The second paper called "On the Approximation of the Riemannian Barycenter" uses the bounds from the above article to compute approximations of the Riemannian barycenter at very low computational cost!

link.springer.com/chapter/10.1...

The first paper called "Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics" studies the geometry of the Stiefel manifold to derive simple and insightful bounds on the computationally untractable geodesic distance.

sciencedirect.com/science/arti...

Details on our research and how to apply to our lab are on our website: gi.ece.ucsb.xn--edu-v113b
@uofcalifornia.bsky.social @ucsantabarbara.bsky.social
@ucsbece.bsky.social @ucsb-cs.bsky.social

And yes, we do play volleyball on the beach nearby🏐🌴

Details on our research and how to apply to our lab are on our website: gi.ece.ucsb.edu.

We hope to hear from you! 👋
@uofcalifornia.bsky.social @ucsantabarbara.bsky.social @ucsbece.bsky.social @ucsb-cs.bsky.social @geometric-intel.bsky.social

From your desk you'll see dolphins, beach volleyball courts, surf spots & more importantly: your colleagues!

@adelemyers.bsky.social @mathildepapillon.bsky.social @franciscoacosta.bsky.social @louisacornelis.bsky.social @abbybertics.bsky.social @bariskurtkaya.bsky.social and gi.ece.ucsb.edu/people

You are specifically interested in AI?

👉 Look at the AI Curriculum from the UCSB Real AI Initiative offered within the CS and the ECE departments.

ai.ece.ucsb.edu/ai-ucsb

@ai-ucsb.bsky.social @ucsbece.bsky.social @ucsb-cs.bsky.social @ucsbengineering.bsky.social

We are physicists, neuroscientists, mathematicians and computer scientists who study intelligence in biological and artificial neural networks and use our findings to build better AI models.

👉 You can join us via UCSB ECE, CS, Math or DYNS PhD programs!

We can't wait to see your innovative solutions! Full details on the tasks and data are on our site:

🔗 geometric-intelligence.github.io/topobench/td...

#TDLChallenge #AI #ML #TAGinDS

A huge thank you to our partners! 🤝

💰 Cash prizes are sponsored by the brilliant team at Arlequin AI.

🏛️ Internships are hosted by the world-class UC Santa Barbara @geometric-intel.bsky.social and EPFL IMOS labs.

Struggling with reproducible benchmarks in TDL? We’ve got you covered.

12+ models tested on 22+ diverse, cross-domain datasets. Tutorials to get you started with topology & higher-order homophily Webpage/Docs: geometric-intelligence.github.io/TopoBench/

Curious about topological liftings? TopoBench lets you experiment with them on your own data! We’ve included 20+ liftings from last year’s TDL Challenge @TAGinDS, @PyT_Team_. Explore them all in our Wiki: github.com/geometric-in... #TDA

At its core, TopoBench is a framework for robust and fair evaluation in TDL. We’re empowering researchers and practitioners to compare models with confidence and push the field forward, together.

For a deep dive into our framework for reproducible benchmarking, our methodology, and key findings, check out the full paper. Paper: arxiv.org/abs/246.06642 #MachineLearning #GNN #DataScience

This was a massive team effort!
Developed & led by @levtelyatnikov.bsky.social , @gbg141.bsky.social , Theodore Papamarkou. With major contributions from @Marco Montagna, Mustafa Hajij, Ghada Zamzmi, Michael T. Schaub, @ninamiolane.bsky.social , & @sscardapane.bsky.social , and many others!

We can’t wait to see what the community builds with TopoBench! Star our repo, read the paper, and bring reproducibility to your TDL research. Contributions and feedback are welcome! #OpenSource #Python #AcademicTwitter

Our research is collaborative at heart:

We work with neuroscientists, physicists, and healthcare professionals to design principled AI that is tailored to data-scarce scientific fields.

You’ll join a vibrant AI community on the golden Californian coast @uofcalifornia.bsky.social 🌴