Bonus: a concrete success story. In the traffic prediction benchmark below, a Geometric GP (powered by GeometricKernels) significantly outperforms GNN Ensembles and Bayesian GNNs in both prediction (RMSE) and uncertainty (NLL) quality. Reproduce it with github.com/vabor112/pem...

💻 GitHub: github.com/geometric-ke...
📄 JMLR Paper: www.jmlr.org/papers/v26/2...

#MachineLearning #GeometricDeepLearning #GaussianProcesses #Kernels #Graphs #Manifolds #JMLR #OpenSource

Huge thanks to my co-authors Peter Mostowsky, @dvinnie.bsky.social, Iskander Azangulov, Noémie Jaquier, @mjhutchinson141.bsky.social, Aditya Ravuri, Leonel Rozo, @avt.im, all contributors and all users!

✅ Spaces: Graphs, Meshes, Hyperspheres, Tori, Hyperbolic spaces, SPD matrices, & Lie Groups (SO(n), SU(n)).
✅ Infrastructure: Run seamlessly on PyTorch, JAX, TensorFlow, or NumPy.
✅ Integrations: Plug-and-play wrappers for GPyTorch & GPJax.

What's in the library? GeometricKernels gives you the principled Heat (Diffusion) and Matérn kernels needed to build these models out-of-the-box.

Why care about kernels in 2026? To build probabilistic models on geometric domains! Kernels drive Gaussian processes. While they famously struggle in high dim-s (images/text), many geometric domains are intrinsically low-dim, making these models shine (road networks/3D surfaces).

Happy to share a major milestone: after years of development, we are officially launching Version 1.0 of the GeometricKernels library!

To top it off, our accompanying paper has just been published in JMLR (MLOSS)! 🎉

github.com/geometric-ke...

Note: I am also recruiting through @ellis.eu PhD program.

Details: vab.im/vacancies/.

I am hiring a fully-funded #PhD in #ML to work at the University of Edinburgh on 𝐠𝐞𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐥𝐞𝐚𝐫𝐧𝐢𝐧𝐠 and 𝐮𝐧𝐜𝐞𝐫𝐭𝐚𝐢𝐧𝐭𝐲 𝐪𝐮𝐚𝐧𝐭𝐢𝐟𝐢𝐜𝐚𝐭𝐢𝐨𝐧.

Application deadline: 31 Dec '25. Starts May/Sep '26.
Details in the reply.

Pls RT and share with anyone interested!

Presenting today at #ICLR2025!
Poster session 1, 10:00-12:30, #427.
Oral Session 2F 16:18-16:30.

iclr.cc/virtual/2025...

Amazingly, Kacper did the bulk of the work for this ICLR oral as his undergrad thesis 💪

Schematic illustration of a scalar-valued residual deep GP with L hidden layers. The last layer is a scalar-valued GP on the manifold. If it is not present, the model is manifold-valued. If it is replaced with a Gaussian vector field (GVF), the model is a vector field on the manifold.

Excited to share our ICLR 2025 oral "Residual Deep Gaussian Processes on Manifolds"!

With @vabor112.bsky.social & @arkrause.bsky.social, we introduce manifold-to-manifold GPs that can be composed together, generalising deep GPs to manifolds. Applications include wind prediction & Bayes opt! 1/n

🚀 𝐏𝐡𝐃 𝐎𝐩𝐩𝐨𝐫𝐭𝐮𝐧𝐢𝐭𝐲 𝐚𝐭 𝐈𝐦𝐩𝐞𝐫𝐢𝐚𝐥

Looking for my first PhD student

🔬 Project: 𝐈𝐦𝐩𝐚𝐜𝐭 𝐨𝐟 𝐞𝐧𝐯𝐢𝐫𝐨𝐧𝐦𝐞𝐧𝐭𝐚𝐥, 𝐯𝐢𝐫𝐚𝐥, 𝐛𝐞𝐡𝐚𝐯𝐢𝐨𝐮𝐫𝐚𝐥 & 𝐩𝐬𝐲𝐜𝐡𝐨-𝐬𝐨𝐜𝐢𝐚𝐥 𝐞𝐱𝐩𝐨𝐬𝐮𝐫𝐞𝐬 𝐨𝐧 𝐡𝐞𝐚𝐥𝐭𝐡

Joint with LSHTM & UKHSA

See links below.

📅 𝐃𝐞𝐚𝐝𝐥𝐢𝐧𝐞: 7 March 2024

📩 Questions? DM me!

#PhD #HealthEquity #ImperialCollege

Gaussian Processes on Cellular Complexes In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gau...

If you are interested in Matérn kernels on more general complexes (cellular/higher dimension), check out arxiv.org/abs/2311.01198 by @miniapeur.bsky.social et al.

Hodge-Compositional Edge Gaussian Processes We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This...

This makes them perform well on tasks ranging from modeling 𝒂𝒓𝒃𝒊𝒕𝒓𝒂𝒈𝒆-𝒇𝒓𝒆𝒆 𝒎𝒂𝒓𝒌𝒆𝒕𝒔 to 𝒑𝒊𝒑𝒆 𝒏𝒆𝒕𝒘𝒐𝒓𝒌𝒔 or 𝒐𝒄𝒆𝒂𝒏 𝒄𝒖𝒓𝒓𝒆𝒏𝒕𝒔 (arxiv.org/abs/2310.19450).

Crucially, the resulting kernels support 𝒂𝒖𝒕𝒐𝒎𝒂𝒕𝒊𝒄 𝒓𝒆𝒍𝒆𝒗𝒂𝒏𝒄𝒆 𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏 of the relative importance of the three Hodge decomposition parts.

On top of these, you can define a 𝑯𝒐𝒅𝒈𝒆-𝒄𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏𝒂𝒍 𝑴𝒂𝒕𝒆́𝒓𝒏 𝒌𝒆𝒓𝒏𝒆𝒍, which is a linear combination of the pure div, pure curl, and harmonic Matérn kernels, each possible with a different set of hyperparameters.

This leads to the 𝑯𝒐𝒅𝒈𝒆 𝑫𝒆𝒄𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏 which splits any edge flow into three parts: pure divergence (curl-free), pure curl (div-free), and harmonic (curl-free & div-free). This allows three different Matérn kernels , one for each part.

However, a simplicial 2-complex offers much more. Its structure allows characterizing key properties of edge flows using the discrete concepts of divergence (𝒅𝒊𝒗) and 𝒄𝒖𝒓𝒍, measuring how edge flows diverge at nodes and circulate along faces.

Matérn Gaussian Processes on Graphs Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process m...

Any simplicial 2-complex comes with a 𝑯𝒐𝒅𝒈𝒆 𝑳𝒂𝒑𝒍𝒂𝒄𝒊𝒂𝒏 matrix, which can be used to define Matérn kernels on its edge set in exactly as in the Matérn GPs on Graphs paper (arxiv.org/abs/2010.15538).

However, if you want to keep it simple and think about graphs rather than simplicial 2-complexes, the interface allows it: the library can define a reasonable set of triangles for you, for any graph you provide.

First, a bit about theory. Mathematically, the kernels are defined on the edge set of a 𝒔𝒊𝒎𝒑𝒍𝒊𝒄𝒊𝒂𝒍 2-𝒄𝒐𝒎𝒑𝒍𝒆𝒙, i.e. a graph along with a set of triangular faces formed by some of its edges.

Good news! GeometricKernels now supports the new 𝑯𝒐𝒅𝒈𝒆-𝒄𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏𝒂𝒍 𝒌𝒆𝒓𝒏𝒆𝒍𝒔 for flow-type data on graphs (thnx Maosheng Yang).

Example notebook: geometric-kernels.github.io/GeometricKer....
For the theory behind, see arxiv.org/abs/2310.19450.

Some details below.

Uncertainty in multivariate, non-Euclidean, and functional spaces: theory and practice - Isaac Newton Institute Contemporary sciences abound in various complex data types (beyond the classical vector description) including graphs, rankings, manifolds, time series, sets,...

Link: newton.ac.uk/event/rclw01/

Check out the workshop "Uncertainty in multivariate, non-Euclidean, and functional spaces: theory and practice"

Where: Isaac Newton Institute, Cambridge
When: 6-9 May 2025

Application deadline: 12 Jan 2025. Link in reply
(contributed talks/posters are welcome)

I will be there!

The NeurIPS Workshop on Bayesian Decision-making and Uncertainty has started - our first talk is by @mvdw.bsky.social!

Join us at East Meeting Room 8, 15, or online!

We are organising the First International Conference on Probabilistic Numerics (ProbNum 2025) at EURECOM in southern France in Sep 2025. Topics: AI, ML, Stat, Sim, and Numerics. Reposts very much appreciated!

probnum25.github.io