The Process Reward Model (PRM) plays a crucial role in mathematical reasoning tasks, requiring high-quality supervised process data. However, we observe that reasoning steps generated by Large Language Models (LLMs) often fail to exhibit strictly incremental information, leading to redundancy that can hinder effective reasoning. To address this issue, we propose CFPRM, a simple yet effective coarse-to-fine strategy. Instead of focusing on the detection of redundant steps, our approach first establishes a coarse-grained window to merge adjacent reasoning steps into unified, holistic steps. The window size is then progressively reduced to extract fine-grained reasoning steps, enabling data collection at multiple granularities for training. By leveraging this hierarchical refinement process, CFPRM mitigates redundancy while preserving essential fine-grained knowledge. Extensive experiments on two reasoning datasets across three loss criteria validate the CFPRM's effectiveness and versatility.

Large Language Models (LLMs) have achieved impressive results in processing text data, which has sparked interest in applying these models beyond textual data, such as graphs. In the field of graph learning, there is a growing interest in harnessing LLMs to comprehend and manipulate graph-structured data. Existing research predominantly focuses on graphs with rich textual features, such as knowledge graphs or text attribute graphs, leveraging LLMs' ability to process text but inadequately addressing graph structure. This work specifically aims to assess and enhance LLMs' abilities to comprehend and utilize the structural knowledge inherent in graph data itself, rather than focusing solely on graphs rich in textual content. To achieve this, we introduce the \textbf{G}raph \textbf{U}nderstanding for \textbf{N}atural Language \textbf{D}riven \textbf{A}nalytical \textbf{M}odel (\model). This model adapts LLMs to better understand and engage with the structure of graph data, enabling them to perform complex reasoning tasks by leveraging the graph's structure itself. Our experimental evaluations on graph reasoning benchmarks not only substantiate that \model~ outperforms the SOTA baselines for comparisons. But also reveals key factors affecting the graph reasoning capabilities of LLMs. Moreover, we provide a theoretical analysis illustrating how reasoning paths can enhance LLMs' reasoning capabilities.

Graph autoencoders (GAEs), as a kind of generative self-supervised learning approach, have shown great potential in recent years. GAEs typically rely on distance-based criteria, such as mean-square-error (MSE), to reconstruct the input graph. However, relying solely on a single reconstruction criterion may lead to a loss of distinctiveness in the reconstructed graph, causing nodes to collapse into similar representations and resulting in sub-optimal performance. To address this issue, we have developed a simple yet effective strategy to preserve the necessary distinctness in the reconstructed graph. Inspired by the knowledge distillation technique, we found that the dual encoder-decoder architecture of GAEs can be viewed as a teacher-student relationship. Therefore, we propose transferring the knowledge of distinctness from the raw graph to the reconstructed graph, achieved through a simple KL constraint. Specifically, we compute pairwise node similarity scores in the raw graph and reconstructed graph. During the training process, the KL constraint is optimized alongside the reconstruction criterion. We conducted extensive experiments across three types of graph tasks, demonstrating the effectiveness and generality of our strategy. This indicates that the proposed approach can be employed as a plug-and-play method to avoid vague reconstructions and enhance overall performance.

Graphs are ubiquitous in real-world scenarios and encompass a diverse range of tasks, from node-, edge-, and graph-level tasks to transfer learning. However, designing specific tasks for each type of graph data is often costly and lacks generalizability. Recent endeavors under the "Pre-training + Fine-tuning" or "Pre-training + Prompt" paradigms aim to design a unified framework capable of generalizing across multiple graph tasks. Among these, graph autoencoders (GAEs), generative self-supervised models, have demonstrated their potential in effectively addressing various graph tasks. Nevertheless, these methods typically employ multi-stage training and require adaptive designs, which on one hand make it difficult to be seamlessly applied to diverse graph tasks and on the other hand overlook the negative impact caused by discrepancies in task objectives between the different stages. To address these challenges, we propose GA^2E, a unified adversarially masked autoencoder capable of addressing the above challenges seamlessly. Specifically, GA^2E proposes to use the subgraph as the meta-structure, which remains consistent across all graph tasks (ranging from node-, edge-, and graph-level to transfer learning) and all stages (both during training and inference). Further, GA^2E operates in a \textbf{"Generate then Discriminate"} manner. It leverages the masked GAE to reconstruct the input subgraph whilst treating it as a generator to compel the reconstructed graphs resemble the input subgraph. Furthermore, GA^2E introduces an auxiliary discriminator to discern the authenticity between the reconstructed (generated) subgraph and the input subgraph, thus ensuring the robustness of the graph representation through adversarial training mechanisms. We validate GA^2E's capabilities through extensive experiments on 21 datasets across four types of graph tasks.

In recent years, contrastive learning has emerged as a dominant self-supervised paradigm, attracting numerous research interests in the field of graph learning. Graph contrastive learning (GCL) aims to embed augmented anchor samples close to each other while pushing the embeddings of other samples (negative samples) apart. However, existing GCL methods require large and diverse negative samples to ensure the quality of embeddings, and recent studies typically leverage samples excluding the anchor and positive samples as negative samples, potentially introducing false negative samples (negatives that share the same class as the anchor). Additionally, this practice can result in heavy computational burden and high time complexity of $O(N^2)$, which is particularly unaffordable for large graphs. To address these deficiencies, we leverage rank learning and propose a simple yet effective model, GraphRank. Specifically, we first generate two graph views through corruption. Then, we compute the similarity of pairwise nodes (anchor node and positive node) in both views, an arbitrary node in the latter view is selected as a negative node, and its similarity with the anchor node is computed. Based on this, we introduce rank-based learning to measure similarity scores which successfully relieve the false negative provlem and decreases the time complexity from $O(N^2)$ to $O(N)$. Moreover, we conducted extensive experiments across multiple graph tasks, demonstrating that GraphRank performs favorably against other cutting-edge GCL methods in various tasks.

Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction fairly may degrade the performance. For example, the interactions of a useless feature may introduce noises; the importance of a feature may also differ when interacting with different features. In this work, we propose a novel model named \emph{Interaction-aware Factorization Machine} (IFM) by introducing Interaction-Aware Mechanism (IAM), which comprises the \emph{feature aspect} and the \emph{field aspect}, to learn flexible interactions on two levels. The feature aspect learns feature interaction importance via an attention network while the field aspect learns the feature interaction effect as a parametric similarity of the feature interaction vector and the corresponding field interaction prototype. IFM introduces more structured control and learns feature interaction importance in a stratified manner, which allows for more leverage in tweaking the interactions on both feature-wise and field-wise levels. Besides, we give a more generalized architecture and propose Interaction-aware Neural Network (INN) and DeepIFM to capture higher-order interactions. To further improve both the performance and efficiency of IFM, a sampling scheme is developed to select interactions based on the field aspect importance. The experimental results from two well-known datasets show the superiority of the proposed models over the state-of-the-art methods.

Rumor blocking is a serious problem in large-scale social networks. Malicious rumors could cause chaos in society and hence need to be blocked as soon as possible after being detected. In this paper, we propose a model of dynamic rumor influence minimization with user experience (DRIMUX). Our goal is to minimize the influence of the rumor (i.e., the number of users that have accepted and sent the rumor) by blocking a certain subset of nodes. A dynamic Ising propagation model considering both the global popularity and individual attraction of the rumor is presented based on realistic scenario. In addition, different from existing problems of influence minimization, we take into account the constraint of user experience utility. Specifically, each node is assigned a tolerance time threshold. If the blocking time of each user exceeds that threshold, the utility of the network will decrease. Under this constraint, we then formulate the problem as a network inference problem with survival theory, and propose solutions based on maximum likelihood principle. Experiments are implemented based on large-scale real world networks and validate the effectiveness of our method.