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The goal of our lab is to find elegant principles for designing effective programming languages and systems for machine learning. Our research projects address concerns from the programming-language side as well as from the machine-learning side, and they span theory and practice. Some of our projects aim at developing efficient inference or parameter-learning algorithms for models written in these languages. Other projects aim at finding clean mathematical bases for these languages, and they involve generalizing the foundations of probability theory, differential geometry and other branches of mathematics, so that the new foundations can account for advanced features of those languages. Yet other projects aim at\ndeveloping program analyses or type systems for these languages that track smoothness properties of programs, and building efficient compilers that can fully exploit modern advanced hardware devices such as GPU and TPU.