Learn Beneficial Noise as Graph Augmentation

Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.

Why Does Dropping Edges Usually Outperform Adding Edges in Graph Contrastive Learning?

Graph contrastive learning (GCL) has been widely used as an effective self-supervised learning method for graph representation learning. However, how to apply adequate and stable graph augmentation to generating proper views for contrastive learning remains an essential problem. Dropping edges is a primary augmentation in GCL while adding edges is not a common method due to its unstable performance. To our best knowledge, there is no theoretical analysis to study why dropping edges usually outperforms adding edges. To answer this question, we introduce a new metric, namely Error Passing Rate (EPR), to quantify how a graph fits the network. Inspired by the theoretical conclusions, we propose a novel GCL algorithm, Error-PAssing-based Graph Contrastive Learning (EPAGCL), which uses both edge adding and edge dropping as its augmentation. To be specific, we generate views by adding and dropping edges according to the weights derived from EPR. Extensive experiments on various real-world datasets are conducted to validate the correctness of our theoretical analysis and the effectiveness of our proposed algorithm.

Data Augmentation of Contrastive Learning is Estimating Positive-incentive Noise

Inspired by the idea of Positive-incentive Noise (Pi-Noise or $\pi$-Noise) that aims at learning the reliable noise beneficial to tasks, we scientifically investigate the connection between contrastive learning and $\pi$-noise in this paper. By converting the contrastive loss to an auxiliary Gaussian distribution to quantitatively measure the difficulty of the specific contrastive model under the information theory framework, we properly define the task entropy, the core concept of $\pi$-noise, of contrastive learning. It is further proved that the predefined data augmentation in the standard contrastive learning paradigm can be regarded as a kind of point estimation of $\pi$-noise. Inspired by the theoretical study, a framework that develops a $\pi$-noise generator to learn the beneficial noise (instead of estimation) as data augmentations for contrast is proposed. The designed framework can be applied to diverse types of data and is also completely compatible with the existing contrastive models. From the visualization, we surprisingly find that the proposed method successfully learns effective augmentations.