Neural Gaussian Similarity Modeling for Differential Graph Structure Learning (2312.09498v1)

Abstract: Graph Structure Learning (GSL) has demonstrated considerable potential in the analysis of graph-unknown non-Euclidean data across a wide range of domains. However, constructing an end-to-end graph structure learning model poses a challenge due to the impediment of gradient flow caused by the nearest neighbor sampling strategy. In this paper, we construct a differential graph structure learning model by replacing the non-differentiable nearest neighbor sampling with a differentiable sampling using the reparameterization trick. Under this framework, we argue that the act of sampling \mbox{nearest} neighbors may not invariably be essential, particularly in instances where node features exhibit a significant degree of similarity. To alleviate this issue, the bell-shaped Gaussian Similarity (GauSim) modeling is proposed to sample non-nearest neighbors. To adaptively model the similarity, we further propose Neural Gaussian Similarity (NeuralGauSim) with learnable parameters featuring flexible sampling behaviors. In addition, we develop a scalable method by transferring the large-scale graph to the transition graph to significantly reduce the complexity. Experimental results demonstrate the effectiveness of the proposed methods.

• The paper introduces a differential framework for graph structure learning that overcomes non-differentiable sampling using Gumbel-Softmax and Neural Gaussian Similarity.
• It presents NeuralGauSim with learnable parameters that dynamically adjust edge sampling probabilities, yielding superior performance against baseline models.
• The method incorporates a transition graph technique that enhances scalability and computational efficiency for handling large and complex graph datasets.

An Overview of Neural Gaussian Similarity Modeling for Differential Graph Structure Learning

The paper investigates Graph Structure Learning (GSL), which is pivotal in the analysis of non-Euclidean data derived from diverse domains. Conventional graph neural networks often confront challenges when graph structures are unknown, requiring end-to-end models that can construct these structures while preserving the integrity of gradient flow. The authors propose an innovative solution to this problem through differential graph structure modeling using Neural Gaussian Similarity Modeling.

Key Contributions

1. Differential Graph Structure Learning: The paper outlines the development of a differential framework for GSL by employing the reparameterization trick with the Gumbel-Softmax distribution. This step addresses the impediment of non-differentiable sampling in traditional nearest neighbor models. The proposed approach leverages Gaussian Similarity (GauSim) to provide a differentiable path, thereby facilitating seamless integration with gradient-based optimization typical in neural networks.
2. Neural Gaussian Similarity (NeuralGauSim): The authors introduce NeuralGauSim, which incorporates learnable parameters to model the edge sampling probability with more flexibility and adaptability than conventional linear models. Theoretical analysis underscores that linear sampling strategies may not be essential in cases of high similarity between node features. NeuralGauSim, with its bell-shaped Gaussian function, allows for dynamic adjustment of sampling probability irrelevant to linear assumptions, thereby optimizing the learning process across varying graph similarities.
3. Transition Graph Structure Learning: Recognizing scalability as a significant bottleneck in large-scale graphs, the authors propose transitioning the graph representation to a more manageable format. This involves transforming the initial feature matrix into a transitional feature set that optimizes both computational efficiency and information retention. This transformation not only alleviates the computational burden but also assures robustness against information loss evident in some random sampling methods.

Experimental Validation

Extensive experiments validate the effectiveness of the proposed methodologies across a suite of datasets representing citation networks, Wikipedia page networks, co-author networks, text, and image classification. The results consistently indicate that NeuralGauSim and its transition graph variant deliver superior performance in learning meaningful embeddings for nodes, affirming its advantages over baseline models such as IDGL, NodeFormer, and SLAPS. Notably, performance improvements are evident even as the complexity of the graphs increases, with NeuralGauSim proving robust in balancing computational demands and precision.

Implications and Future Directions

The implications of this research extend into various domains where graph-structured data are prevalent. By overcoming traditional barriers to gradient flow with non-differentiable elements, this framework significantly bolsters the capability of GSL algorithms to perform efficiently and effectively.

Theoretically, this work posits that the Gaussian similarity model can adapt to dynamic feature environments, suggesting a rich area for further exploration into adaptive models for even more generalized graph types, including heterogeneous and multiplex graphs.

Practically, the scalability offered by the transition graph method envisions real-world applications that require processing vast quantities of data quickly and reliably, such as social media networks, biological networks, and integrated data systems found in complex software architectures.

Conclusion

In conclusion, the paper presents a substantial advancement in GSL through Neural Gaussian Similarity Modeling, providing a novel paradigm that addresses both the differentiation and scalability challenges inherent in traditional graph learning approaches. Future research could expand upon these findings by exploring even more sophisticated representations and varied applications, consolidating the strength and adaptability of this framework in the broader landscape of machine learning and artificial intelligence.