Just because some purely recurrent models suffer from being hard to optimize and inefficient on today's hardware, they are not necessarily bad models of language. We demonstrate this by the extent to which these models can still be improved by a combination of a slightly better recurrent cell, architecture, objective, as well as optimization. In the process, we establish a new state of the art for language modelling on small datasets and on Enwik8 with dynamic evaluation.

Tail Averaging improves on Polyak averaging's non-asymptotic behaviour by excluding a number of leading iterates of stochastic optimization from its calculations. In practice, with a finite number of optimization steps and a learning rate that cannot be annealed to zero, Tail Averaging can get much closer to a local minimum point of the training loss than either the individual iterates or the Polyak average. However, the number of leading iterates to ignore is an important hyperparameter, and starting averaging too early or too late leads to inefficient use of resources or suboptimal solutions. Our work focusses on improving generalization, which makes setting this hyperparameter even more difficult, especially in the presence of other hyperparameters and overfitting. Furthermore, before averaging starts, the loss is only weakly informative of the final performance, which makes early stopping unreliable. To alleviate these problems, we propose an anytime variant of Tail Averaging intended for improving generalization not pure optimization, that has no hyperparameters and approximates the optimal tail at all optimization steps. Our algorithm is based on two running averages with adaptive lengths bounded in terms of the optimal tail length, one of which achieves approximate optimality with some regularity. Requiring only the additional storage for two sets of weights and periodic evaluation of the loss, the proposed Two-Tailed Averaging algorithm is a practical and widely applicable method for improving generalization.

A common failure mode of density models trained as variational autoencoders is to model the data without relying on their latent variables, rendering these variables useless. Two contributing factors, the underspecification of the model and the looseness of the variational lower bound, have been studied separately in the literature. We weave these two strands of research together, specifically the tighter bounds of Monte-Carlo objectives and constraints on the mutual information between the observable and the latent variables. Estimating the mutual information as the average Kullback-Leibler divergence between the easily available variational posterior $q(z|x)$ and the prior does not work with Monte-Carlo objectives because $q(z|x)$ is no longer a direct approximation to the model's true posterior $p(z|x)$. Hence, we construct estimators of the Kullback-Leibler divergence of the true posterior from the prior by recycling samples used in the objective, with which we train models of continuous and discrete latents at much improved rate-distortion and no posterior collapse. While alleviated, the tradeoff between modelling the data and using the latents still remains, and we urge for evaluating inference methods across a range of mutual information values.

Recurrent neural network grammars (RNNG) are generative models of language which jointly model syntax and surface structure by incrementally generating a syntax tree and sentence in a top-down, left-to-right order. Supervised RNNGs achieve strong language modeling and parsing performance, but require an annotated corpus of parse trees. In this work, we experiment with unsupervised learning of RNNGs. Since directly marginalizing over the space of latent trees is intractable, we instead apply amortized variational inference. To maximize the evidence lower bound, we develop an inference network parameterized as a neural CRF constituency parser. On language modeling, unsupervised RNNGs perform as well their supervised counterparts on benchmarks in English and Chinese. On constituency grammar induction, they are competitive with recent neural language models that induce tree structures from words through attention mechanisms.

We show that dropout training is best understood as performing MAP estimation concurrently for a family of conditional models whose objectives are themselves lower bounded by the original dropout objective. This discovery allows us to pick any model from this family after training, which leads to a substantial improvement on regularisation-heavy language modelling. The family includes models that compute a power mean over the sampled dropout masks, and their less stochastic subvariants with tighter and higher lower bounds than the fully stochastic dropout objective. We argue that since the deterministic subvariant's bound is equal to its objective, and the highest amongst these models, the predominant view of it as a good approximation to MC averaging is misleading. Rather, deterministic dropout is the best available approximation to the true objective.