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Recommender systems embody significant commercial value and represent crucial intellectual property. However, the integrity of these systems is constantly challenged by malicious actors seeking to steal their underlying models. Safeguarding against such threats is paramount to upholding the rights and interests of the model owner. While model watermarking has emerged as a potent defense mechanism in various domains, its direct application to recommender systems remains unexplored and non-trivial. In this paper, we address this gap by introducing Autoregressive Out-of-distribution Watermarking (AOW), a novel technique tailored specifically for recommender systems. Our approach entails selecting an initial item and querying it through the oracle model, followed by the selection of subsequent items with small prediction scores. This iterative process generates a watermark sequence autoregressively, which is then ingrained into the model's memory through training. To assess the efficacy of the watermark, the model is tasked with predicting the subsequent item given a truncated watermark sequence. Through extensive experimentation and analysis, we demonstrate the superior performance and robust properties of AOW. Notably, our watermarking technique exhibits high-confidence extraction capabilities and maintains effectiveness even in the face of distillation and fine-tuning processes.

We study the nonlinear steady Boltzmann equation in the half space, with phase transition and Dirichlet boundary condition. In particular, we study the regularity of the solution to the half-space problem in the situation that the gas is in contact with its condensed phase. We propose a novel kinetic weight and establish a weighted $C^1$ estimate under the spatial domain $x\in [0,\infty)$, which is unbounded and not strictly convex. Additionally, we prove the $W^{1,p}$ estimate without any weight for $p<2$.

Recent advancements in anomaly detection have seen the efficacy of CNN- and transformer-based approaches. However, CNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Mamba-based models, with their superior long-range modeling and linear efficiency, have garnered substantial attention. This study pioneers the application of Mamba to multi-class unsupervised anomaly detection, presenting MambaAD, which consists of a pre-trained encoder and a Mamba decoder featuring (Locality-Enhanced State Space) LSS modules at multi-scales. The proposed LSS module, integrating parallel cascaded (Hybrid State Space) HSS blocks and multi-kernel convolutions operations, effectively captures both long-range and local information. The HSS block, utilizing (Hybrid Scanning) HS encoders, encodes feature maps into five scanning methods and eight directions, thereby strengthening global connections through the (State Space Model) SSM. The use of Hilbert scanning and eight directions significantly improves feature sequence modeling. Comprehensive experiments on six diverse anomaly detection datasets and seven metrics demonstrate state-of-the-art performance, substantiating the method's effectiveness.

Compared with only pursuing recommendation accuracy, the explainability of a recommendation model has drawn more attention in recent years. Many graph-based recommendations resort to informative paths with the attention mechanism for the explanation. Unfortunately, these attention weights are intentionally designed for model accuracy but not explainability. Recently, some researchers have started to question attention-based explainability because the attention weights are unstable for different reproductions, and they may not always align with human intuition. Inspired by the counterfactual reasoning from causality learning theory, we propose a novel explainable framework targeting path-based recommendations, wherein the explainable weights of paths are learned to replace attention weights. Specifically, we design two counterfactual reasoning algorithms from both path representation and path topological structure perspectives. Moreover, unlike traditional case studies, we also propose a package of explainability evaluation solutions with both qualitative and quantitative methods. We conduct extensive experiments on three real-world datasets, the results of which further demonstrate the effectiveness and reliability of our method., Comment: accepted by TKDE

We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion between these two specular regions. The boundary is assumed to be motionless and isothermal. Our main focus is on constructing global-in-time small-amplitude solutions around global Maxwellians for the corresponding initial-boundary value problem. The proof relies on the $L^2$ hypocoercivity at the linear level, utilizing the weak formulation and various functional inequalities on the test functions, such as Poincar\'e and Korn inequalities. It also extends to the linear problem involving Maxwell boundary conditions, where the accommodation coefficient can be a piecewise constant function on the boundary, allowing for more general bounded domains. Moreover, we develop a delicate application of the $L^2-L^\infty$ bootstrap argument, which relies on the specific geometry of our domains, to effectively handle this mixed-type boundary condition., Comment: 32 pages. All comments are welcome

Reconstruction-based approaches have achieved remarkable outcomes in anomaly detection. The exceptional image reconstruction capabilities of recently popular diffusion models have sparked research efforts to utilize them for enhanced reconstruction of anomalous images. Nonetheless, these methods might face challenges related to the preservation of image categories and pixel-wise structural integrity in the more practical multi-class setting. To solve the above problems, we propose a Difusion-based Anomaly Detection (DiAD) framework for multi-class anomaly detection, which consists of a pixel-space autoencoder, a latent-space Semantic-Guided (SG) network with a connection to the stable diffusion's denoising network, and a feature-space pre-trained feature extractor. Firstly, The SG network is proposed for reconstructing anomalous regions while preserving the original image's semantic information. Secondly, we introduce Spatial-aware Feature Fusion (SFF) block to maximize reconstruction accuracy when dealing with extensively reconstructed areas. Thirdly, the input and reconstructed images are processed by a pre-trained feature extractor to generate anomaly maps based on features extracted at different scales. Experiments on MVTec-AD and VisA datasets demonstrate the effectiveness of our approach which surpasses the state-of-the-art methods, e.g., achieving 96.8/52.6 and 97.2/99.0 (AUROC/AP) for localization and detection respectively on multi-class MVTec-AD dataset. Code will be available at https://lewandofskee.github.io/projects/diad., Comment: Accepted by AAAI 2024

Understanding the architecture is vital for effectively maintaining and managing large software systems. However, as software systems evolve over time, their architectures inevitably change. To keep up with the change, architects need to track the implementation-level changes and update the architectural documentation accordingly, which is time-consuming and error-prone. Therefore, many automatic architecture recovery techniques have been proposed to ease this process. Despite efforts have been made to improve the accuracy of architecture recovery, existing solutions still suffer from two limitations. First, most of them only use one or two type of information for the recovery, ignoring the potential usefulness of other sources. Second, they tend to use the information in a coarse-grained manner, overlooking important details within it. To address these limitations, we propose SARIF, a fully automated architecture recovery technique, which incorporates three types of comprehensive information, including dependencies, code text and folder structure. SARIF can recover architecture more accurately by thoroughly analyzing the details of each type of information and adaptively fusing them based on their relevance and quality. To evaluate SARIF, we collected six projects with published ground-truth architectures and three open-source projects labeled by our industrial collaborators. We compared SARIF with nine state-of-the-art techniques using three commonly-used architecture similarity metrics and two new metrics. The experimental results show that SARIF is 36.1% more accurate than the best of the previous techniques on average. By providing comprehensive architecture, SARIF can help users understand systems effectively and reduce the manual effort of obtaining ground-truth architectures.

In this paper, we consider a distributed stochastic non-convex optimization problem, which is about minimizing a sum of $n$ local cost functions over a network with only zeroth-order information. A novel single-loop Decentralized Zeroth-Order Variance Reduction algorithm, called DZOVR, is proposed, which combines two-point gradient estimation, momentum-based variance reduction technique, and gradient tracking. Under mild assumptions, we show that the algorithm is able to achieve $\mathcal{O}(dn^{-1}\epsilon^{-3})$ sampling complexity at each node to reach an $\epsilon$-accurate stationary point and also exhibits network-independent and linear speedup properties. To the best of our knowledge, this is the first stochastic decentralized zeroth-order algorithm that achieves this sampling complexity. Numerical experiments demonstrate that DZOVR outperforms the other state-of-the-art algorithms and has network-independent and linear speedup properties.

The robustness of recommender systems has become a prominent topic within the research community. Numerous adversarial attacks have been proposed, but most of them rely on extensive prior knowledge, such as all the white-box attacks or most of the black-box attacks which assume that certain external knowledge is available. Among these attacks, the model extraction attack stands out as a promising and practical method, involving training a surrogate model by repeatedly querying the target model. However, there is a significant gap in the existing literature when it comes to defending against model extraction attacks on recommender systems. In this paper, we introduce Gradient-based Ranking Optimization (GRO), which is the first defense strategy designed to counter such attacks. We formalize the defense as an optimization problem, aiming to minimize the loss of the protected target model while maximizing the loss of the attacker's surrogate model. Since top-k ranking lists are non-differentiable, we transform them into swap matrices which are instead differentiable. These swap matrices serve as input to a student model that emulates the surrogate model's behavior. By back-propagating the loss of the student model, we obtain gradients for the swap matrices. These gradients are used to compute a swap loss, which maximizes the loss of the student model. We conducted experiments on three benchmark datasets to evaluate the performance of GRO, and the results demonstrate its superior effectiveness in defending against model extraction attacks.

In this short note, we prove an $L^6$-control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to the specular reflection boundary condition, in which we crucially used the Korn's inequality \cite{DV2} and the system of symmetric Poisson equations \cite{Bernou}.

We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to $W^{1,p}_x$ for any $p<3$. We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially fast as $t \rightarrow \infty$., Comment: 51 pages, accepted in ARMA

Currently, graph learning models are indispensable tools to help researchers explore graph-structured data. In academia, using sufficient training data to optimize a graph model on a single device is a typical approach for training a capable graph learning model. Due to privacy concerns, however, it is infeasible to do so in real-world scenarios. Federated learning provides a practical means of addressing this limitation by introducing various privacy-preserving mechanisms, such as differential privacy (DP) on the graph edges. However, although DP in federated graph learning can ensure the security of sensitive information represented in graphs, it usually causes the performance of graph learning models to degrade. In this paper, we investigate how DP can be implemented on graph edges and observe a performance decrease in our experiments. In addition, we note that DP on graph edges introduces noise that perturbs graph proximity, which is one of the graph augmentations in graph contrastive learning. Inspired by this, we propose leveraging graph contrastive learning to alleviate the performance drop resulting from DP. Extensive experiments conducted with four representative graph models on five widely used benchmark datasets show that contrastive learning indeed alleviates the models' DP-induced performance drops., Comment: Accepted by Information Sciences

Graph contrastive learning has emerged as a powerful tool for unsupervised graph representation learning. The key to the success of graph contrastive learning is to acquire high-quality positive and negative samples as contrasting pairs for the purpose of learning underlying structural semantics of the input graph. Recent works usually sample negative samples from the same training batch with the positive samples, or from an external irrelevant graph. However, a significant limitation lies in such strategies, which is the unavoidable problem of sampling false negative samples. In this paper, we propose a novel method to utilize \textbf{C}ounterfactual mechanism to generate artificial hard negative samples for \textbf{G}raph \textbf{C}ontrastive learning, namely \textbf{CGC}, which has a different perspective compared to those sampling-based strategies. We utilize counterfactual mechanism to produce hard negative samples, which ensures that the generated samples are similar to, but have labels that different from the positive sample. The proposed method achieves satisfying results on several datasets compared to some traditional unsupervised graph learning methods and some SOTA graph contrastive learning methods. We also conduct some supplementary experiments to give an extensive illustration of the proposed method, including the performances of CGC with different hard negative samples and evaluations for hard negative samples generated with different similarity measurements., Comment: ACCEPTED BY WWW'2023

With the rapid growth of software, using third-party libraries (TPLs) has become increasingly popular. The prosperity of the library usage has provided the software engineers with handful of methods to facilitate and boost the program development. Unfortunately, it also poses great challenges as it becomes much more difficult to manage the large volume of libraries. Researches and studies have been proposed to detect and understand the TPLs in the software. However, most existing approaches rely on syntactic features, which are not robust when these features are changed or deliberately hidden by the adversarial parties. Moreover, these approaches typically model each of the imported libraries as a whole, therefore, cannot be applied to scenarios where the host software only partially uses the library code segments. To detect both fully and partially imported TPLs at the semantic level, we propose ModX, a framework that leverages novel program modularization techniques to decompose the program into finegrained functionality-based modules. By extracting both syntactic and semantic features, it measures the distance between modules to detect similar library module reuse in the program. Experimental results show that ModX outperforms other modularization tools by distinguishing more coherent program modules with 353% higher module quality scores and beats other TPL detection tools with on average 17% better in precision and 8% better in recall.

Medication recommendation is a crucial task for intelligent healthcare systems. Previous studies mainly recommend medications with electronic health records (EHRs). However, some details of interactions between doctors and patients may be ignored or omitted in EHRs, which are essential for automatic medication recommendation. Therefore, we make the first attempt to recommend medications with the conversations between doctors and patients. In this work, we construct DIALMED, the first high-quality dataset for medical dialogue-based medication recommendation task. It contains 11,996 medical dialogues related to 16 common diseases from 3 departments and 70 corresponding common medications. Furthermore, we propose a Dialogue structure and Disease knowledge aware Network (DDN), where a QA Dialogue Graph mechanism is designed to model the dialogue structure and the knowledge graph is used to introduce external disease knowledge. The extensive experimental results demonstrate that the proposed method is a promising solution to recommend medications with medical dialogues. The dataset and code are available at https://github.com/f-window/DialMed., Comment: Accepted as a long paper at COLING 2022

Recently, transformers have shown promising performance in learning graph representations. However, there are still some challenges when applying transformers to real-world scenarios due to the fact that deep transformers are hard to train from scratch and the quadratic memory consumption w.r.t. the number of nodes. In this paper, we propose Graph Masked Autoencoders (GMAEs), a self-supervised transformer-based model for learning graph representations. To address the above two challenges, we adopt the masking mechanism and the asymmetric encoder-decoder design. Specifically, GMAE takes partially masked graphs as input, and reconstructs the features of the masked nodes. The encoder and decoder are asymmetric, where the encoder is a deep transformer and the decoder is a shallow transformer. The masking mechanism and the asymmetric design make GMAE a memory-efficient model compared with conventional transformers. We show that, when serving as a conventional self-supervised graph representation model, GMAE achieves state-of-the-art performance on both the graph classification task and the node classification task under common downstream evaluation protocols. We also show that, compared with training in an end-to-end manner from scratch, we can achieve comparable performance after pre-training and fine-tuning using GMAE while simplifying the training process.

Graph contrastive learning is the state-of-the-art unsupervised graph representation learning framework and has shown comparable performance with supervised approaches. However, evaluating whether the graph contrastive learning is robust to adversarial attacks is still an open problem because most existing graph adversarial attacks are supervised models, which means they heavily rely on labels and can only be used to evaluate the graph contrastive learning in a specific scenario. For unsupervised graph representation methods such as graph contrastive learning, it is difficult to acquire labels in real-world scenarios, making traditional supervised graph attack methods difficult to be applied to test their robustness. In this paper, we propose a novel unsupervised gradient-based adversarial attack that does not rely on labels for graph contrastive learning. We compute the gradients of the adjacency matrices of the two views and flip the edges with gradient ascent to maximize the contrastive loss. In this way, we can fully use multiple views generated by the graph contrastive learning models and pick the most informative edges without knowing their labels, and therefore can promisingly support our model adapted to more kinds of downstream tasks. Extensive experiments show that our attack outperforms unsupervised baseline attacks and has comparable performance with supervised attacks in multiple downstream tasks including node classification and link prediction. We further show that our attack can be transferred to other graph representation models as well.

Unsupervised graph representation learning has emerged as a powerful tool to address real-world problems and achieves huge success in the graph learning domain. Graph contrastive learning is one of the unsupervised graph representation learning methods, which recently attracts attention from researchers and has achieved state-of-the-art performances on various tasks. The key to the success of graph contrastive learning is to construct proper contrasting pairs to acquire the underlying structural semantics of the graph. However, this key part is not fully explored currently, most of the ways generating contrasting pairs focus on augmenting or perturbating graph structures to obtain different views of the input graph. But such strategies could degrade the performances via adding noise into the graph, which may narrow down the field of the applications of graph contrastive learning. In this paper, we propose a novel graph contrastive learning method, namely \textbf{D}ual \textbf{S}pace \textbf{G}raph \textbf{C}ontrastive (DSGC) Learning, to conduct graph contrastive learning among views generated in different spaces including the hyperbolic space and the Euclidean space. Since both spaces have their own advantages to represent graph data in the embedding spaces, we hope to utilize graph contrastive learning to bridge the spaces and leverage advantages from both sides. The comparison experiment results show that DSGC achieves competitive or better performances among all the datasets. In addition, we conduct extensive experiments to analyze the impact of different graph encoders on DSGC, giving insights about how to better leverage the advantages of contrastive learning between different spaces.

In recent years, graph neural networks (GNNs) have emerged as a successful tool in a variety of graph-related applications. However, the performance of GNNs can be deteriorated when noisy connections occur in the original graph structures; besides, the dependence on explicit structures prevents GNNs from being applied to general unstructured scenarios. To address these issues, recently emerged deep graph structure learning (GSL) methods propose to jointly optimize the graph structure along with GNN under the supervision of a node classification task. Nonetheless, these methods focus on a supervised learning scenario, which leads to several problems, i.e., the reliance on labels, the bias of edge distribution, and the limitation on application tasks. In this paper, we propose a more practical GSL paradigm, unsupervised graph structure learning, where the learned graph topology is optimized by data itself without any external guidance (i.e., labels). To solve the unsupervised GSL problem, we propose a novel StrUcture Bootstrapping contrastive LearnIng fraMEwork (SUBLIME for abbreviation) with the aid of self-supervised contrastive learning. Specifically, we generate a learning target from the original data as an "anchor graph", and use a contrastive loss to maximize the agreement between the anchor graph and the learned graph. To provide persistent guidance, we design a novel bootstrapping mechanism that upgrades the anchor graph with learned structures during model learning. We also design a series of graph learners and post-processing schemes to model the structures to learn. Extensive experiments on eight benchmark datasets demonstrate the significant effectiveness of our proposed SUBLIME and high quality of the optimized graphs., Comment: 12 pages, 7 figures. Accepted by The Web Conf 2022

Mixup is a data augmentation method that generates new data points by mixing a pair of input data. While mixup generally improves the prediction performance, it sometimes degrades the performance. In this paper, we first identify the main causes of this phenomenon by theoretically and empirically analyzing the mixup algorithm. To resolve this, we propose GenLabel, a simple yet effective relabeling algorithm designed for mixup. In particular, GenLabel helps the mixup algorithm correctly label mixup samples by learning the class-conditional data distribution using generative models. Via extensive theoretical and empirical analysis, we show that mixup, when used together with GenLabel, can effectively resolve the aforementioned phenomenon, improving the generalization performance and the adversarial robustness.

Recent advances in path-based explainable recommendation systems have attracted increasing attention thanks to the rich information provided by knowledge graphs. Most existing explainable recommendations only utilize static knowledge graphs and ignore the dynamic user-item evolutions, leading to less convincing and inaccurate explanations. Although there are some works that realize that modelling user's temporal sequential behaviour could boost the performance and explainability of the recommender systems, most of them either only focus on modelling user's sequential interactions within a path or independently and separately of the recommendation mechanism. In this paper, we propose a novel Temporal Meta-path Guided Explainable Recommendation leveraging Reinforcement Learning (TMER-RL), which utilizes reinforcement item-item path modelling between consecutive items with attention mechanisms to sequentially model dynamic user-item evolutions on dynamic knowledge graph for explainable recommendation. Compared with existing works that use heavy recurrent neural networks to model temporal information, we propose simple but effective neural networks to capture users' historical item features and path-based context to characterize the next purchased item. Extensive evaluations of TMER on two real-world datasets show state-of-the-art performance compared against recent strong baselines., Comment: arXiv admin note: substantial text overlap with arXiv:2101.01433

Recently, lots of algorithms have been proposed for learning a fair classifier from decentralized data. However, many theoretical and algorithmic questions remain open. First, is federated learning necessary, i.e., can we simply train locally fair classifiers and aggregate them? In this work, we first propose a new theoretical framework, with which we demonstrate that federated learning can strictly boost model fairness compared with such non-federated algorithms. We then theoretically and empirically show that the performance tradeoff of FedAvg-based fair learning algorithms is strictly worse than that of a fair classifier trained on centralized data. To bridge this gap, we propose FedFB, a private fair learning algorithm on decentralized data. The key idea is to modify the FedAvg protocol so that it can effectively mimic the centralized fair learning. Our experimental results show that FedFB significantly outperforms existing approaches, sometimes matching the performance of the centrally trained model., Comment: 39 pages, 7 figures

As an essential ingredient of modern deep learning, attention mechanism, especially self-attention, plays a vital role in the global correlation discovery. However, is hand-crafted attention irreplaceable when modeling the global context? Our intriguing finding is that self-attention is not better than the matrix decomposition (MD) model developed 20 years ago regarding the performance and computational cost for encoding the long-distance dependencies. We model the global context issue as a low-rank recovery problem and show that its optimization algorithms can help design global information blocks. This paper then proposes a series of Hamburgers, in which we employ the optimization algorithms for solving MDs to factorize the input representations into sub-matrices and reconstruct a low-rank embedding. Hamburgers with different MDs can perform favorably against the popular global context module self-attention when carefully coping with gradients back-propagated through MDs. Comprehensive experiments are conducted in the vision tasks where it is crucial to learn the global context, including semantic segmentation and image generation, demonstrating significant improvements over self-attention and its variants., Comment: ICLR 2021

User purchasing prediction with multi-behavior information remains a challenging problem for current recommendation systems. Various methods have been proposed to address it via leveraging the advantages of graph neural networks (GNNs) or multi-task learning. However, most existing works do not take the complex dependencies among different behaviors of users into consideration. They utilize simple and fixed schemes, like neighborhood information aggregation or mathematical calculation of vectors, to fuse the embeddings of different user behaviors to obtain a unified embedding to represent a user's behavioral patterns which will be used in downstream recommendation tasks. To tackle the challenge, in this paper, we first propose the concept of hyper meta-path to construct hyper meta-paths or hyper meta-graphs to explicitly illustrate the dependencies among different behaviors of a user. How to obtain a unified embedding for a user from hyper meta-paths and avoid the previously mentioned limitations simultaneously is critical. Thanks to the recent success of graph contrastive learning, we leverage it to learn embeddings of user behavior patterns adaptively instead of assigning a fixed scheme to understand the dependencies among different behaviors. A new graph contrastive learning based framework is proposed by coupling with hyper meta-paths, namely HMG-CR, which consistently and significantly outperforms all baselines in extensive comparison experiments., Comment: Accepted by ICDM 2021 as a regular paper

Advertising is critical to many online e-commerce platforms such as e-Bay and Amazon. One of the important signals that these platforms rely upon is the click-through rate (CTR) prediction. The recent popularity of multi-modal sharing platforms such as TikTok has led to an increased interest in online micro-videos. It is, therefore, useful to consider micro-videos to help a merchant target micro-video advertising better and find users' favourites to enhance user experience. Existing works on CTR prediction largely exploit unimodal content to learn item representations. A relatively minimal effort has been made to leverage multi-modal information exchange among users and items. We propose a model to exploit the temporal user-item interactions to guide the representation learning with multi-modal features, and further predict the user click rate of the micro-video item. We design a Hypergraph Click-Through Rate prediction framework (HyperCTR) built upon the hyperedge notion of hypergraph neural networks, which can yield modal-specific representations of users and micro-videos to better capture user preferences. We construct a time-aware user-item bipartite network with multi-modal information and enrich the representation of each user and item with the generated interests-based user hypergraph and item hypergraph. Through extensive experiments on three public datasets, we demonstrate that our proposed model significantly outperforms various state-of-the-art methods., Comment: 9 pages,8 figures,Proceedings of the 30th ACM International Conference on Information and Knowledge Management

Hashtag, a product of user tagging behavior, which can well describe the semantics of the user-generated content personally over social network applications, e.g., the recently popular micro-videos. Hashtags have been widely used to facilitate various micro-video retrieval scenarios, such as search engine and categorization. In order to leverage hashtags on micro-media platform for effective e-commerce marketing campaign, there is a demand from e-commerce industry to develop a mapping algorithm bridging its categories and micro-video hashtags. In this demo paper, we therefore proposed a novel solution called TagPick that incorporates clues from all user behavior metadata (hashtags, interactions, multimedia information) as well as relational data (graph-based network) into a unified system to reveal the correlation between e-commerce categories and hashtags in industrial scenarios. In particular, we provide a tag-level popularity strategy to recommend the relevant hashtags for e-Commerce platform (e.g., eBay)., Comment: 4 pages,2 figures,CIKM2021,Demonstration Paper

Hypergraphs have been becoming a popular choice to model complex, non-pairwise, and higher-order interactions for recommender system. However, compared with traditional graph-based methods, the constructed hypergraphs are usually much sparser, which leads to a dilemma when balancing the benefits of hypergraphs and the modelling difficulty. Moreover, existing sequential hypergraph recommendation overlooks the temporal modelling among user relationships, which neglects rich social signals from the recommendation data. To tackle the above shortcomings of the existing hypergraph-based sequential recommendations, we propose a novel architecture named Hyperbolic Hypergraph representation learning method for Sequential Recommendation (H2SeqRec) with pre-training phase. Specifically, we design three self-supervised tasks to obtain the pre-training item embeddings to feed or fuse into the following recommendation architecture (with two ways to use the pre-trained embeddings). In the recommendation phase, we learn multi-scale item embeddings via a hierarchical structure to capture multiple time-span information. To alleviate the negative impact of sparse hypergraphs, we utilize a hyperbolic space-based hypergraph convolutional neural network to learn the dynamic item embeddings. Also, we design an item enhancement module to capture dynamic social information at each timestamp to improve effectiveness. Extensive experiments are conducted on two real-world datasets to prove the effectiveness and high performance of the model.

The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the regularity of both dynamical and steady Boltzmann equation in strictly convex domain with the Cercignani-Lampis (C-L) boundary condition. The C-L boundary condition describes the intermediate reflection law between diffuse reflection and specular reflection via two accommodation coefficients. We construct local weighted $C^1$ dynamical solution using repeated interaction through the characteristic. When we assume small fluctuation to the wall temperature and accommodation coefficients, we construct weighted $C^1$ steady solution., Comment: arXiv admin note: text overlap with arXiv:1906.01808, arXiv:2103.14665

Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides theoretical analysis and empirical results on when and where to use hyperbolic space and hyperbolic embeddings in recommender systems. Specifically, we answer the questions that which type of models and datasets are more suited for hyperbolic space, as well as which latent size to choose. We evaluate our answers by comparing the performance of Euclidean space and hyperbolic space on different latent space models in both general item recommendation domain and social recommendation domain, with 6 widely used datasets and different latent sizes. Additionally, we propose a new metric learning based recommendation method called SCML and its hyperbolic version HSCML. We evaluate our conclusions regarding hyperbolic space on SCML and show the state-of-the-art performance of hyperbolic space by comparing HSCML with other baseline methods.

This paper explores the use of hyperbolic geometry and deep learning techniques for recommendation. We present Hyperbolic Neural Collaborative Recommender (HNCR), a deep hyperbolic representation learning method that exploits mutual semantic relations among users/items for collaborative filtering (CF) tasks. HNCR contains two major phases: neighbor construction and recommendation framework. The first phase introduces a neighbor construction strategy to construct a semantic neighbor set for each user and item according to the user-item historical interaction. In the second phase, we develop a deep framework based on hyperbolic geometry to integrate constructed neighbor sets into recommendation. Via a series of extensive experiments, we show that HNCR outperforms its Euclidean counterpart and state-of-the-art baselines., Comment: arXiv admin note: substantial text overlap with arXiv:2102.09389

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^\infty$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^\infty$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate., Comment: Chen, H., Kim, C. & Li, Q. Local Well-Posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition. J Stat Phys 179, 535-631 (2020). https://doi.org/10.1007/s10955-020-02545-9