Graph diffusion equations are intimately related to graph neural networks (GNNs) and have recently attracted attention as a principled framework for analyzing GNN dynamics, formalizing their expressive power, and justifying architectural choices. One key open questions in graph learning is the generalization capabilities of GNNs. A major limitation of current approaches hinges on the assumption that the graph topologies in the training and test sets come from the same distribution. In this paper, we make steps towards understanding the generalization of GNNs by exploring how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies. We first show deficiencies in the generalization capability of existing models built upon local diffusion on graphs, stemming from the exponential sensitivity to topology variation. Our subsequent analysis reveals the promise of non-local diffusion, which advocates for feature propagation over fully-connected latent graphs, under the assumption of a specific data-generating condition. In addition to these findings, we propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations that have a closed-form solution backed up with theoretical guarantees of desired generalization under topological distribution shifts. The new model, functioning as a versatile graph Transformer, demonstrates superior performance across a wide range of graph learning tasks.

PewDiePie has conceded his hard-fought battle with T-Series with a music video of his own. The YouTube star whose real name is Felix Kjellberg has finally stopped being the site's biggest channel – a slot he held for years – after a challenge from T-Series, which hosts Indian music videos and has grown quickly. Over recent months, the two channels have fought to get control of the top spot, with PewDiePie's fans using a whole host of publicity techniques in an attempt to keep him as its most popular channel. We'll tell you what's true. You can form your own view. But T-Series kept outpacing its growth and has now settled as YouTube's biggest channel.

The battle between PewDiePie and T-Series to be the world's most popular YouTube channel has taken a bizarre turn, after billionaire entrepreneur Elon Musk revealed he hosted PewDiePie's'meme review'. PewDiePie, whose real name is Felix Kjelberg, has been the top channel on the world's most popular video-sharing platform since 2013. His dominance has been challenged in recent months by the Indian channel, which posts Bollywood film trailers and music videos. The rise of T-Series has proved controversial within some corners of the YouTube community, seen as a David vs Goliath-style contest between an independent creator and a major corporate brand. For PewDiePie supporters, T-Series' popularity reflects a perceived shift in YouTube's focus towards larger brands that have more potential for generating revenue.