Steven De Keninck

Ok. This is my life’s work as seen by C Jaimungal. Done in near isolation from community for reasons I do not grasp, Geometric Unity has never received this kind of treatment in 40 yrs. I’m sort of speechless and don’t know what to say. except “Thank you.” before I watch it. 🙏

To understand rotations, you must first understand reflections. My CGI2025 talk on coordinate free circular splines. youtu.be/m317-cYs8q4

Logarithmic maps are incredibly useful for algorithms on surfaces--they're local 2D coordinates centered at a given source. @yousufmsoliman and I found a better way to compute log maps w/ fast short-time heat flow in "The Affine Heat Method" presented @ SGP2025 today! 🧵

🚨 If you're interested in interpretable Neural Operators and AI4Science, I'll see you at #ICLR2025, Poster #32, Poster Session 3, Hall 3 + Hall 2B, Singapore EXPO, April 25th!🇸🇬 📜 read it here: lnkd.in/dvi_S6Dm

I've updated my blog post to walk through the remaining technical details of our Surface Winding Numbers algorithm: now the calculus of the algorithm is explained a bit more in detail. The post, paper, code, etc. is all here: nzfeng.github.io/research/WNoDS…

ENGAGE workshop is back! This workshop focusing on Geometric Algebra, has deadlines approaching: Abstract submission: April 31, 2025. Paper submission: May 2, 2025. Check it out! engage-workshop.org #GeometricAlgebra

Study the blade. bivector.net

Our paper got a prize :) Cheers to lead author @johannbrehmer, and fellow co-authors Sönke Behrends, and @TacoCohen. Our results hint that yes, also at large scale of data and compute, if your data has symmetries, you might be better off building these into your network.

Entropy is one of those formulas that many of us learn, swallow whole, and even use regularly without really understanding. (E.g., where does that “log” come from? Are there other possible formulas?) Yet there's an intuitive & almost inevitable way to arrive at this expression.

I have always been disappointed that more instruction sets don’t have peak-efficiency block move and fill operations. REP MOVS/STOS in x86/x64 is still pretty great, although not optimal in all cases. news.ycombinator.com/item?id=120479… There is certainly a bias against it due to not being…

Nice work, @TacoCohen, @pimdehaan, @johannbrehmer and co!

Does equivariance matter at scale? Should a model rather learn equi- and invariances from data or should the architecture have the equiv property? This work provides some insights, and SCALING LAWS for each. P: arxiv.org/abs/2410.23179

Re. Geometric Algebra for Physics Teaching: in mechanics class, I'm now introducing the wedge product *before* the cross-product, with the latter defined in terms of former (as a special case in 3D). The revolution is coming slowly. lol @enkimute

In our preprint, for the 1st time we make neural operators equivariant with respect to PDE symmetry groups. These can be very complicated, and often only the Lie algebra is known, so a universal method is needed - a 🧵. 🔗 Read the full paper here: arxiv.org/abs/2410.02698

C++ code is out! The Signed Heat Method has been added to geometry-central. In 3D, compute generalized SDFs to point clouds, triangle meshes, and polygon meshes. The method should "just work" on geometry with holes, intersections, nonmanifold-ness, etc. Links below 🔽

Signed distance functions (SDFs) are fundamental tools in graphics, vision, and physics simulation. But how do you get a high-quality SDF from messy, real-world input? At #SIGGRAPH2024, we introduced a simple method for turning "broken" geometry into a well-behaved SDF. <🧵>

Meeting my heroes at SIGGRAPH. @keenanisalive

Moths are attracted to lights because of the same mathematics that underlies twistor theory and compactification in theoretical physics: projective geometry. It all starts from a simple observation: translations are just rotations whose center is located "at infinity". (1/11)

Go GA !