability is differ...

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded-lear...