Minimum-Risk Training of Approximate CRF-Based NLP Systems

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Structured Attention Networks (2017, methodology): “The differentiability of inference algorithms over graphical models has previously been noted by various researchers (Li & Eisner, 2009; Domke, 2011; Stoyanov et al., 2011; Stoyanov & Eisner, 2012; Gormley et al., 2015), primarily outside the area of deep learning.”
Learning Graphical Model Parameters with Approximate Marginal Inference (2013, methodology): “Thus, the loss gradient is efﬁciently computable, at least in principle, by reverse-mode automatic differentiation (au-todiff), an approach explored by Stovanov et al. [36], [52].”
Approximation-Aware Dependency Parsing by Belief Propagation (2015, methodology): “Another natural extension of this work is to explore other types of factors: here we considered only exponential-family potential functions (commonly used in CRFs), but any differentiable function would be appropriate, such as a neural network.”