Optimizing Differentiable Relaxations of Coreference Evaluation Metrics

Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017), pages 390–399, Vancouver, Canada, August 3 - August 4, 2017. c⃝2017 Association for Computational Linguistics Optimizing Differentiable Relaxations of Coreference Evaluation Metrics Phong Le1 Ivan Titov1,2 1ILLC, University of Amsterdam 2ILCC, School of Informatics, University of Edinburgh p.le@uva.nl ititov@inf.ed.ac.uk Abstract Coreference evaluation metrics are hard to optimize directly as they are non- differentiable functions, not easily decom- posable into elementary decisions. Con- sequently, most approaches optimize ob- jectives only indirectly related to the end goal, resulting in suboptimal performance. Instead, we propose a differentiable re- laxation that lends itself to gradient-based optimisation, thus bypassing the need for reinforcement learning or heuristic mod- ification of cross-entropy. We show that by modifying the training objective of a competitive neural coreference system, we obtain a substantial gain in performance. This suggests that our approach can be re- garded as a viable alternative to using rein- forcement learning or more computation- ally expensive imitation learning. 1 Introduction Coreference resolution is the task of identifying all mentions which refer to the same entity in a docu- ment. It has been shown beneficial in many natural language processing (NLP) applications, includ- ing question answering (Hermann et al., 2015) and information extraction (Kehler, 1997), and often regarded as a prerequisite to any text understand- ing task. Coreference resolution can be regarded as a clustering problem: each cluster corresponds to a single entity and consists of all its mentions in a given text. Consequently, it is natural to eval- uate predicted clusters by comparing them with the ones annotated by human experts, and this is exactly what the standard metrics (e.g., MUC, B3, CEAF) do. In contrast, most state-of-the- art systems are optimized to make individual co- reference decisions, and such losses are only indi- rectly related to the metrics. One way to deal with this challenge is to op- timize directly the non-differentiable metrics us- ing reinforcement learning (RL), for example, re- lying on the REINFORCE policy gradient algo- rithm (Williams, 1992). However, this approach has not been very successful, which, as suggested by Clark and Manning (2016a), is possibly due to the discrepancy between sampling decisions at training time and choosing the highest rank- ing ones at test time. A more successful alter- native is using a ‘roll-out’ stage to associate cost with possible decisions, as in Clark and Manning (2016a), but it is computationally expensive. Imi- tation learning (Ma et al., 2014b; Clark and Man- ning, 2015), though also exploiting metrics, re- quires access to an expert policy, with exact poli- cies not directly computable for the metrics of in- terest. In this work, we aim at combining the best of both worlds by proposing a simple method that can turn popular coreference evaluation metrics into differentiable functions of model parameters. As we show, this function can be computed re- cursively using scores of individual local deci- sions, resulting in a simple and efficient estima- tion procedure. The key idea is to replace …

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