A Continuous Relaxation of Beam Search for End-to-end Training of Neural Sequence Models

Beam search is a desirable choice of test-time decoding algorithm for neural sequence models because it potentially avoids search errors made by simpler greedy methods. However, typical cross entropy training procedures for these models do not directly consider the behaviour of the final decoding method. As a result, for cross-entropy trained models, beam decoding can sometimes yield reduced test performance when compared with greedy decoding. In order to train models that can more effectively make use of beam search, we propose a new training procedure that focuses on the final loss metric (e.g. Hamming loss) evaluated on the output of beam search. While well-defined, this "direct loss" objective is itself discontinuous and thus difficult to optimize. Hence, in our approach, we form a sub-differentiable surrogate objective by introducing a novel continuous approximation of the beam search decoding procedure. In experiments, we show that optimizing this new training objective yields substantially better results on two sequence tasks (Named Entity Recognition and CCG Supertagging) when compared with both cross entropy trained greedy decoding and cross entropy trained beam decoding baselines.Comment: Updated for clarity and notational consistenc

Gradient-based Inference for Networks with Output Constraints

Practitioners apply neural networks to increasingly complex problems in natural language processing, such as syntactic parsing and semantic role labeling that have rich output structures. Many such structured-prediction problems require deterministic constraints on the output values; for example, in sequence-to-sequence syntactic parsing, we require that the sequential outputs encode valid trees. While hidden units might capture such properties, the network is not always able to learn such constraints from the training data alone, and practitioners must then resort to post-processing. In this paper, we present an inference method for neural networks that enforces deterministic constraints on outputs without performing rule-based post-processing or expensive discrete search. Instead, in the spirit of gradient-based training, we enforce constraints with gradient-based inference (GBI): for each input at test-time, we nudge continuous model weights until the network's unconstrained inference procedure generates an output that satisfies the constraints. We study the efficacy of GBI on three tasks with hard constraints: semantic role labeling, syntactic parsing, and sequence transduction. In each case, the algorithm not only satisfies constraints but improves accuracy, even when the underlying network is state-of-the-art.Comment: AAAI 201