New Anisotropic Gauss-Bonnet Black Holes in Five Dimensions at the Critical Point

We obtain new vacuum static black hole solutions with anisotropic horizons in Einstein-Gauss-Bonnet gravity with a negative cosmological constant in five dimensions. The translational invariance along one direction on the 3-dimensional horizon cross section is broken. The Gauss-Bonnet coupling {\alpha} is at the critical point where there is one single AdS vacuum. These solutions does not appear in the form of a warped product, i.e. they lack a common warping factor, and the metric contains 2 arbitrary functions, h(r) of the radial coordinate r and H(y) of the horizon coordinate y -- some degeneracy in the metric. The nontrivial horizon and the degeneracy may be closely related to the critical value of {\alpha}. We introduce the process of obtaining the solutions and some of their properties, and also prove a uniqueness theorem for the case when there is a common warping factor for the rest two directions.Comment: 8pages, no figures. arXiv admin note: text overlap with arXiv:2105.0848

High-Dimensional Bayesian Optimization via Semi-Supervised Learning with Optimized Unlabeled Data Sampling

We introduce a novel semi-supervised learning approach, named Teacher-Student Bayesian Optimization ($\texttt{TSBO}$), integrating the teacher-student paradigm into BO to minimize expensive labeled data queries for the first time. $\texttt{TSBO}$ incorporates a teacher model, an unlabeled data sampler, and a student model. The student is trained on unlabeled data locations generated by the sampler, with pseudo labels predicted by the teacher. The interplay between these three components implements a unique selective regularization to the teacher in the form of student feedback. This scheme enables the teacher to predict high-quality pseudo labels, enhancing the generalization of the GP surrogate model in the search space. To fully exploit $\texttt{TSBO}$, we propose two optimized unlabeled data samplers to construct effective student feedback that well aligns with the objective of Bayesian optimization. Furthermore, we quantify and leverage the uncertainty of the teacher-student model for the provision of reliable feedback to the teacher in the presence of risky pseudo-label predictions. $\texttt{TSBO}$ demonstrates significantly improved sample-efficiency in several global optimization tasks under tight labeled data budgets.Comment: 15 page

Building Program Vector Representations for Deep Learning

Deep learning has made significant breakthroughs in various fields of artificial intelligence. Advantages of deep learning include the ability to capture highly complicated features, weak involvement of human engineering, etc. However, it is still virtually impossible to use deep learning to analyze programs since deep architectures cannot be trained effectively with pure back propagation. In this pioneering paper, we propose the "coding criterion" to build program vector representations, which are the premise of deep learning for program analysis. Our representation learning approach directly makes deep learning a reality in this new field. We evaluate the learned vector representations both qualitatively and quantitatively. We conclude, based on the experiments, the coding criterion is successful in building program representations. To evaluate whether deep learning is beneficial for program analysis, we feed the representations to deep neural networks, and achieve higher accuracy in the program classification task than "shallow" methods, such as logistic regression and the support vector machine. This result confirms the feasibility of deep learning to analyze programs. It also gives primary evidence of its success in this new field. We believe deep learning will become an outstanding technique for program analysis in the near future.Comment: This paper was submitted to ICSE'1