We propose a new self-organizing hierarchical softmax formulation for neural-network-based language models over large vocabularies. Instead of using a predefined hierarchical structure, our approach is capable of learning word clusters with clear syntactical and semantic meaning during the language model training process. We provide experiments on standard benchmarks for language modeling and sentence compression tasks. We find that this approach is as fast as other efficient softmax approximations, while achieving comparable or even better performance relative to similar full softmax models.
Sampling based approaches approximate the normalization in the denominator of the softmax with some other loss that is cheap to compute. However, sampling based approaches are only useful at training time. During inference, the full softmax still needs to be computed to obtain a normalized probability. These approaches have been successfully applied to language modeling @cite_31 , machine translation @cite_26 , and computer vision @cite_15 .
@cite_31 @cite_26 @cite_15
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Training neural network language models over large vocabularies is still computationally very costly compared to count-based models such as Kneser-Ney. At the same time, neural language models are gaining popularity for many applications such as speech recognition and machine translation whose success depends on scalability. We present a systematic comparison of strategies to represent and train large vocabularies, including softmax, hierarchical softmax, target sampling, noise contrastive estimation and self normalization. We further extend self normalization to be a proper estimator of likelihood and introduce an efficient variant of softmax. We evaluate each method on three popular benchmarks, examining performance on rare words, the speed accuracy trade-off and complementarity to Kneser-Ney. Search algorithms incorporating some form of topic model have a long history in information retrieval. For example, cluster-based retrieval has been studied since the 60s and has recently produced good results in the language model framework. An approach to building topic models based on a formal generative model of documents, Latent Dirichlet Allocation (LDA), is heavily cited in the machine learning literature, but its feasibility and effectiveness in information retrieval is mostly unknown. In this paper, we study how to efficiently use LDA to improve ad-hoc retrieval. We propose an LDA-based document model within the language modeling framework, and evaluate it on several TREC collections. Gibbs sampling is employed to conduct approximate inference in LDA and the computational complexity is analyzed. We show that improvements over retrieval using cluster-based models can be obtained with reasonable efficiency. We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.