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Visual attention, which assigns weights to image regions according to their relevance to a question, is considered as an indispensable part by most Visual Question Answering models. Although the questions may involve complex relations among multiple regions, few attention models can effectively encode such cross-region relations. In this paper, we demonstrate the importance of encoding such relations by showing the limited effective receptive field of ResNet on two datasets, and propose to model the visual attention as a multivariate distribution over a grid-structured Conditional Random Field on image regions. We demonstrate how to convert the iterative inference algorithms, Mean Field and Loopy Belief Propagation, as recurrent layers of an end-to-end neural network. We empirically evaluated our model on 3 datasets, in which it surpasses the best baseline model of the newly released CLEVR dataset [13] by 9.5%, and the best published model on the VQA dataset [3] by 1.25%. Source code is available at https: //github.com/zhuchen03/vqa-sva.

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.

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