arXiv subjects
Publications and source records attributed to Trung Tran.
We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $\Omega(n \log n)$ queries.
In this work, we study the experts problem in the distributed setting where an expert's cost needs to be aggregated across multiple servers. Our study considers various communication models such as the message-passing model and the broadcast model, along with multiple aggregation functions, such as summing and taking the $\ell_p$ norm of an expert's cost across servers. We propose the first communication-efficient protocols that achieve near-optimal regret in these settings, even against a strong adversary who can choose the inputs adaptively. Additionally, we give a conditional lower bound showing that the communication of our protocols is nearly optimal. Finally, we implement our protocols and demonstrate empirical savings on the HPO-B benchmarks.
While advanced image captioning systems are increasingly describing images coherently and exactly, recent progress in continual learning allows deep learning models to avoid catastrophic forgetting. However, the domain where image captioning working with continual learning has not yet been explored. We define the task in which we consolidate continual learning and image captioning as continual image captioning. In this work, we propose ContCap, a framework generating captions over a series of new tasks coming, seamlessly integrating continual learning into image captioning besides addressing catastrophic forgetting. After proving forgetting in image captioning, we propose various techniques to overcome the forgetting dilemma by taking a simple fine-tuning schema as the baseline. We split MS-COCO 2014 dataset to perform experiments in class-incremental settings without revisiting dataset of previously provided tasks. Experiments show remarkable improvements in the performance on the old tasks while the figures for the new surprisingly surpass fine-tuning. Our framework also offers a scalable solution for continual image or video captioning.
Intuitively, an envelope of a family of curves is a curve that is tangent to a member of the family at each point. Here we use envelopes of families of circles to study objects from matrix theory and hyperbolic geometry. First we explore relationships between numerical ranges of $2\times 2$ matrices and families of circles to study the elliptical range theorem. Then we deduce a relationship between envelopes and the boundaries of families of intersecting circles and use it to find the boundaries of various families of pseudohyperbolic disks.