This paper explores the integration of symbolic logic knowledge into deep neural networks for learning from noisy crowd labels. We introduce Logic-guided Learning from Noisy Crowd Labels (Logic-LNCL), an EM-alike iterative logic knowledge distillation framework that learns from both noisy labeled data and logic rules of interest. Unlike traditional EM methods, our framework contains a ``pseudo-E-step'' that distills from the logic rules a new type of learning target, which is then used in the ``pseudo-M-step'' for training the classifier. Extensive evaluations on two real-world datasets for text sentiment classification and named entity recognition demonstrate that the proposed framework improves the state-of-the-art and provides a new solution to learning from noisy crowd labels.
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