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We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether R\'enyi entropies of independent sums decrease when one of the summands is contracted by a $1$-Lipschitz map. We answer this question affirmatively in various cases.

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We explain the methodology used to create the data submitted to HuMob Challenge, a data analysis competition for human mobility prediction. We adopted a personalized model to predict the individual's movement trajectory from their data, instead of predicting from the overall movement, based on the hypothesis that human movement is unique to each person. We devised the features such as the date and time, activity time, days of the week, time of day, and frequency of visits to POI (Point of Interest). As additional features, we incorporated the movement of other individuals with similar behavior patterns through the employment of clustering. The machine learning model we adopted was the Support Vector Regression (SVR). We performed accuracy through offline assessment and carried out feature selection and parameter tuning. Although overall dataset provided consists of 100,000 users trajectory, our method use only 20,000 target users data, and do not need to use other 80,000 data. Despite the personalized model's traditional feature engineering approach, this model yields reasonably good accuracy with lower computational cost.

Its numerous applications make multi-human 3D pose estimation a remarkably impactful area of research. Nevertheless, assuming a multiple-view system composed of several regular RGB cameras, 3D multi-pose estimation presents several challenges. First of all, each person must be uniquely identified in the different views to separate the 2D information provided by the cameras. Secondly, the 3D pose estimation process from the multi-view 2D information of each person must be robust against noise and potential occlusions in the scenario. In this work, we address these two challenges with the help of deep learning. Specifically, we present a model based on Graph Neural Networks capable of predicting the cross-view correspondence of the people in the scenario along with a Multilayer Perceptron that takes the 2D points to yield the 3D poses of each person. These two models are trained in a self-supervised manner, thus avoiding the need for large datasets with 3D annotations.

We introduce SHARCS for adaptive inference that takes into account the hardness of input samples. SHARCS can train a router on any transformer network, enabling the model to direct different samples to sub-networks with varying widths. Our experiments demonstrate that: (1) SHARCS outperforms or complements existing per-sample adaptive inference methods across various classification tasks in terms of accuracy vs. FLOPs; (2) SHARCS generalizes across different architectures and can be even applied to compressed and efficient transformer encoders to further improve their efficiency; (3) SHARCS can provide a 2 times inference speed up at an insignificant drop in accuracy.

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack's distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack's estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack's estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

Knowledge graph entity typing (KGET) aims at inferring plausible types of entities in knowledge graphs. Existing approaches to KGET focus on how to better encode the knowledge provided by the neighbors and types of an entity into its representation. However, they ignore the semantic knowledge provided by the way in which types can be clustered together. In this paper, we propose a novel method called Multi-view Contrastive Learning for knowledge graph Entity Typing (MCLET), which effectively encodes the coarse-grained knowledge provided by clusters into entity and type embeddings. MCLET is composed of three modules: i) Multi-view Generation and Encoder module, which encodes structured information from entity-type, entity-cluster and cluster-type views; ii) Cross-view Contrastive Learning module, which encourages different views to collaboratively improve view-specific representations of entities and types; iii) Entity Typing Prediction module, which integrates multi-head attention and a Mixture-of-Experts strategy to infer missing entity types. Extensive experiments show the strong performance of MCLET compared to the state-of-the-art

We provide a new characterization of both belief update and belief revision in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of states, a Kripke belief relation and a Lewis selection function. Adding a valuation to a frame yields a model. Given a model and a state, we identify the initial belief set K with the set of formulas that are believed at that state and we identify either the updated belief set or the revised belief set, prompted by the input represented by formula A, as the set of formulas that are the consequent of conditionals that (1) are believed at that state and (2) have A as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the AGM belief revision functions, in the following sense: (1) each model gives rise to a partial belief function that can be completed into a full KM/AGM update/revision function, and (2) for every KM/AGM update/revision function there is a model whose associated belief function coincides with it. The difference between update and revision can be reduced to two semantic properties that appear in a stronger form in revision relative to update, thus confirming the finding by Peppas et al. (1996) that, "for a fixed theory K, revising K is much the same as updating K"

The core of information retrieval (IR) is to identify relevant information from large-scale resources and return it as a ranked list to respond to user's information need. Recently, the resurgence of deep learning has greatly advanced this field and leads to a hot topic named NeuIR (i.e., neural information retrieval), especially the paradigm of pre-training methods (PTMs). Owing to sophisticated pre-training objectives and huge model size, pre-trained models can learn universal language representations from massive textual data, which are beneficial to the ranking task of IR. Since there have been a large number of works dedicating to the application of PTMs in IR, we believe it is the right time to summarize the current status, learn from existing methods, and gain some insights for future development. In this survey, we present an overview of PTMs applied in different components of IR system, including the retrieval component, the re-ranking component, and other components. In addition, we also introduce PTMs specifically designed for IR, and summarize available datasets as well as benchmark leaderboards. Moreover, we discuss some open challenges and envision some promising directions, with the hope of inspiring more works on these topics for future research.

Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-viewcontrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, two extensions of HeCo are designed to generate harder negative samples with high quality, which further boosts the performance of HeCo. Extensive experiments conducted on a variety of real-world networks show the superior performance of the proposed methods over the state-of-the-arts.

Graph neural networks (GNNs) have been proven to be effective in various network-related tasks. Most existing GNNs usually exploit the low-frequency signals of node features, which gives rise to one fundamental question: is the low-frequency information all we need in the real world applications? In this paper, we first present an experimental investigation assessing the roles of low-frequency and high-frequency signals, where the results clearly show that exploring low-frequency signal only is distant from learning an effective node representation in different scenarios. How can we adaptively learn more information beyond low-frequency information in GNNs? A well-informed answer can help GNNs enhance the adaptability. We tackle this challenge and propose a novel Frequency Adaptation Graph Convolutional Networks (FAGCN) with a self-gating mechanism, which can adaptively integrate different signals in the process of message passing. For a deeper understanding, we theoretically analyze the roles of low-frequency signals and high-frequency signals on learning node representations, which further explains why FAGCN can perform well on different types of networks. Extensive experiments on six real-world networks validate that FAGCN not only alleviates the over-smoothing problem, but also has advantages over the state-of-the-arts.

Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.

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