Despite the widespread adoption of Graph Neural Networks (GNNs), these models often incorporate off-the-shelf normalization layers like BatchNorm or InstanceNorm, which were not originally designed for GNNs. Consequently, these normalization layers may not effectively capture the unique characteristics of graph-structured data, potentially even weakening the expressive power of the overall architecture. While existing graph-specific normalization layers have been proposed, they often struggle to offer substantial and consistent benefits. In this paper, we propose GRANOLA, a novel graph-adaptive normalization layer. Unlike existing normalization layers, GRANOLA normalizes node features by adapting to the specific characteristics of the graph, particularly by generating expressive representations of its nodes, obtained by leveraging the propagation of Random Node Features (RNF) in the graph. We provide theoretical results that support our design choices as well as an extensive empirical evaluation demonstrating the superior performance of GRANOLA over existing normalization techniques. Furthermore, GRANOLA emerges as the top-performing method among all baselines in the same time complexity class of Message Passing Neural Networks (MPNNs).

Despite the widespread adoption of Graph Neural Networks (GNNs), these models often incorporate off-the-shelf normalization layers like BatchNorm or InstanceNorm, which were not originally designed for GNNs. Consequently, these normalization layers may not effectively capture the unique characteristics of graph-structured data, potentially even weakening the expressive power of the overall architecture. While existing graph-specific normalization layers have been proposed, they often struggle to offer substantial and consistent benefits. In this paper, we propose GRANOLA, a novel graph-adaptive normalization layer. Unlike existing normalization layers, GRANOLA normalizes node features by adapting to the specific characteristics of the graph, particularly by generating expressive representations of its nodes, obtained by leveraging the propagation of Random Node Features (RNF) in the graph.

In recent years, significant efforts have been made to refine the design of Graph Neural Network (GNN) layers, aiming to overcome diverse challenges, such as limited expressive power and oversmoothing. Despite their widespread adoption, the incorporation of off-the-shelf normalization layers like BatchNorm or InstanceNorm within a GNN architecture may not effectively capture the unique characteristics of graph-structured data, potentially reducing the expressive power of the overall architecture. Moreover, existing graph-specific normalization layers often struggle to offer substantial and consistent benefits. In this paper, we propose GRANOLA, a novel graph-adaptive normalization layer. Unlike existing normalization layers, GRANOLA normalizes node features by adapting to the specific characteristics of the graph, particularly by generating expressive representations of its neighborhood structure, obtained by leveraging the propagation of Random Node Features (RNF) in the graph. We present theoretical results that support our design choices. Our extensive empirical evaluation of various graph benchmarks underscores the superior performance of GRANOLA over existing normalization techniques. Furthermore, GRANOLA emerges as the top-performing method among all baselines within the same time complexity of Message Passing Neural Networks (MPNNs).

Over the past two decades or so eCommerce has undergone a major change. The speed of this change has been, and continues to be, amazing. The world wide web got invented in 1989, became available on the Internet in 1991; first web sites humbly started as additional marketing channels, with corporate web sites giving information on the company and a product catalogue; 1994 the Netscape browser arrived. In 1995 Amazon got founded – and the story started to take off. In 2000 we saw US online shopping eclipsing the 25 billion dollar mark.

We expected so much from "a technology platform that uses natural language processing and machine learning to reveal insights from large amounts of unstructured data." And what did we get? @!!@# Granola. Bear Naked Granola uses Watson to make custom suggestions for mixing your own granola which they will then ship to your door, ten bucks for ten ounces. At first glance, it sounds like an idiotic waste of resources. After all, 50 ingredients is not exactly a large amount of unstructured data.