Large Reasoning Models (LRMs) have recently demonstrated impressive performance across a range of reasoning tasks by generating intermediate thoughts. However, these models can suffer from overthinking—generating excessive tokens that contribute little to final accuracy while increasing inference cost. To mitigate this, we propose TIV (Thought Injection via Vectors), an innovative framework that compresses token-level reasoning into compact vectors without sacrificing performance. Rather than generating explicit thoughts, TIV injects learnable vectors into the post-attention hidden states of the final token across Transformer layers, enabling implicit and lightweight reasoning. We further introduce a two-stage reinforcement learning strategy: the first stage calibrates the model's reasoning distribution, and the second distills it into a vector-based policy optimized for both accuracy and brevity. Experiments on three reasoning benchmarks show that TIV preserves over 99% of the original accuracy while reducing output length by more than 65% on average, reaching up to 80% in some cases. Moreover, TIV consistently achieves superior trade-offs between accuracy and efficiency compared to existing methods, distinguishing itself as a state-of-the-art (SOTA) approach for efficient reasoning in LRMs.

Abstract Hypergraph decomposition is a fundamental problem in hypergraph analysis which breaks down hypergraphs into cohesive subgraphs and functional units with dense interactions. Hyperedge intersections and overlaps capture the unique property of shared elements (vertices) between groups (hyperedges) in hypergraphs, revealing cohesive substructures not apparent when focusing solely on individual connections. Despite the significance of hyperedge overlap as a measure of hypergraph cohesiveness, existing models for hypergraph decomposition fail to capture this feature. In this paper, we study the problem of hypergraph decomposition with intersection bounds. We propose the ( k , s )-core, a new cohesive subgraph model incorporating both a vertex degree constraint k and a hyperedge intersection constraint s . This model includes two types: (1) strong ( k , s )-cores, where connected hyperedges share at least s vertices, enforcing strong hyperedge overlap, and (2) weak ( k , s )-cores, where hyperedges are connected through s -walks, allowing for a looser overlap. We prove that our definition of ( k , s )-cores exhibits uniqueness and hierarchical properties. Based on the properties, we develop two decomposition algorithms: a bottom-up algorithm for strong ( k , s )-cores, which uses a heuristic hyperedge removal mechanism to maintain consistent decomposition results and employs a union-find data structure for efficient connectivity identification, and a top-down algorithm for weak ( k , s )-cores that preserves the subgraph containment relationship. Our algorithms achieve traversal efficiency by processing each hyperedge in the hypergraph only once. Additionally, all ( k , s )-cores can be efficiently stored with minimal memory overhead. Comprehensive experiments and case studies show that the ( k , s )-core model outperforms existing methods in capturing cohesive subgraphs with overlaps in hypergraphs. Furthermore, the proposed algorithms demonstrate high efficiency and scalability, making them well-suited for real-world hypergraphs.

Abstract Graph Neural Networks (GNNs) have become essential for solving graph-level tasks, such as classification and regression, across diverse domains including social networks and biology. However, existing GNNs struggle with the expressivity that captures complex structural patterns, and the generalization that ensures robust performance on diverse and noisy datasets. To address these challenges, we propose a novel GNN model that integrates a k -path rooted subgraph encoder, an adaptive graph contrastive learning approach, and a consistency-aware loss. The k -path rooted subgraph encoder enhances expressivity by capturing and distinguishing intricate substructures, with theoretical guarantees for counting paths and cycles. The adaptive graph contrastive learning framework improves generalization by generating domain-aware graph augmentations based on edge importance, while the consistency-aware loss ensures task-relevant properties are preserved across augmented views. Extensive experiments on 26 datasets spanning graph classification, regression, and realistic scenarios such as noise, class imbalance, and few-shot learning show that our model achieves superior performance against 18 state-of-the-art GNN models in both effectiveness and efficiency. The code is released in https://anonymous.4open.science/r/GEGNN .

An area of research on communities in signed networks aims to find structures in which each user in the graph is connected to other members in their community by more positive edges than negative edges, indicating a positive experience for the user. However, some of these communities are ‘echo chambers', a rising area of concern in modern discourse regarding social media, which contain almost exclusively positive edges indicating all users trust each other with little or no push-back. Here exists an interesting contradiction, when finding a ‘positive’ community often times the resulting structure may be the negative ‘echo chamber’. In this work we propose a signed graph community substructure named the$(\epsilon,\ \phi)$-Clique which is the best of both worlds, where each user is happy to be in their community (indicated by have a proportion of positive edges$\geq\epsilon$for each node) as well as there existing a level of disagreement in the system (indicated by the community having a proportion of negative edges$\geq \phi$). From this definition, we design algorithms to exactly find the Maximum$(\epsilon,\ \phi)$-Clique containing a query user, utilising heuristics to combat the NP-Hard and NP-Hard to approximate nature of the problem. We perform experiments to examine the improvements in efficiency of our algorithms to the proposed baseline as well as examine example community outputs to show the effectiveness of our structure.

Many real-world binary relations can be modelled as bipartite graphs, which can be inherently temporal and each edge is associated with a timestamp. The ( α, β )-core, a popular structure that requires minimum degrees over two layers of vertices, is useful for understanding the organisation of bipartite networks. However, the temporal property has rarely been considered in cohesive subgraph mining in bipartite graphs. This gap prevents the finding of time-sensitive ( α, β )-cores in real-world applications. In this paper, we aim at finding ( α, β )-cores within any time window over a temporal bipartite graph. To address this problem, we propose a novel DAG (Directed Acyclic Graph)-like hierarchy with qualified time windows to describe the temporal containment property of the ( α, β )-core. Furthermore, we construct the superior-optimized index which significantly optimizes space complexity and guarantees efficient query performance. We also propose a maintenance approach that can efficiently update the index by removing stale information and incorporating newly inserted temporal edges. Extensive experiments are conducted on eight real-world graphs and the results show the effectiveness and efficiency of our indexes.

Signed bipartite graphs represent relationships between two sets of entities, including both positive and negative interactions, allowing for a more comprehensive modeling of real-world networks. In this work, we focus on the detection of cohesive subgraphs in signed bipartite graphs by leveraging the concept of balanced butterflies. A balanced butterfly is a cycle of length 4 that is considered stable if it contains an even number of negative edges. We propose a novel model called the balanced ( k , ϵ)-bitruss, which provides a concise representation of cohesive signed bipartite subgraphs while enabling control over density ( k ) and balance (ϵ). We prove that finding the largest balanced ( k , ϵ)-bitruss is NP-hard and cannot be efficiently approximated to a significant extent. Furthermore, we extend the unsigned butterfly counting framework to efficiently compute both balanced and unbalanced butterflies. Based on this technique, we develop two greedy heuristic algorithms: one that prioritizes followers and another that focuses on balanced support ratios. Experimental results demonstrate that the greedy approach based on balanced support ratios outperforms the follower-based approach in terms of both efficiency and effectiveness.

Community search (CS) aims at personalized subgraph discovery which is the key to understanding the organisation of many real-world networks. CS in undirected networks has attracted significant attention from researchers, including many solutions for various cohesive subgraph structures and for different levels of dynamism with edge insertions and deletions, while they are much less considered for directed graphs. In this paper, we propose incremental solutions of CS based on the D-truss in dynamic directed graphs, where the D-truss is a cohesive subgraph structure defined based on two types of triangles in directed graphs. We first analyze the theoretical boundedness of D-truss given edge insertions and deletions, then we present basic single-update algorithms. To improve the efficiency, we propose an order-based D-Index, associated batch-update algorithms and a fully-dynamic query algorithm. Our extensive experiments on real-world graphs show that our proposed solution achieves a significant speedup compared to the SOTA solution, the scalability over updates is also verified.

Online social networks have greatly facilitated our lives but have also propagated the spreading of rumours. Traditional works mostly find rumors from content, but content can be strategically manipulated to evade such detection, making these methods brittle. To improve the accuracy and robustness of rumor detection, we propose to integrate and exploit the content, propagation structure, and temporal relations because information in the networks always spreads dynamically with significant structures. In this paper, we propose a novel rumor detection framework in online temporal networks via structure learning. Specifically, to exploit the propagation structure, we propose a novel hyperedge walking strategy on a meta-hyperedge graph to learn the representations of sub-structures in the networks. Then a hyperedge expansion method is proposed to generate more global structural features. The expanded hyperedges are more hierarchical, making the learned structural embeddings more expressive. To make full use of content, we design a hypergraph learning model using hyperedge expansion to fuse node content with structural features and generate comprehensive representations for the entire graph. To exploit temporal relations, we design a masked temporal attention unit for learning the evolving patterns of the network. Extensive evaluations with six state-of-the-art baselines on two real-world datasets demonstrate the superiority of our solution.

Owing to its nature of scalability and privacy by design, federated learning (FL) has received increasing interest in decentralized deep learning. FL has also facilitated recent research on upscaling and privatizing personalized recommendation services, using on-device data to learn recommender models locally. These models are then aggregated globally to obtain a more performant model while maintaining data privacy. Typically, federated recommender systems (FRSs) do not take into account the lack of resources and data availability at the end-devices. In addition, they assume that the interaction data between users and items is i.i.d. and stationary across end-devices (i.e., users), and that all local recommender models can be directly averaged without considering the user’s behavioral diversity. However, in real scenarios, recommendations have to be made on end-devices with sparse interaction data and limited resources. Furthermore, users’ preferences are heterogeneous and they frequently visit new items. This makes their personal preferences highly skewed, and the straightforwardly aggregated model is thus ill-posed for such non-i.i.d. data. In this article, we propose Resource Efficient Federated Recommender System (ReFRS) to enable decentralized recommendation with dynamic and diversified user preferences. On the device side, ReFRS consists of a lightweight self-supervised local model built upon the variational autoencoder for learning a user’s temporal preference from a sequence of interacted items. On the server side, ReFRS utilizes a scalable semantic sampler to adaptively perform model aggregation within each identified cluster of similar users. The clustering module operates in an asynchronous and dynamic manner to support efficient global model update and cope with shifting user interests. As a result, ReFRS achieves superior performance in terms of both accuracy and scalability, as demonstrated by comparative experiments on real datasets.

Abstract Uncertain butterflies are one of, if not the, most important graphlet structures on uncertain bipartite networks. In this paper, we examine the uncertain butterfly structure (in which the existential probability of the graphlet is greater than or equal to a threshold parameter), as well as the global Uncertain Butterfly Counting Problem (to count the total number of these instances over an entire network). To solve this task, we propose a non-trivial exact baseline ( UBFC ), as well as an improved algorithm ( IUBFC ) which we show to be faster both theoretically and practically. We also design two sampling frameworks ( UBS and PES ) which can sample either a vertex, edge or wedge from the network uniformly and estimate the global count quickly. Furthermore, a notable butterfly-based community structure which has been examined in the past is the k -bitruss. We adapt this community structure onto the uncertain bipartite graph setting and introduce the Uncertain Bitruss Decomposition Problem (which can be used to directly answer any k -bitruss search query for any k ). We then propose an exact algorithm ( UBitD ) to solve our problem with three variations in deriving the initial uncertain support. Using a range of networks with different edge existential probability distributions, we validate the efficiency and effectiveness of our solutions.

Bipartite graphs are naturally used to model relationships between two different types of entities. On bipartite graphs, maximum biclique search is a fundamental problem that aims to find the complete bipartite subgraph (biclique) with the maximum number of edges and is widely adopted for many applications such as anomaly detection in E-commerce and social network analysis. However, maximum biclique search only identifies the biclique whose size is globally maximum, whereas fast microscopic (personalized) analysis is needed in many real-world scenarios. For instance, when a suspected user is identified in an E-commerce network (e.g., a user-product network), it is important to quickly find the anomalous group containing the user and send the group of users for further human expert investigation. To fill this research gap, for the first time, we study the efficient personalized maximum biclique search problem, which aims to find the maximum biclique containing a specific query vertex in real-time. Apart from online computation algorithms, we explore index-based approaches and propose the PMBC-Index. With the PMBC-Index, the query algorithm is up to five orders of magnitude faster than the baseline algorithms. Furthermore, effective pruning strategies and parallelization techniques are devised to support efficient index construction. Extensive experiments on 10 real-world graphs validate both the effectiveness and the efficiency of our proposed techniques.

Mining cohesive subgraphs on bipartite graphs is an important task. The k -bitruss is one of many popular cohesive subgraph models, which is the maximal subgraph where each edge is contained in at least k butterflies. The bitruss decomposition problem is to find all k -bitrusses for k ≥ 0. Dealing with large graphs is often beyond the capability of a single machine due to its limited memory and computational power, leading to a need for efficiently processing large graphs in a distributed environment. However, all current solutions are for a single machine and a centralized environment, where processors can access the graph or auxiliary indexes randomly and globally. It is difficult to directly deploy such algorithms on a shared-nothing model. In this paper, we propose distributed algorithms for bitruss decomposition. We first propose SC-HBD as the baseline, which uses H -function to define bitruss numbers and computes them iteratively to a fix point in parallel. We then introduce a subgraph-centric peeling method SC-PBD, which peels edges in batches over different butterfly complete subgraphs. We then introduce local indexes on each fragment, study the butterfly-aware edge partition problem including its hardness, and propose an effective partitioner. Finally we present the bitruss butterfly-complete subgraph concept, and divide and conquer DC-BD method with optimization strategies. Extensive experiments show the proposed methods solve graphs with 30 trillion butterflies in 2.5 hours, while existing parallel methods under shared-memory model fail to scale to such large graphs.

When considering uncertain bipartite networks, the number of instances of the popular graphlet structure the butterfly may be used as an important metric to quickly gauge information about the network. This Uncertain Butterfly Count has practical usages in a variety of areas such as biomedical/biological fields, E-Commerce and road networks. In this paper we formally define the uncertain butterfly structure (in which the existential probability of the butterfly is greater than or equal to some user-defined threshold t ) as well as the Uncertain Butterfly Counting Problem (to determine the number of unique instances of this structure on any uncertain bipartite network). We then examine exact solutions by proposing a non-trivial baseline (UBFC) as well as an improved solution (IUBFC) which reduces the time complexity and employs heuristics to further reduce the runtime in practice. In addition to exact solutions, we propose two approximate solutions via sampling, UBS and PES , which can be used to quickly estimate the Uncertain Butterfly Count, a powerful tool when the exact count is unnecessary. Using a range of networks with different edge existential probability distributions, we validate the efficiency and effectiveness of our solutions.

Session-based Recommendation (SR) is the task of recommending the next item based on previously recorded user interactions. In this work, we study SR in a practical streaming scenario, namely Streaming Session-based Recommendation (SSR), which is a more challenging task due to (1) the uncertainty of user behaviors, and (2) the continuous, large-volume, high-velocity nature of the session data. Recent studies address (1) by exploiting the attention mechanism in Recurrent Neural Network (RNN) to better model the user's current intent, which leads to promising improvements. However, the proposed attention models are based solely on the current session. Moreover, existing studies only perform SR under static offline settings and none of them explore (2). In this work, we target SSR and propose a Streaming Session-based Recommendation Machine (SSRM) to tackle these two challenges. Specifically, to better understand the uncertainty of user behaviors, we propose a Matrix Factorization (MF) based attention model, which improves the commonly used attention mechanism by leveraging the user's historical interactions. To deal with the large-volume and high-velocity challenge, we introduce a reservoir-based streaming model where an active sampling strategy is proposed to improve the efficiency of model updating. We conduct extensive experiments on two real-world datasets. The experimental results demonstrate the superiority of the SSRM method compared to several state-of-the-art methods in terms of MRR and Recall.