Thread by @mmbronstein

After a hiatus, a new series of blogs posts. Do differential geometry and algebraic topology sound too exotic for ML? In recent works, we show that tools from these fields bring a new perspective on graph neural networks

First post in the series:

towardsdatascience.com/graph-neural-n…

Based on recent works with @CristianBodnar @ffabffrasca @kneppkatt @wangyg85 @pl219_Cambridge @guidomontufar @b_p_chamberlain @migorinova @stefan_webb @emaros96 @aittalam James Rowbottom, Jake Topping, Xiaowen Dong, Francesco Di Giovanni

Cool animation of Cora graph evolution by James Rowbottom

Part II will discuss topological message passing.

Part III will deal with geometric flows and non-euclidean diffusion PDEs on graphs.

Part IV will show how the over-squashing phenomena relate to graph curvature, and offer a graph rewiring approach inspired by the Ricci flow.

@_JRowbottom

Beltrami flow (BLEND) #NeurIPS2021 paper: arxiv.org/abs/2110.09443

GRAND #ICML2021 paper: arxiv.org/abs/2106.10934

Topological message passing #ICML2021 and #NeurIPS2021 papers:
arxiv.org/abs/2103.03212
arxiv.org/abs/2106.12575