Global Generation of Adjoint Line Bundles on Projective 55-folds

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally generated.Comment: Final version to appear in manuscripta mathematica. We notice that mistakes were introduced by the journal to some fractions in the form "expression/expression" which should be read as "(expression)/(expression)

Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Visual7W: Grounded Question Answering in Images

We have seen great progress in basic perceptual tasks such as object recognition and detection. However, AI models still fail to match humans in high-level vision tasks due to the lack of capacities for deeper reasoning. Recently the new task of visual question answering (QA) has been proposed to evaluate a model's capacity for deep image understanding. Previous works have established a loose, global association between QA sentences and images. However, many questions and answers, in practice, relate to local regions in the images. We establish a semantic link between textual descriptions and image regions by object-level grounding. It enables a new type of QA with visual answers, in addition to textual answers used in previous work. We study the visual QA tasks in a grounded setting with a large collection of 7W multiple-choice QA pairs. Furthermore, we evaluate human performance and several baseline models on the QA tasks. Finally, we propose a novel LSTM model with spatial attention to tackle the 7W QA tasks.Comment: CVPR 201

Scene Graph Generation by Iterative Message Passing

Understanding a visual scene goes beyond recognizing individual objects in isolation. Relationships between objects also constitute rich semantic information about the scene. In this work, we explicitly model the objects and their relationships using scene graphs, a visually-grounded graphical structure of an image. We propose a novel end-to-end model that generates such structured scene representation from an input image. The model solves the scene graph inference problem using standard RNNs and learns to iteratively improves its predictions via message passing. Our joint inference model can take advantage of contextual cues to make better predictions on objects and their relationships. The experiments show that our model significantly outperforms previous methods for generating scene graphs using Visual Genome dataset and inferring support relations with NYU Depth v2 dataset.Comment: CVPR 201