Language models (LMs) are statistical models that calculate probabilities over sequences of words or other discrete symbols. Currently two major paradigms for language modeling exist: count-based n-gram models, which have advantages of scalability and test-time speed, and neural LMs, which often achieve superior modeling performance. We demonstrate how both varieties of models can be unified in a single modeling framework that defines a set of probability distributions over the vocabulary of words, and then dynamically calculates mixture weights over these distributions. This formulation allows us to create novel hybrid models that combine the desirable features of count-based and neural LMs, and experiments demonstrate the advantages of these approaches.
A number of alternative methods focus on interpolating LMs of multiple varieties such as in-domain and out-of-domain LMs @cite_32 @cite_12 @cite_17 . Perhaps most relevant is 's work on learning to interpolate multiple LMs using log-linear models. This differs from our work in that it learns functions to estimate the fallback probabilities @math in Eq. instead of @math , and does not cover interpolation of @math -gram components, non-linearities, or the connection with neural network LMs. Also conceptually similar is work on adaptation of @math -gram LMs, which start with @math -gram probabilities @cite_26 @cite_18 @cite_13 @cite_5 and adapt them based on the distribution of the current document, albeit in a linear model. There has also been work incorporating binary @math -gram features into neural language models, which allows for more direct learning of @math -gram weights @cite_33 , but does not afford many of the advantages of the proposed model such as the incorporation of count-based probability estimates. Finally, recent works have compared @math -gram and neural models, finding that neural models often perform better in perplexity, but @math -grams have their own advantages such as effectiveness in extrinsic tasks @cite_35 and better modeling of rare words @cite_15 .
@cite_35 @cite_18 @cite_26 @cite_33 @cite_32 @cite_5 @cite_15 @cite_13 @cite_12 @cite_17
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In this paper, we investigate and compare three different possibilities to convert recurrent neural network language models (RNNLMs) into backoff language models (BNLM). While RNNLMs often outperform traditional n-gram approaches in the task of language modeling, their computational demands make them unsuitable for an efficient usage during decoding in an LVCSR system. It is, therefore, of interest to convert them into BNLMs in order to integrate their information into the decoding process. This paper compares three different approaches: a text based conversion, a probability based conversion and an iterative conversion. The resulting language models are evaluated in terms of perplexity and mixed error rate in the context of the Code-Switching data corpus SEAME. Although the best results are obtained by combining the results of all three approaches, the text based conversion approach alone leads to significant improvements on the SEAME corpus as well while offering the highest computational efficiency. In total, the perplexity can be reduced by 11.4 relative on the evaluation set and the mixed error rate by 3.0 relative on the same data set. We propose a new method for creating computationally efficient convolutional neural networks (CNNs) by using low-rank representations of convolutional filters. Rather than approximating filters in previously-trained networks with more efficient versions, we learn a set of small basis filters from scratch; during training, the network learns to combine these basis filters into more complex filters that are discriminative for image classification. To train such networks, a novel weight initialization scheme is used. This allows effective initialization of connection weights in convolutional layers composed of groups of differently-shaped filters. We validate our approach by applying it to several existing CNN architectures and training these networks from scratch using the CIFAR, ILSVRC and MIT Places datasets. Our results show similar or higher accuracy than conventional CNNs with much less compute. Applying our method to an improved version of VGG-11 network using global max-pooling, we achieve comparable validation accuracy using 41 less compute and only 24 of the original VGG-11 model parameters; another variant of our method gives a 1 percentage point increase in accuracy over our improved VGG-11 model, giving a top-5 center-crop validation accuracy of 89.7 while reducing computation by 16 relative to the original VGG-11 model. Applying our method to the GoogLeNet architecture for ILSVRC, we achieved comparable accuracy with 26 less compute and 41 fewer model parameters. Applying our method to a near state-of-the-art network for CIFAR, we achieved comparable accuracy with 46 less compute and 55 fewer parameters. We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order- @math tensor @math of the form @math , where @math is a signal-to-noise ratio, @math is a unit vector, and @math is a random noise tensor, the goal is to recover the planted vector @math . For the case that @math has iid standard Gaussian entries, we give an efficient algorithm to recover @math whenever @math , and certify that the recovered vector is close to a maximum likelihood estimator, all with high probability over the random choice of @math . The previous best algorithms with provable guarantees required @math . In the regime @math , natural tensor-unfolding-based spectral relaxations for the underlying optimization problem break down (in the sense that their integrality gap is large). To go beyond this barrier, we use convex relaxations based on the sum-of-squares method. Our recovery algorithm proceeds by rounding a degree- @math sum-of-squares relaxations of the maximum-likelihood-estimation problem for the statistical model. To complement our algorithmic results, we show that degree- @math sum-of-squares relaxations break down for @math , which demonstrates that improving our current guarantees (by more than logarithmic factors) would require new techniques or might even be intractable. Finally, we show how to exploit additional problem structure in order to solve our sum-of-squares relaxations, up to some approximation, very efficiently. Our fastest algorithm runs in nearly-linear time using shifted (matrix) power iteration and has similar guarantees as above. The analysis of this algorithm also confirms a variant of a conjecture of Montanari and Richard about singular vectors of tensor unfoldings. We consider the task of learning a classifier for semantic segmentation using weak supervision in the form of image labels specifying objects present in the image. Our method uses deep convolutional neural networks (cnns) and adopts an Expectation-Maximization (EM) based approach. We focus on the following three aspects of EM: (i) initialization; (ii) latent posterior estimation (E-step) and (iii) the parameter update (M-step). We show that saliency and attention maps, bottom-up and top-down cues respectively, of images with single objects (simple images) provide highly reliable cues to learn an initialization for the EM. Intuitively, given weak supervisions, we first learn to segment simple images and then move towards the complex ones. Next, for updating the parameters (M step), we propose to minimize the combination of the standard softmax loss and the KL divergence between the latent posterior distribution (obtained using the E-step) and the likelihood given by the cnn. This combination is more robust to wrong predictions made by the E step of the EM algorithm. Extensive experiments and discussions show that our method is very simple and intuitive, and outperforms the state-of-the-art method with a very high margin of 3.7 and 3.9 on the PASCAL VOC12 train and test sets respectively, thus setting new state-of-the-art results.