Many of the leading approaches in language modeling introduce novel, complex and specialized architectures. We take existing state-of-the-art word level language models based on LSTMs and QRNNs and extend them to both larger vocabularies as well as character-level granularity. When properly tuned, LSTMs and QRNNs achieve state-of-the-art results on character-level (Penn Treebank, enwik8) and word-level (WikiText-103) datasets, respectively. Results are obtained in only 12 hours (WikiText-103) to 2 days (enwik8) using a single modern GPU.
Additional improvements in the model can be obtained through dynamic evaluation @cite_17 and mixture-of-softmaxes @cite_0 but since our goal is to evaluate the underlying model, we employ no such strategies in addition.
@cite_0 @cite_17
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We present methodology for using dynamic evaluation to improve neural sequence models. Models are adapted to recent history via a gradient descent based mechanism, causing them to assign higher probabilities to re-occurring sequential patterns. Dynamic evaluation outperforms existing adaptation approaches in our comparisons. Dynamic evaluation improves the state-of-the-art word-level perplexities on the Penn Treebank and WikiText-2 datasets to 51.1 and 44.3 respectively, and the state-of-the-art character-level cross-entropies on the text8 and Hutter Prize datasets to 1.19 bits char and 1.08 bits char respectively. In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, ( (x_0, ,x_p,y) ), subject to coupled linear equality constraints. Our ADMM updates each of the primal variables (x_0, ,x_p,y ), followed by updating the dual variable. We separate the variable y from (x_i )’s as it has a special role in our analysis. The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, ( _q ) quasi-norm, Schatten-q quasi-norm ( (0<q<1 )), minimax concave penalty (MCP), and smoothly clipped absolute deviation penalty. It also allows nonconvex constraints such as compact manifolds (e.g., spherical, Stiefel, and Grassman manifolds) and linear complementarity constraints. Also, the (x_0 )-block can be almost any lower semi-continuous function. By applying our analysis, we show, for the first time, that several ADMM algorithms applied to solve nonconvex models in statistical learning, optimization on manifold, and matrix decomposition are guaranteed to converge. Our results provide sufficient conditions for ADMM to converge on (convex or nonconvex) monotropic programs with three or more blocks, as they are special cases of our model. ADMM has been regarded as a variant to the augmented Lagrangian method (ALM). We present a simple example to illustrate how ADMM converges but ALM diverges with bounded penalty parameter ( ). Indicated by this example and other analysis in this paper, ADMM might be a better choice than ALM for some nonconvex nonsmooth problems, because ADMM is not only easier to implement, it is also more likely to converge for the concerned scenarios. In this letter, we propose a conceptually simple and intuitive learning objective function, i.e., additive margin softmax, for face verification. In general, face verification tasks can be viewed as metric learning problems, even though lots of face verification models are trained in classification schemes. It is possible when a large-margin strategy is introduced into the classification model to encourage intraclass variance minimization. As one alternative, angular softmax has been proposed to incorporate the margin. In this letter, we introduce another kind of margin to the softmax loss function, which is more intuitive and interpretable. Experiments on LFW and MegaFace show that our algorithm performs better when the evaluation criteria are designed for very low false alarm rate. Iterative compiler optimization has been shown to outperform static approaches. This, however, is at the cost of large numbers of evaluations of the program. This paper develops a new methodology to reduce this number and hence speed up iterative optimization. It uses predictive modelling from the domain of machine learning to automatically focus search on those areas likely to give greatest performance. This approach is independent of search algorithm, search space or compiler infrastructure and scales gracefully with the compiler optimization space size. Off-line, a training set of programs is iteratively evaluated and the shape of the spaces and program features are modelled. These models are learnt and used to focus the iterative optimization of a new program. We evaluate two learnt models, an independent and Markov model, and evaluate their worth on two embedded platforms, the Texas Instrument C67I3 and the AMD Au1500. We show that such learnt models can speed up iterative search on large spaces by an order of magnitude. This translates into an average speedup of 1.22 on the TI C6713 and 1.27 on the AMD Au1500 in just 2 evaluations.