Using Random Noise Equivariantly to Boost Graph Neural Networks Universally

• URL: http://arxiv.org/abs/2502.02479v1
• Date: Tue, 04 Feb 2025 16:54:28 GMT
• Title: Using Random Noise Equivariantly to Boost Graph Neural Networks Universally
• Authors: Xiyuan Wang, Muhan Zhang,
• Abstract summary: Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. This paper lays down a theoretical framework that elucidates the increased sample complexity when random noise into GNNs without careful design. We propose Equivariant Noise GNN (ENGNN), a novel architecture that harnesses the symmetrical properties of noise to sample complexity and bolster generalization.
• Score: 27.542173012315413
• License:
• Abstract: Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures tailored to exploit noise for specific tasks excel yet lack broad applicability. This paper tackles these issues by laying down a theoretical framework that elucidates the increased sample complexity when introducing random noise into GNNs without careful design. We further propose Equivariant Noise GNN (ENGNN), a novel architecture that harnesses the symmetrical properties of noise to mitigate sample complexity and bolster generalization. Our experiments demonstrate that using noise equivariantly significantly enhances performance on node-level, link-level, subgraph, and graph-level tasks and achieves comparable performance to models designed for specific tasks, thereby offering a general method to boost expressivity across various graph tasks.

Related papers

• Noise-Resilient Unsupervised Graph Representation Learning via Multi-Hop Feature Quality Estimation [53.91958614666386]
  Unsupervised graph representation learning (UGRL) based on graph neural networks (GNNs) We propose a novel UGRL method based on Multi-hop feature Quality Estimation (MQE)
  arXiv  Detail & Related papers  (2024-07-29T12:24:28Z)
• DEGNN: Dual Experts Graph Neural Network Handling Both Edge and Node Feature Noise [5.048629544493508]
  Graph Neural Networks (GNNs) have achieved notable success in various applications over graph data. Recent research has revealed that real-world graphs often contain noise, and GNNs are susceptible to noise in the graph. We present DEGNN, a novel GNN model designed to adeptly mitigate noise in both edges and node features.
  arXiv  Detail & Related papers  (2024-04-14T10:04:44Z)
• Feature Noise Boosts DNN Generalization under Label Noise [65.36889005555669]
  The presence of label noise in the training data has a profound impact on the generalization of deep neural networks (DNNs) In this study, we introduce and theoretically demonstrate a simple feature noise method, which directly adds noise to the features of training data.
  arXiv  Detail & Related papers  (2023-08-03T08:31:31Z)
• Walking Noise: On Layer-Specific Robustness of Neural Architectures against Noisy Computations and Associated Characteristic Learning Dynamics [1.5184189132709105]
  We discuss the implications of additive, multiplicative and mixed noise for different classification tasks and model architectures. We propose a methodology called Walking Noise which injects layer-specific noise to measure the robustness. We conclude with a discussion of the use of this methodology in practice, among others, discussing its use for tailored multi-execution in noisy environments.
  arXiv  Detail & Related papers  (2022-12-20T17:09:08Z)
• How Powerful is Implicit Denoising in Graph Neural Networks [33.01155523195073]
  We conduct a comprehensive theoretical study and analyze when and why the implicit denoising happens in GNNs. Our theoretical analysis suggests that the implicit denoising largely depends on the connectivity, the graph size, and GNN architectures. We derive a robust graph convolution, where the smoothness of the node representations and the implicit denoising effect can be enhanced.
  arXiv  Detail & Related papers  (2022-09-29T02:19:39Z)
• A Comparative Study on Robust Graph Neural Networks to Structural Noises [12.44737954516764]
  Graph neural networks (GNNs) learn node representations by passing and aggregating messages between neighboring nodes. GNNs could be vulnerable to structural noise because of the message passing mechanism where noise may be propagated through the entire graph. We conduct a comprehensive and systematical comparative study on different types of robust GNNs under consistent structural noise settings.
  arXiv  Detail & Related papers  (2021-12-11T21:01:29Z)
• VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization [70.8567058758375]
  VQ-GNN is a universal framework to scale up any convolution-based GNNs using Vector Quantization (VQ) without compromising the performance. Our framework avoids the "neighbor explosion" problem of GNNs using quantized representations combined with a low-rank version of the graph convolution matrix.
  arXiv  Detail & Related papers  (2021-10-27T11:48:50Z)
• Stochastic Aggregation in Graph Neural Networks [9.551282469099887]
  Graph neural networks (GNNs) manifest pathologies including over-smoothing and limited power discriminating. We present a unifying framework for aggregation (STAG) in GNNs, where noise is (adaptively) injected into the aggregation process from the neighborhood to form node embeddings.
  arXiv  Detail & Related papers  (2021-02-25T02:52:03Z)
• Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections [73.95786440318369]
  We focus on the so-called implicit effect' of GNIs, which is the effect of the injected noise on the dynamics of gradient descent (SGD) We show that this effect induces an asymmetric heavy-tailed noise on gradient updates. We then formally prove that GNIs induce an implicit bias', which varies depending on the heaviness of the tails and the level of asymmetry.
  arXiv  Detail & Related papers  (2021-02-13T21:28:09Z)
• Learning to Drop: Robust Graph Neural Network via Topological Denoising [50.81722989898142]
  We propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of Graph Neural Networks (GNNs) PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. We show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.
  arXiv  Detail & Related papers  (2020-11-13T18:53:21Z)
• A Unified View on Graph Neural Networks as Graph Signal Denoising [49.980783124401555]
  Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models can be regarded as solving a graph denoising problem. We instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes.
  arXiv  Detail & Related papers  (2020-10-05T04:57:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.