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The Gatsby Unit PhD program pioneered the integration of theoretical neuroscience and machine learning in a single curriculum. Our distinctive methodology focuses on creating mathematical frameworks to analyze learning, perception, and behavior in both biological and artificial systems. Candidates must apply directly through the Gatsby Unit's online application system. As a premier institution for Computational and Theoretical Neuroscience and Machine Learning, we explore the fundamental mechanisms of cognition through algorithmic development. The program fosters exceptional collaboration among theorists and with other UCL research units, including the Sainsbury Wellcome Centre for Neural Circuits and Behaviour (SWC) and the Centre for Computational Statistics and Machine Learning (CSML). The academic experience is enriched by research presentations, discussion groups, guest lectures, and conference opportunities. All faculty members provide guidance to PhD candidates, extending beyond primary supervision.