In a single-slot recommendation system, users are only exposed to one item at a time, and the system cannot collect user feedback on multiple items simultaneously. Therefore, only pointwise modeling solutions can be adopted, focusing solely on modeling the likelihood of clicks or conversions for items by users to learn user-item preferences, without the ability to capture the ranking information among different items directly. However, since user-side information is often much more abundant than item-side information, the model can quickly learn the differences in user intrinsic tendencies, which are independent of the items they are exposed to. This can cause these intrinsic tendencies to become a shortcut bias for the model, leading to insufficient mining of the most concerned user-item preferences. To solve this challenge, we introduce the Breaker model. Breaker integrates an auxiliary task of user representation clustering with a multi-tower structure for cluster-specific preference modeling. By clustering user representations, we ensure that users within each cluster exhibit similar characteristics, which increases the complexity of the pointwise recommendation task on the user side. This forces the multi-tower structure with cluster-driven parameter learning to better model user-item preferences, ultimately eliminating shortcut biases related to user intrinsic tendencies. In terms of training, we propose a delayed parameter update mechanism to enhance training stability and convergence, enabling end-to-end joint training of the auxiliary clustering and classification tasks. Both offline and online experiments demonstrate that our method surpasses the baselines. It has already been deployed and is actively serving tens of millions of users daily on Meituan, one of the most popular e-commerce platforms for services.

Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and examine their effect within the context of this particular game. Although our paper does not solve the 7-in-a-row game, our experiments indicate that we have made significant progress towards it.

We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph $K_n$, where Maker's goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for $n = 8$ and $n = 9$. Then we use an inductive argument to show that, independent of who starts, Maker can win the game if and only if $n \geq 8$. This, in particular, resolves in the affirmative the long-standing conjecture of Papaioannou. We also study two standard positional games related to Hamiltonicity game. For Hamiltonian Path game, we show that Maker can claim a Hamiltonian path if and only if $n \geq 5$, independent of who starts. Next, we look at Fixed Hamiltonian Path game, where the goal of Maker is to claim a Hamiltonian path between two predetermined vertices. We prove that if Maker starts the game, he wins if and only if $n \geq 7$, and if Breaker starts, Maker wins if and only if $n \geq 8$. Using this result, we are able to improve the previously best upper bound on the smallest number of edges a graph on $n$ vertices can have, knowing that Maker can win the Maker-Breaker Hamiltonicity game played on its edges. To resolve the outcomes of the mentioned games on small (finite) boards, we devise algorithms for efficiently searching game trees and then obtain our results with the help of a computer.

Since the seminal work of Sampath et al. in 1996, despite the subsequent flourishing of techniques on diagnosis of discrete-event systems (DESs), the basic notions of fault and diagnosis have been remaining conceptually unchanged. Faults are defined at component level and diagnoses incorporate the occurrences of component faults within system evolutions: diagnosis is context-free. As this approach may be unsatisfactory for a complex DES, whose topology is organized in a hierarchy of abstractions, we propose to define different diagnosis rules for different subsystems in the hierarchy. Relevant fault patterns are specified as regular expressions on patterns of lower-level subsystems. Separation of concerns is achieved and the expressive power of diagnosis is enhanced: each subsystem has its proper set of diagnosis rules, which may or may not depend on the rules of other subsystems. Diagnosis is no longer anchored to components: it becomes context-sensitive. The approach yields seemingly contradictory but nonetheless possible scenarios: a subsystem can be normal despite the faulty behavior of a number of its components (positive paradox); also, it can be faulty despite the normal behavior of all its components (negative paradox).