# Achievement

## Mathematical theory of experience-driven conceptual development

## Research Achievements

### Mathematical theory of experience-driven conceptual development

Trainee Saxe, together with IGERT Faculty Ganguli and McClelland developed a mathematical theory of experience-driven conceptual development, capturing a wide range of findings, including the finding that infants generally acquire broad categorical distinctions (i.e., plant/animal) before finer-scale distinctions (i.e., dog/cat), often exhibiting rapid, or stage-like transitions. They developed a mathematical theory of hierarchical category learning through an analysis of the learning dynamics of multilayer networks exposed to hierarchically structured data. The theory yields new exact solutions to the nonlinear dynamics of error correcting learning in deep, three layer networks. These solutions reveal that networks learn input-output covariation structure on a time scale that is inversely proportional to its statistical strength.

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