Improved Dropout for Shallow and Deep Learning

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptimal for the sake of convergence. In this paper, we propose to use multinomial sampling for dropout, i.e., sampling features or neurons according to a multinomial distribution with different probabilities for different features/neurons. To exhibit the optimal dropout probabilities, we analyze the shallow learning with multinomial dropout and establish the risk bound for stochastic optimization. By minimizing a sampling dependent factor in the risk bound, we obtain a distribution-dependent dropout with sampling probabilities dependent on the second order statistics of the data distribution. To tackle the issue of evolving distribution of neurons in deep learning, we propose an efficient adaptive dropout (named \textbf{evolutional dropout}) that computes the sampling probabilities on-the-fly from a mini-batch of examples. Empirical studies on several benchmark datasets demonstrate that the proposed dropouts achieve not only much faster convergence and but also a smaller testing error than the standard dropout. For example, on the CIFAR-100 data, the evolutional dropout achieves relative improvements over 10\% on the prediction performance and over 50\% on the convergence speed compared to the standard dropout.Comment: In NIPS 201

VQS: Linking Segmentations to Questions and Answers for Supervised Attention in VQA and Question-Focused Semantic Segmentation

Rich and dense human labeled datasets are among the main enabling factors for the recent advance on vision-language understanding. Many seemingly distant annotations (e.g., semantic segmentation and visual question answering (VQA)) are inherently connected in that they reveal different levels and perspectives of human understandings about the same visual scenes --- and even the same set of images (e.g., of COCO). The popularity of COCO correlates those annotations and tasks. Explicitly linking them up may significantly benefit both individual tasks and the unified vision and language modeling. We present the preliminary work of linking the instance segmentations provided by COCO to the questions and answers (QAs) in the VQA dataset, and name the collected links visual questions and segmentation answers (VQS). They transfer human supervision between the previously separate tasks, offer more effective leverage to existing problems, and also open the door for new research problems and models. We study two applications of the VQS data in this paper: supervised attention for VQA and a novel question-focused semantic segmentation task. For the former, we obtain state-of-the-art results on the VQA real multiple-choice task by simply augmenting the multilayer perceptrons with some attention features that are learned using the segmentation-QA links as explicit supervision. To put the latter in perspective, we study two plausible methods and compare them to an oracle method assuming that the instance segmentations are given at the test stage.Comment: To appear on ICCV 201

Computational grid generation for the design of free-form shells with complex boundary conditions

Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.</p