In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[EX Q]: We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.
[EX A]: Weighted Tree Automata Approximation by Singular Value Truncation

[EX Q]: Evolution of visual object recognition architectures based on Convolutional Neural Networks & Convolutional Deep Belief Networks paradigms has revolutionized artificial Vision Science. These architectures extract & learn the real world hierarchical visual features utilizing supervised & unsupervised learning approaches respectively. Both the approaches yet cannot scale up realistically to provide recognition for a very large number of objects as high as 10K. We propose a two level hierarchical deep learning architecture inspired by divide & conquer principle that decomposes the large scale recognition architecture into root & leaf level model architectures. Each of the root & leaf level models is trained exclusively to provide superior results than possible by any 1-level deep learning architecture prevalent today. The proposed architecture classifies objects in two steps. In the first step the root level model classifies the object in a high level category. In the second step, the leaf level recognition model for the recognized high level category is selected among all the leaf models. This leaf level model is presented with the same input object image which classifies it in a specific category. Also we propose a blend of leaf level models trained with either supervised or unsupervised learning approaches. Unsupervised learning is suitable whenever labelled data is scarce for the specific leaf level models. Currently the training of leaf level models is in progress; where we have trained 25 out of the total 47 leaf level models as of now. We have trained the leaf models with the best case top-5 error rate of 3.2% on the validation data set for the particular leaf models. Also we demonstrate that the validation error of the leaf level models saturates towards the above mentioned accuracy as the number of epochs are increased to more than sixty. The top-5 error rate for the entire two-level architecture needs to be computed in conjunction with the error rates of root & all the leaf models. The realization of this two level visual recognition architecture will greatly enhance the accuracy of the large scale object recognition scenarios demanded by the use cases as diverse as drone vision, augmented reality, retail, image search & retrieval, robotic navigation, targeted advertisements etc.
[EX A]: HIERARCHICAL DEEP LEARNING ARCHITECTURE FOR 10K OBJECTS CLASSIFICATION

[EX Q]: Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the socalled safe rules for the Lasso. Based on duality gap considerations, our new rules create safe test regions whose diameters converge to zero, provided that one relies on a converging solver. This property helps screening out more variables, for a wider range of regularization parameter values. In addition to faster convergence, we prove that we correctly identify the active sets (supports) of the solutions in finite time. While our proposed strategy can cope with any solver, its performance is demonstrated using a coordinate descent algorithm particularly adapted to machine learning use cases. Significant computing time reductions are obtained with respect to previous safe rules.
[EX A]:
Mind the duality gap: safer rules for the Lasso