Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as "self-normalization", which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking. We prove upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributions that self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions.

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as "self-normalization", which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking. We prove upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributions that self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions.

Globally normalized neural sequence models are considered superior to their locally normalized equivalents because they may ameliorate the effects of label bias. However, when considering high-capacity neural parametrizations that condition on the whole input sequence, both model classes are theoretically equivalent in terms of the distributions they are capable of representing. Thus, the practical advantage of global normalization in the context of modern neural methods remains unclear. In this paper, we attempt to shed light on this problem through an empirical study. We extend an approach for search-aware training via a continuous relaxation of beam search (Goyal et al., 2017b) in order to enable training of globally normalized recurrent sequence models through simple backpropagation. We then use this technique to conduct an empirical study of the interaction between global normalization, high-capacity encoders, and search-aware optimization. We observe that in the context of inexact search, globally normalized neural models are still more effective than their locally normalized counterparts. Further, since our training approach is sensitive to warm-starting with pre-trained models, we also propose a novel initialization strategy based on self-normalization for pre-training globally normalized models. We perform analysis of our approach on two tasks: CCG supertagging and Machine Translation, and demonstrate the importance of global normalization under different conditions while using search-aware training.

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as ``self-normalization'', which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking.We prove upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributionsthat self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions on both real and synthetic datasets.

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as "self-normalization", which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking. We prove generalization bounds on the estimated variance of normalizers and upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributions that self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions.