Notable instances of this architecture include, e.g., [33,37,51,105],and the spectral approaches proposed in, e.g., [14, 29, 64, 81]--all of which descend from early work in [65, 80, 102, 97]. Fork =1,the power ofthe algorithm has been completely characterized [4,63]. In general, a different mappingM()could be used, depending on the neighborhood information that we would like to aggregate. The following result relates the power of thek-WLandδ-k-WL. Proposition1(restated, Proposition 1 in the main text).

In the following, we review related work from graph kernels, GNNs, and theory. More recently, graph kernels' developments have emphasized scalability, focusing on Notable instances of this architecture include, e.g., [ Sato et al. studied the limits of GNNs when applied to combinatorial problems. Finally, there exists a new line of work focusing on extending GNNs to hypergraphs, see, e.g., [ We briefly describe the Weisfeiler-Leman algorithm and, along the way, introduce our notation. Let k be a fixed positive integer. The successive refinement steps are also called rounds or iterations .

Out-of-distribution (OOD) detection aims to identify OOD inputs from unknown classes, which is important for the reliable deployment of machine learning models in the open world. Various scoring functions are proposed to distinguish it from in-distribution (ID) data. However, existing methods generally focus on excavating the discriminative information from a single input, which implicitly limits its representation dimension. In this work, we introduce a novel perspective, i.e., employing different common corruptions on the input space, to expand that. We reveal an interesting phenomenon termed confidence mutation, where the confidence of OOD data can decrease significantly under the corruptions, while the ID data shows a higher confidence expectation considering the resistance of semantic features. Based on that, we formalize a new scoring method, namely, Confidence aVerage (CoVer), which can capture the dynamic differences by simply averaging the scores obtained from different corrupted inputs and the original ones, making the OOD and ID distributions more separable in detection tasks.

Artificial intelligence (AI) technologies and deployments are becoming even more widespread, thanks to a combination of growing amounts of data, faster processing power, and increasingly powerful algorithms. Indeed, as AI technologies make their way into virtually every industry, enabling machines to speak, listen, move, and make decisions in unprecedented ways, a wide range of use cases are illustrating the potential business opportunities, attracting new investment, and driving changes to existing business processes. According to a new report from Tractica, AI implementations now encompass 258 discrete use cases, and the worldwide market for AI software stands at $8.1 billion as of the end of 2018, a figure the market intelligence firm forecasts to rise to $105.8 billion annually by 2025. "The AI opportunity spans a wide range of industries and geographies, from advertising and automotive, to transportation and telecommunications," says principal analyst Keith Kirkpatrick. "A significant portion of the overall revenue is concentrated in highly domain-specific markets with high-volume data needs and ontologies, as well as those with growing applications for machine perception."