In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that eigenvalues for the normalized Laplacian matrix are distinct from each other, thus expecting a polynomial filter to have a high fitting ability. However, this paper empirically observes that normalized Laplacian matrices frequently possess repeated eigenvalues. Moreover, we theoretically establish that the number of distinguishable eigenvalues plays a pivotal role in determining the expressive power of spectral graph neural networks. In light of this observation, we propose an eigenvalue correction strategy that can free polynomial filters from the constraints of repeated eigenvalue inputs. Concretely, the proposed eigenvalue correction strategy enhances the uniform distribution of eigenvalues, thus mitigating repeated eigenvalues, and improving the fitting capacity and expressive power of polynomial filters. Extensive experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.

Deep cross-media hashing provides an efficient semantic representation learning solution for large-scale cross-media retrieval. The existing methods only consider the inter-media or intra-media semantic association learning, ignore the guiding of semantic structure information, and have weak reasoning ability for implicit fine-grained semantic associations. To tackle this problem, we propose a novel structures aware fine-grained contrastive adversarial hashing method for cross-media retrieval. A novel cross-media contrastive adversarial hash network is constructed for the first time, which integrates the cross-media and intra-media contrastive learning and multi-modal adversarial learning, aiming at maximizing the semantic association between different modalities, and improving the semantic discrimination and consistency of cross-media unified hash representation, thereby the inter-media and intra-media semantic preserving ability can be well enhanced; A fine-grained cross-media semantic feature learning method based on fine-grained semantic reasoning with transformers is proposed, which captures fine-grained salient features of different modalities for semantic association learning, and enhances the reasoning ability of fine-grained implicit semantic association; A semantic label graph convolutional network guided cross-media semantic association learning strategy is proposed, which makes full use of semantic structure information to enhance the learning ability of implicit cross-media semantic associations. Extensive experiments on several large-scale cross-media benchmark datasets demonstrate that the proposed method outperforms the state-of-the-art methods.

In the evolving landscape of recommender systems, Graph Contrastive Learning (GCL) has become a prominent method for enhancing recommendation performance by alleviating the issue of data sparsity. However, existing GCL-based recommendations often overlook the control of shared information between the contrastive views. In this paper, we initially analyze and experimentally demonstrate these methods often lead to the issue of augmented representation collapse, where the representations between views become excessively similar, diminishing their distinctiveness. To address this issue, we propose the Information-Controllable Graph Contrastive Learning (IGCL) framework, a novel approach that focuses on optimizing the shared information between views to include as much relevant information for the recommendation task as possible while maintaining an appropriate level. In particular, we design the Collaborative Signals Enhanced Augmentation module to infuse the augmented representation with rich, task-relevant collaborative signals. Furthermore, the Information-Controllable Contrastive Learning module is designed to direct control over the magnitude of shared information between the contrastive views to avoid over-similarity. Extensive experiments on three public datasets demonstrate the effectiveness of IGCL, showcasing significant improvements in performance and the capability to alleviate augmented representation collapse.

The task of Knowledge-Based Question Generation (KBQG) involves generating natural language questions from structured knowledge sources, posing unique challenges in balancing linguistic diversity and semantic relevance. Existing models often focus on maximizing surface-level similarity to ground-truth questions, neglecting the need for diverse syntactic forms and leading to semantic drift during generation. To overcome these challenges, we propose Refine-Reinforced Diverse Question Generation (R2DQG), a two-phase framework leveraging a generation-then-refinement paradigm. The Generator first constructs a diverse set of expressive templates using dependency parse tree similarity, capturing a wide range of syntactic patterns and styles. These templates guide the creation of question drafts, ensuring both diversity and semantic relevance. In the second phase, a Corrector module refines the drafts to mitigate semantic drift and enhance overall coherence and quality. Experiments on public datasets show that R2DQG outperforms state-of-the-art models in generating diverse, contextually accurate questions. Moreover, synthetic datasets generated by R2DQG enhance downstream QA performance, underscoring the practical utility of our approach.