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Wenxiang Zhu

Publications and source records attributed to Wenxiang Zhu.

3 recordsLinked to original sources

A Snail Race Problem

Inspired by Problem 17 from the 2024 American Mathematics Competition (AMC) 10B, this work focuses on enumerating the distinct outcomes of a snail race with specified number of ties of a certain type. We begin by developing a recurrence relation and subsequently derive a closed-form formula for the number of possible outcomes using the exponential generating function method. Two special cases of the problem are considered in detail. Our analysis also explores the connections between the solution to this problem and the ordered Bell numbers, Stirling numbers of the second kind, and partial Bell polynomials.

math.CO

Continual Transfer Learning for Cross-Domain Click-Through Rate Prediction at Taobao

As one of the largest e-commerce platforms in the world, Taobao's recommendation systems (RSs) serve the demands of shopping for hundreds of millions of customers. Click-Through Rate (CTR) prediction is a core component of the RS. One of the biggest characteristics in CTR prediction at Taobao is that there exist multiple recommendation domains where the scales of different domains vary significantly. Therefore, it is crucial to perform cross-domain CTR prediction to transfer knowledge from large domains to small domains to alleviate the data sparsity issue. However, existing cross-domain CTR prediction methods are proposed for static knowledge transfer, ignoring that all domains in real-world RSs are continually time-evolving. In light of this, we present a necessary but novel task named Continual Transfer Learning (CTL), which transfers knowledge from a time-evolving source domain to a time-evolving target domain. In this work, we propose a simple and effective CTL model called CTNet to solve the problem of continual cross-domain CTR prediction at Taobao, and CTNet can be trained efficiently. Particularly, CTNet considers an important characteristic in the industry that models has been continually well-trained for a very long time. So CTNet aims to fully utilize all the well-trained model parameters in both source domain and target domain to avoid losing historically acquired knowledge, and only needs incremental target domain data for training to guarantee efficiency. Extensive offline experiments and online A/B testing at Taobao demonstrate the efficiency and effectiveness of CTNet. CTNet is now deployed online in the recommender systems of Taobao, serving the main traffic of hundreds of millions of active users.

cs.IR

Axially symmetric volume constrained anisotropic mean curvature flow

We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume, we show that the flow exists for all time. Numerical simulations of the curvature flow are presented.

math.DG