# Achievement

## Mathematical theory provides unified explanation

### Project

IGERT: Unifying the Science of Language

### University

Johns Hopkins University

(Baltimore, MD)

### PI

## Research Achievements

### Mathematical theory provides unified explanation

Trainee Manuel Vindiola, working with core faculty Profs. McCloskey and Smolensky, has developed a simple mathematical theory that provides a unified explanation for a challenging ensemble of phenomena arising from the cognitive mechanisms for sequencing items: storing sequences and spelling them out one item at a time. Clues to these mechanisms come from 'perseveration' errors in, e.g., spelling a list of words: substituting, for a letter in one word, a letter from a previous word. Vindiola’s theory deploys two simple ideas: the similarity of items and of positions is encoded in the inner product of their neural activation vectors; and the binding of items to their positions is encoded by the outer product of those vectors. This mechanism provides a unified explanation of why perseverations are more likely to preserve: which half of the word the letter falls in; the letter's position, measured from either word edge; and the category of the letter, consonant or vowel.

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