On the classification of certain 1-connected 7-manifolds and related problems

In this article, we give a classification of closed, smooth, spin, 1-connected 7-manifolds whose integral cohomology ring is isomorphic to that of $\mathbb{C}P^2\times S^3$. We also prove that if a closed, smooth, spin, 1-connected 7-manifold has integral cohomology ring isomorphic to that of $\mathbb{C}P^2\times S^3$ or $S^2\times S^5$, then it admits a Riemannian metric with positive Ricci curvature.Comment: 20 page

Relative Importance Sampling For Off-Policy Actor-Critic in Deep Reinforcement Learning

Off-policy learning is more unstable compared to on-policy learning in reinforcement learning (RL). One reason for the instability of off-policy learning is a discrepancy between the target ($\pi$) and behavior (b) policy distributions. The discrepancy between $\pi$ and b distributions can be alleviated by employing a smooth variant of the importance sampling (IS), such as the relative importance sampling (RIS). RIS has parameter $\beta\in[0, 1]$ which controls smoothness. To cope with instability, we present the first relative importance sampling-off-policy actor-critic (RIS-Off-PAC) model-free algorithms in RL. In our method, the network yields a target policy (the actor), a value function (the critic) assessing the current policy ($\pi$) using samples drawn from behavior policy. We use action value generated from the behavior policy in reward function to train our algorithm rather than from the target policy. We also use deep neural networks to train both actor and critic. We evaluated our algorithm on a number of Open AI Gym benchmark problems and demonstrate better or comparable performance to several state-of-the-art RL baselines

MatchZoo: A Learning, Practicing, and Developing System for Neural Text Matching

Text matching is the core problem in many natural language processing (NLP) tasks, such as information retrieval, question answering, and conversation. Recently, deep leaning technology has been widely adopted for text matching, making neural text matching a new and active research domain. With a large number of neural matching models emerging rapidly, it becomes more and more difficult for researchers, especially those newcomers, to learn and understand these new models. Moreover, it is usually difficult to try these models due to the tedious data pre-processing, complicated parameter configuration, and massive optimization tricks, not to mention the unavailability of public codes sometimes. Finally, for researchers who want to develop new models, it is also not an easy task to implement a neural text matching model from scratch, and to compare with a bunch of existing models. In this paper, therefore, we present a novel system, namely MatchZoo, to facilitate the learning, practicing and designing of neural text matching models. The system consists of a powerful matching library and a user-friendly and interactive studio, which can help researchers: 1) to learn state-of-the-art neural text matching models systematically, 2) to train, test and apply these models with simple configurable steps; and 3) to develop their own models with rich APIs and assistance