Understanding over-squashing and bottlenecks on graphs via curvature | Ricci Flow | Paper Explained
❤️ Become The AI Epiphany Patreon ❤️ https://www.patreon.com/theaiepiphany 👨👩👧👦 Join our Discord community 👨👩👧👦 https://discord.gg/peBrCpheKE In this video I cover the "Understanding over-squashing and bottlenecks on graphs via curvature" paper that introduces a new graph rewiring method that alleviates the problem of over-squashing by borrowing ideas from the field of differential geometry. The main workhorse behind the method is the discrete version of Ricci curvature (balanced Froman curvature) and an analog of Ricci Flow as applied to graphs. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ✅ Paper: https://arxiv.org/abs/2111.14522 ✅ M. Bronstein's blog: https://towardsdatascience.com/over-squashing-bottlenecks-and-graph-ricci-curvature-c238b7169e16 ✅Excellent Ricci-flow video: https://www.youtube.com/watch?v=PwRl5W-whTs&ab_channel=Aleph0 ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ⌚️ Timetable: 00:00 Bottlenecks and over-squashing in graphs 04:42 The concept of Ricci curvature and flow 11:10 Message passing neural networks and notation 16:45 Formalizing the concept of over-squashing 22:05 Balanced Forman Curvature 31:15 Connecting curvature with over-squashing 37:10 Connection with the Cheeger constant and spectral theory 41:20 SDRF - Stochastic Discrete Ricci Flow 47:47 Results, graph statistics, and limitations ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 💰 BECOME A PATREON OF THE AI EPIPHANY ❤️ If these videos, GitHub projects, and blogs help you, consider helping me out by supporting me on Patreon! The AI Epiphany - https://www.patreon.com/theaiepiphany One-time donation - https://www.paypal.com/paypalme/theaiepiphany Huge thank you to these AI Epiphany patreons: Eli Mahler Kevin Stone Petar Veličković ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 💼 LinkedIn - https://www.linkedin.com/in/aleksagordic/ 🐦 Twitter - https://twitter.com/gordic_aleksa 👨👩👧👦 Discord - https://discord.gg/peBrCpheKE 📺 YouTube - https://www.youtube.com/c/TheAIEpiphany/ 📚 Medium - https://gordicaleksa.medium.com/ 💻 GitHub - https://github.com/gordicaleksa 📢 AI Newsletter - https://aiepiphany.substack.com/ ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ #ricciflow #geometric #graphs
