Deep Reasoning Networks for Unsupervised Pattern De-mixing with Constraint Reasoning

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Di Chen, Yiwei Bai, Wenting Zhao, Sebastian Ament, John Gregoire, Carla Gomes


<p>We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with constraint reasoning for solving pattern de-mixing problems, typically in an unsupervised or very-weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining constraint reasoning with stochastic-gradient-based neural network optimization. Our motivating task is from materials discovery and concerns inferring crystal structures of materials from X-ray diffraction data (Crystal-Structure-Phase-Mapping). Given the complexity of its underlying scientific domain, we start by introducing DRNets on an analogous but much simpler task: de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku). On Multi-MNIST-Sudoku, DRNets almost perfectly recovered the mixed Sudokus' digits, with 100\% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. On Crystal-Structure-Phase-Mapping, DRNets significantly outperform the state of the art and experts' capabilities, recovering more precise and physically meaningful crystal structures.</p>