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Evaluation using simulation and real-world scenes shows the effectiveness of the proposed approach in estimating both surface normal and reflectances.VQA is a task to answer natural language questions tied to the content of visual images. Most VQA approaches apply attention mechanism to focus on the relevant visual objects and/or consider the relations between objects via off-the-shelf methods in visual relation reasoning. LB100 However, they still suffer from several drawbacks. First, they mostly model the simple relations between objects, which results in many complicated questions cannot be answered correctly, because of failing to provide sufficient knowledge. Second, they seldom leverage the harmony cooperation of visual appearance feature and relation feature. To solve these problems, we propose a novel end-to-end VQA model, termed Multi-modal Relation Attention Network (MRA-Net). The proposed model explores both textual and visual relations to improve performance and interpretability. In specific, we devise 1) a self-guided word relation attention scheme, which explore the latent semantic relations between words; 2) two questionadaptive visual relation attention modules that can extract not only the fine-grained and precise binary relations between objects but also the more sophisticated trinary relations. Both question-related visual relations provide more and deeper visual semantics, thereby improving the visual reasoning ability of question answering. Furthermore, the proposal combines appearance feature with relations to reconcile the two types of features.We show that existing upsampling operators can be unified using the notion of the index function. This notion is inspired by an observation in the decoding process of deep image matting where indices-guided unpooling can often recover boundary details considerably better than other upsampling operators such as bilinear interpolation. By viewing the indices as a function of the feature map, we introduce the concept of 'learning to index', and present a novel index-guided encoder-decoder framework where indices are learned adaptively from data and are used to guide downsampling and upsampling stages, without extra training supervision. At the core of this framework is a new learnable module, termed Index Network (IndexNet), which dynamically generates indices conditioned on the feature map. IndexNet can be used as a plug-in applicable to almost all convolutional networks that have coupled downsampling and upsampling stages, enabling the networks to dynamically capture variations of local patterns. In particular, we instantiate, investigate five families of IndexNet, highlight their superiority in delivering spatial information over other upsampling operators with experiments on synthetic data, and demonstrate their effectiveness on four dense prediction tasks, including image matting, image denoising, semantic segmentation, and monocular depth estimation. Code and is available at https//git.io/IndexNet.Large-scale distributed training of deep neural networks results in models with worse generalization performance as a result of the increase in the effective mini-batch size. Previous approaches attempt to address this problem by varying the learning rate and batch size over epochs and layers, or (SP-NGD), a principled approach for training models that allows them to attain similar generalization performance to models trained with first-order optimization methods, but with accelerated convergence. Furthermore, SP-NGD scales to large mini-batch sizes with a negligible computational overhead as compared to first-order methods. We evaluated SP-NGD on a benchmark task where highly optimized first-order methods are available as references training a ResNet-50 model for image classification on ImageNet. We demonstrate convergence to a top-1 validation accuracy of 75.4% in 5.5 minutes using a mini-batch size of 32,768 with 1,024 GPUs, as well as an accuracy of 74.9% with an extremely large mini-batch size of 131,072 in 873 steps of SP-NGD.Geometric deep learning is a relatively nascent field that has attracted significant attention in the recent past. This is partly due to the ready availability of manifold-valued data. In this paper we present a novel theoretical framework for developing deep neural networks to cope with manifold-valued fields as inputs. We also present a novel architecture to realize this theory and call it a ManifoldNet. Analogous to convolutions in vector spaces which are equivalent to computing weighted sums, manifold-valued data 'convolutions' can be defined using the weighted Frechet Mean (wFM), an intrinsic operation. The hidden layers of ManifoldNet compute wFM of their inputs, where the weights are to be learnt. Since wFM is an intrinsic operation, the processed data remain on the manifold as they propagate through the hidden layers. To reduce the computational burden, we present a provably convergent recursive algorithm for wFM computation. Additionaly, for non-constant curvature manifolds, we prove that each wFM layer is non-collapsible and a contraction mapping. We also prove that the wFM is equivariant to the symmetry group action admitted by the manifold on which the data reside. To showcase the performance of ManifoldNet, we present several experiments from vision and medical imaging.To build a flexible and interpretable model for document analysis, we develop deep autoencoding topic model(DATM) that uses a hierarchy of gamma distributions to construct its multi-stochastic-layer generative network. In order to provide scalable posterior inference for the parameters of the generative network, we develop topic-layer-adaptive stochastic gradient Riemannian MCMC that jointly learns simplex constrained global parameters across all layers and topics, with topic and layer specific learning rates. Given a posterior sample of the global parameters, in order to efficiently infer the local latent representations of a document under DATM across all stochastic layers, we propose a Weibull upward-downward variational encoder that deterministically propagates information upward via a deep neural network, followed by a Weibull distribution based stochastic downward generative model. To jointly model documents and their associated labels, we further propose supervised DATM that enhances the discriminative power of its latent representations.

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