š® Working on ML on curved manifolds? Don't miss out on Jacobi Fields! š®
I wrote a quick, highly visual and hopefully accessible introduction to the topic: "Jacobi Fields in Machine Learning" š¤ Check it out here: olgatticus.github.io/blog/jacobi-...!
We find it does great on non-isomorphic graph distinction by evaluating on BREC icml.cc/virtual/2024...
and as an inductive bias on ZINC (compared to other homomorphism and subgraph count methods)
Not all is lost because we can approximate our true metric by sampling computable graphs (of a nice treewidth) and also homomorphisms!
Interested in the analysis of GNN expressive power, limitations of the WL test or more in general in the definition of complete metrics on graphs? š
Check out this super cool work led by
@martin.topology.rocks !š„
Under mild assumptions, we prove our metric:
1.Ā Is šøššš šššš regarding the isomorphic distinction.
2.Ā Is š šššššš¶šš¾šš š¾ššš¶šš¾š¶šš.
3. Can š¹š¾ššš¾šššš¾šš½ induced subgraphs (even if a retraction exists)!
4. Has a š»š¾ššš ššš ššššš than the metric space induced by WL.
However... It's hard to compute :(
Inspired by the šš³š°š®š°š·-šš¢š¶š“š“š„š°š³š§ distance, we define distortion as the maximum difference of the attributes of a graph š and a graph š' through a homomorphism. We construct a metric from this š„šŖš“šµš°š³šµšŖš°šÆ by taking the homomorphism providing the infimum result and looking at both directions!
To kick off the PhD journey with @pseudomanifold.topology.rocks:
What are the limitations of the WL metric, and what is an šŖšÆš§š°š³š®š¢šµšŖš·š¦ š®š¦šµš³šŖš¤?
We answer these questions with our ššæš®š½šµ šš¼šŗš¼šŗš¼šæš½šµš¶ššŗ šš¶ššš¼šæšš¶š¼š»
arxiv.org/abs/2511.03068
@olgatticus.bsky.social, Kavir and @erikjbekkers.bsky.social
š LOGML26ā Mentor applications!
š Imperial College London | 13ā17 July 2026
Mentor a project team. Attend talks, socials, networking events. šø Travel support available.
Deadline: 18 March 2026(AoE)
Apply: logml.ai/apply.html
#LOGML #MachineLearning #SummerSchool
An intuitive introduction to Jacobi fields and their applications in machine learning on Riemannian manifolds.
olgatticus.github.io
Iām pleased to share that I've been selected as a Fellow of the 2026 Thinking About Thinking Program!
Iām grateful to join a global, research-led ecosystem engaging thoughtfully with how AI is developed, governed, and understood.
@geometric-intel.bsky.social @ai-ucsb.bsky.social
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore featur...
arxiv.org
Martin Carrasco
Martin Carrasco
Martin Carrasco
Martin Carrasco
Martin Carrasco
Olga Zaghen
Olga Zaghen
To kick off the PhD journey with @pseudomanifold.topology.rocks:
What are the limitations of the WL metric, and what is an šŖšÆš§š°š³š®š¢šµšŖš·š¦ š®š¦šµš³šŖš¤?
We answer these questions with our ššæš®š½šµ šš¼šŗš¼šŗš¼šæš½šµš¶ššŗ šš¶ššš¼šæšš¶š¼š»
arxiv.org/abs/2511.03068
@olgatticus.bsky.social, Kavir and @erikjbekkers.bsky.social
LOGML Summer School
Bastian Grossenbacher-Rieck
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore featur...
