Dynamics of generalized tachyon field

We investigate the dynamics of generalized tachyon field in FRW spacetime. We obtain the autonomous dynamical system for the general case. Because the general autonomous dynamical system cannot be solved analytically, we discuss two cases in detail: $\beta=1$ and $\beta=2$. We find the critical points and study their stability. At these critical points, we also consider the stability of the generalized tachyon field, which is as important as the stability of critical points. The possible final states of the universe are discussed.Comment: 9 pages, 5 figures, published versio

Generalized Delayed Feedback Model with Post-Click Information in Recommender Systems

Predicting conversion rate (e.g., the probability that a user will purchase an item) is a fundamental problem in machine learning based recommender systems. However, accurate conversion labels are revealed after a long delay, which harms the timeliness of recommender systems. Previous literature concentrates on utilizing early conversions to mitigate such a delayed feedback problem. In this paper, we show that post-click user behaviors are also informative to conversion rate prediction and can be used to improve timeliness. We propose a generalized delayed feedback model (GDFM) that unifies both post-click behaviors and early conversions as stochastic post-click information, which could be utilized to train GDFM in a streaming manner efficiently. Based on GDFM, we further establish a novel perspective that the performance gap introduced by delayed feedback can be attributed to a temporal gap and a sampling gap. Inspired by our analysis, we propose to measure the quality of post-click information with a combination of temporal distance and sample complexity. The training objective is re-weighted accordingly to highlight informative and timely signals. We validate our analysis on public datasets, and experimental performance confirms the effectiveness of our method.Comment: NeurIPS'2