Viacheslav Borovitskiy

My group at the University of Edinburgh is recruiting #PhD students for 2027! 🎓 We are GLUEd: Geometric Learning & Uncertainty in Edinburgh. Group: vab.im/group/ How to apply: vab.im/vacancies/ 1/2

My first paper with my first PhD student @pedrocvieira.bsky.social just landed on arXiv! 🎉 “Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?” Spoiler alert: the answer is largely no—at least, not much more than a single model does. 🧵👇 📄 arxiv.org/abs/2605.22593

🔹 Convexity? Message passing GNNs find different weights but learn remarkably similar functions—even where they fail. We hypothesize the architecture induces function-space convexity, making them behave like linear models despite their depth. Formalizing this is an open problem.

My first paper with my first PhD student @pedrocvieira.bsky.social just landed on arXiv! 🎉 “Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?” Spoiler alert: the answer is largely no—at least, not much more than a single model does. 🧵👇 📄 arxiv.org/abs/2605.22593

Since Bayesian GCNs did much better, standard ensembling seemed to be the culprit. Pedro dug in to see if this was an isolated anomaly or a general phenomenon pertaining to message passing GNNs (like GCNs and GATs). Here is what we found: 👇

My first paper with my first PhD student @pedrocvieira.bsky.social just landed on arXiv! 🎉 “Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?” Spoiler alert: the answer is largely no—at least, not much more than a single model does. 🧵👇 📄 arxiv.org/abs/2605.22593

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...

💻 GitHub: github.com/geometric-ke... 📄 JMLR Paper: www.jmlr.org/papers/v26/2... #MachineLearning #GeometricDeepLearning #GaussianProcesses #Kernels #Graphs #Manifolds #JMLR #OpenSource

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...

✅ 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.

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...

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).

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!

Details: vab.im/vacancies/.

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.

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

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.

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

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.

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.

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.

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).

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.

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.

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!