Despite their wide applicability, deep learning systems often fail to exactly capture simple “known” features of many problem domains, such as those governed by physical laws or those that incorporate decision-making procedures. In this talk, I will present methods for these types of structural constraints — such as those associated with decision making, optimization problems, or physical simulation — directly into the predictions of a deep network. Our tool for achieving this will be the use of so-called “implicit layers” in deep models: layers that are defined implicitly in terms of conditions we would like them to satisfy, rather than via explicit computation graphs. l discuss how we can use these layers to embed (exact) physical constraints, robust control criteria, and task-based objectives, all within modern deep learning models. I will also highlight several applications of this work in reinforcement learning, control, energy systems, and other settings, and discuss generalizations and directions for f
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