Interpreting and Unifying Graph Neural Networks with An Optimization Framework (2101.11859v1)

Abstract: Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.

• The paper introduces a unified framework that interprets diverse GNN propagation mechanisms as solutions to an optimization problem.
• It reframes the propagation process through a feature fitting function over graph kernels paired with a regularization term, linking models like GCN, PPNP/APPNP, JKNet, and DAGNN.
• The research further develops novel GNN models, GNN-LF and GNN-HF, which flexibly adjust filtering capabilities to enhance node representation and mitigate over-smoothing.

Interpreting and Unifying Graph Neural Networks with An Optimization Framework

In the field of machine learning, Graph Neural Networks (GNNs) have become pivotal for tasks involving graph-structured data. This paper seeks to address the lack of cohesive understanding among the numerous GNN propagation mechanisms by proposing a unified optimization framework that elucidates the intrinsic connections between them.

The research posits that all notable GNN propagation techniques can ultimately be understood as the solution to an optimization problem. This optimization problem consists of a feature fitting function over graph kernels, accompanied by a graph regularization term. In essence, this unified perspective demonstrates that the diversity of GNN architectures can be encapsulated within a singular framework, thus offering a macroscopic view of their varied mechanisms.

The novel contribution of this paper lies in two particular advancements. First, the researchers introduce a general framework via which pre-existing GNNs can be analyzed, thereby providing a systematic way to compare their propagation mechanisms. This is accomplished by reframing the propagation process as an optimization problem, where the solution to this optimization yields the GNN's learned node representations. This insight is leveraged to deduce that the propagation mechanisms of popular GNN models, including but not limited to GCN, PPNP/APPNP, and more recent designs like JKNet and DAGNN, are essentially aiming to solve variants of this optimization problem.

Secondly, building on the insights drawn from this framework, the authors propose novel GNN models — termed GNN-LF (Low-pass Filtering) and GNN-HF (High-pass Filtering) — which enhance the expressive power of GNNs by incorporating more flexible filtering capabilities in the node feature space. These models offer improved performance by allowing the adjustment of graph convolutional kernels to exhibit either low-pass or high-pass filtering characteristics. This flexibility is instrumental in alleviating the issue of over-smoothing, often encountered when stacking multiple GNN layers.

The models are supported by the theoretical analysis of their convergence and expressive powers, underscoring their effectiveness in maintaining rich node representations over extensive propagation depths. Experimentation on numerous benchmark datasets highlights that these newly devised GNNs surpass state-of-the-art baselines in terms of classification accuracy and robustness against over-smoothing.

In practical terms, understanding GNNs through this proposed optimization framework provides a clear path for designing more sophisticated models that can dynamically adjust to various graph-structured data environments. Additionally, it opens avenues for future research directions that could further refine GNN architectures by exploring bespoke objective functions tailored to specific needs or constraints inherent to particular datasets or tasks. Theoretical implications extend to more profound inquiries into the nature of information propagation on graphs, particularly in how diverse forms of node interdependence can be modeled and utilized effectively.

The paper, therefore, contributes not merely a toolkit for analyzing existing GNNs but also a blueprint for future explorations and innovations within the field of graph-based learning systems.