Analyzing the stability of graph neural networks (GNNs) under topological perturbations is key to understanding their transferability and the role of each architecture component. However, stability has been investigated only for particular architectures, questioning whether it holds for a broader spectrum of GNNs or only for a few instances. To answer this question, we study the stability of EdgeNet: a general GNN framework that unifies more than twenty solutions including the convolutional and attention-based classes, as well as graph isomorphism networks and hybrid architectures. We prove that all GNNs within the EdgeNet framework are stable to topological perturbations. By studying the effect of different EdgeNet categories on the stability, we show that GNNs with fewer degrees of freedom in their parameter space, linked to a lower representational capacity, are more stable. The key factor yielding this trade-off is the eigenvector misalignment between the EdgeNet parameter matrices and the graph shift operator. For example, graph convolutional neural networks that assign a single scalar per signal shift (hence, with a perfect alignment) are more stable than the more involved node or edge-varying counterparts. Extensive numerical results corroborate our theoretical findings and highlight the role of different architecture components in the trade-off.

We present a new encoder-decoder generative network dubbed EdgeNet, which introduces a novel encoder-decoder framework for data-driven auction design in online e-commerce advertising. We break the neural auction paradigm of Generalized-Second-Price(GSP), and improve the utilization efficiency of data while ensuring the economic characteristics of the auction mechanism. Specifically, EdgeNet introduces a transformer-based encoder to better capture the mutual influence among different candidate advertisements. In contrast to GSP based neural auction model, we design an autoregressive decoder to better utilize the rich context information in online advertising auctions. EdgeNet is conceptually simple and easy to extend to the existing end-to-end neural auction framework. We validate the efficiency of EdgeNet on a wide range of e-commercial advertising auction, demonstrating its potential in improving user experience and platform revenue.

Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged as a parameterization to capture detail at the node level with a reduced number of parameters and complexity. Following this rationale, this paper puts forth a general framework that unifies state-of-the-art graph neural networks (GNNs) through the concept of EdgeNet. An EdgeNet is a GNN architecture that allows different nodes to use different parameters to weigh the information of different neighbors. By extrapolating this strategy to more iterations between neighboring nodes, the EdgeNet learns edge- and neighbor-dependent weights to capture local detail. This is the most general local operation that a node can do and encompasses under one formulation all graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs). In writing different GNN architectures with a common language, EdgeNets highlight specific architecture advantages and limitations, while providing guidelines to improve their capacity without compromising their local implementation. For instance, we show that GCNNs have a parameter sharing structure that induces permutation equivariance. This can be an advantage or a limitation, depending on the application. When it is a limitation, we propose hybrid approaches and provide insights to develop several other solutions that promote parameter sharing without enforcing permutation equivariance. Another interesting conclusion is the unification of GCNNs and GATs -approaches that have been so far perceived as separate. In particular, we show that GATs are GCNNs on a graph that is learned from the features. This particularization opens the doors to develop alternative attention mechanisms for improving discriminatory power.

Despite the importance of handwritten numeral classification, a robust and effective method for a widely used language like Arabic is still due. This study focuses to overcome two major limitations of existing works: data diversity and effective learning method. Hence, the existing Arabic numeral datasets have been merged into a single dataset and augmented to introduce data diversity. Moreover, a novel deep model has been proposed to exploit diverse data samples of unified dataset. The proposed deep model utilizes the low-level edge features by propagating them through residual connection. To make a fair comparison with the proposed model, the existing works have been studied under the unified dataset. The comparison experiments illustrate that the unified dataset accelerates the performance of the existing works. Moreover, the proposed model outperforms the existing state-of-the-art Arabic handwritten numeral classification methods and obtain an accuracy of 99.59% in the validation phase. Apart from that, different state-of-the-art classification models have studied with the same dataset to reveal their feasibility for the Arabic numeral classification. Code available at http://github.com/sharif-apu/EdgeNet.