Uploaded April 2022 | Updated September 2026, 1 week ago
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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.
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β Paper: arxiv.org/abs/2111.14522
β M. Bronstein's blog: towardsdatascience.com/over-squashing-bottlenecks-and-graph-ricci-curvature-c238b7169e16
β Excellent Ricci-flow video: youtube.com/watch?v=PwRl5W-whTs&ab_channel=Aleph0
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
βοΈ 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
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
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Huge thank you to these AI Epiphany patreons:
Eli Mahler
Kevin Stone
Petar VeliΔkoviΔ
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β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
#ricciflow #geometric #graphs
β€οΈ Become The AI Epiphany Patreon β€οΈ
patreon.com/theaiepiphany
π¨βπ©βπ§βπ¦ Join our Discord community π¨βπ©βπ§βπ¦
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.
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
β Paper: arxiv.org/abs/2111.14522
β M. Bronstein's blog: towardsdatascience.com/over-squashing-bottlenecks-and-graph-ricci-curvature-c238b7169e16
β Excellent Ricci-flow video: youtube.com/watch?v=PwRl5W-whTs&ab_channel=Aleph0
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
βοΈ 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
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
π° BECOME A PATREON OF THE AI EPIPHANY β€οΈ
If these videos, GitHub projects, and blogs help you,
consider helping me out by supporting me on Patreon!
The AI Epiphany - patreon.com/theaiepiphany
One-time donation - paypal.com/paypalme/theaiepiphany
Huge thank you to these AI Epiphany patreons:
Eli Mahler
Kevin Stone
Petar VeliΔkoviΔ
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
πΌ LinkedIn - linkedin.com/in/aleksagordic
π¦ Twitter - twitter.com/gordic_aleksa
π¨βπ©βπ§βπ¦ Discord - discord.gg/peBrCpheKE
πΊ YouTube - youtube.com/c/TheAIEpiphany
π Medium - gordicaleksa.medium.com
π» GitHub - github.com/gordicaleksa
π’ AI Newsletter - aiepiphany.substack.com
β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬β¬
#ricciflow #geometric #graphs
