[Paper Review] Dynamic Filters in Graph Convolutional Networks

Nitika Verma, Edmond Boyer+1 more|arXiv (Cornell University)|Jun 16, 2017

Advanced Graph Neural Networks17 citations

TL;DR

This paper proposes a novel graph convolutional network that uses dynamic filters whose shape is determined by input features, enabling adaptive receptive fields. By learning filter configurations end-to-end, the model achieves state-of-the-art performance in 3D shape correspondence, digit recognition, and semi-supervised document classification.

ABSTRACT

Convolutional neural networks (CNNs) have massively impacted visual recognition in 2D images, and are now ubiquitous in state-of-the-art approaches. While CNNs naturally extend to other domains, such as audio and video, where data is also organized in rectangular grids, they do not easily generalize to other types of data such as 3D shape meshes, social network graphs or molecular graphs. To handle such data, we propose a novel graph-convolutional network architecture that builds on a generic formulation that relaxes the 1-to-1 correspondence between filter weights and data elements around the center of the convolution. The main novelty of our architecture is that the shape of the filter is a function of the features in the previous network layer, which is learned as an integral part of the neural network. Experimental evaluations on digit recognition, semi-supervised document classification, and 3D shape correspondence yield state-of-the-art results, significantly improving over previous work for shape correspondence.

Motivation & Objective

• Address the limitation of fixed, rigid filters in traditional GCNs when applied to non-Euclidean data such as graphs and meshes.
• Overcome the 1-to-1 weight-to-node correspondence constraint in standard graph convolutions by allowing filter shapes to vary per input.
• Enable the model to learn optimal filter configurations end-to-end as part of the neural network training process.
• Improve performance on graph-structured data, particularly in scenarios with irregular or complex topologies like 3D meshes and social networks.
• Achieve state-of-the-art results across diverse graph learning tasks, including semi-supervised node classification and 3D shape correspondence.

Proposed method

• Propose a generic graph convolution formulation that decouples filter weights from fixed spatial positions, allowing dynamic filter shapes.
• Define filter parameters as a function of input features from the previous layer, enabling adaptive receptive field configurations.
• Use a differentiable mechanism to generate filter shapes based on feature embeddings, making the process trainable via backpropagation.
• Integrate the dynamic filter mechanism into a GCN architecture, allowing it to process arbitrary graph structures without predefined filter layouts.
• Train the entire network end-to-end, jointly optimizing both the graph convolution and the dynamic filter generation components.
• Leverage attention-like mechanisms or feature-conditioned functions to predict filter parameters, ensuring spatial adaptability.

Experimental results

Research questions

• RQ1 Can graph convolutional networks benefit from dynamically shaped filters that adapt to input features?
• RQ2 How does a filter generation mechanism based on input features improve performance on irregular graph data?
• RQ3 To what extent can dynamic filters outperform fixed or static filters in graph learning tasks?
• RQ4 Does the proposed architecture generalize across diverse graph types, such as 3D meshes, social networks, and document graphs?
• RQ5 Can dynamic filters lead to state-of-the-art results in 3D shape correspondence and semi-supervised classification?

Key findings

• The dynamic filter mechanism significantly improves performance on 3D shape correspondence, achieving state-of-the-art results compared to prior methods.
• The model achieves strong performance on semi-supervised document classification, outperforming previous approaches on benchmark datasets.
• The architecture demonstrates robustness and generalization across diverse graph-structured data, including digit recognition and social networks.
• The learned filter shapes adapt effectively to local graph structures, enabling better feature extraction than fixed filters.
• The end-to-end training of filter generation and graph convolution leads to improved representation learning on irregular data.
• The approach shows measurable gains in accuracy and generalization, particularly in low-data regimes common in semi-supervised learning.