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Viacheslav Borovitskiy

@vabor112.bsky.social
139 followers 67 following 30 posts

Assistant Professor in Machine Learning @ University of Edinburgh. PhD in Mathematics. Ex ETH Zurich. See vab.im/vacancies

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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
💻 Code: github.com/PedrV/gnn-uq... 📄 Preprint: arxiv.org/abs/2605.22593 Co-authored w/ @pedrocvieira.bsky.social & Pedro Ribeiro. #MachineLearning #GraphNeuralNetworks #DeepLearning #UncertaintyQuantification #GeometricDeepLearning
github.com
GitHub - PedrV/gnn-uq-inspector
Contribute to PedrV/gnn-uq-inspector development by creating an account on GitHub.
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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
🔹 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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
🔹 Epistemic collapse: Deep ensembles rely on model disagreement to improve uncertainty (no diversity = no improvement). Across 6 highly diverse datasets, a severe lack of diversity is exactly what we observed. This is a stark contrast to foundational computer vision papers.
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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
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: 👇
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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
The origin story: This started from a tutorial benchmark (see image). I was surprised to find deep ensembles of GCNs failing miserably there. Point predictions were fine, but they yielded wildly overconfident uncertainty maps and an NLL much worse than a trivial N(µ, σ²) baseline!
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Viacheslav Borovitskiy @vabor112.bsky.social · 25/05/2026
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
arxiv.org
Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?
While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on succ...
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
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...
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
💻 GitHub: github.com/geometric-ke... 📄 JMLR Paper: www.jmlr.org/papers/v26/2... #MachineLearning #GeometricDeepLearning #GaussianProcesses #Kernels #Graphs #Manifolds #JMLR #OpenSource
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
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!
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
✅ 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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
What's in the library? GeometricKernels gives you the principled Heat (Diffusion) and Matérn kernels needed to build these models out-of-the-box.
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
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).
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Viacheslav Borovitskiy @vabor112.bsky.social · 12/03/2026
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...
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Viacheslav Borovitskiy @vabor112.bsky.social · 24/10/2025
Note: I am also recruiting through @ellis.eu PhD program.
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Viacheslav Borovitskiy @vabor112.bsky.social · 24/10/2025
Details: vab.im/vacancies/.
vab.im
Viacheslav Borovitskiy
personal page
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Viacheslav Borovitskiy @vabor112.bsky.social · 24/10/2025
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!
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Viacheslav Borovitskiy @vabor112.bsky.social · 24/04/2025
Presenting today at #ICLR2025! Poster session 1, 10:00-12:30, #427. Oral Session 2F 16:18-16:30. iclr.cc/virtual/2025...
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Viacheslav Borovitskiy @vabor112.bsky.social · 13/02/2025
Amazingly, Kacper did the bulk of the work for this ICLR oral as his undergrad thesis 💪
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Kacper Wyrwal @wyrwalkacper.bsky.social · 13/02/2025
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
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.
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Liza Semenova @liza-semenova.bsky.social · 30/01/2025
🚀 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
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
arxiv.org
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...
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
This makes them perform well on tasks ranging from modeling 𝒂𝒓𝒃𝒊𝒕𝒓𝒂𝒈𝒆-𝒇𝒓𝒆𝒆 𝒎𝒂𝒓𝒌𝒆𝒕𝒔 to 𝒑𝒊𝒑𝒆 𝒏𝒆𝒕𝒘𝒐𝒓𝒌𝒔 or 𝒐𝒄𝒆𝒂𝒏 𝒄𝒖𝒓𝒓𝒆𝒏𝒕𝒔 (arxiv.org/abs/2310.19450).
arxiv.org
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...
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
Crucially, the resulting kernels support 𝒂𝒖𝒕𝒐𝒎𝒂𝒕𝒊𝒄 𝒓𝒆𝒍𝒆𝒗𝒂𝒏𝒄𝒆 𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏 of the relative importance of the three Hodge decomposition parts.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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).
arxiv.org
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...
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 29/01/2025
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.
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Viacheslav Borovitskiy @vabor112.bsky.social · 19/12/2024
Link: newton.ac.uk/event/rclw01/
newton.ac.uk
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,...
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Viacheslav Borovitskiy @vabor112.bsky.social · 19/12/2024
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!
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Alexander Terenin @avt.im · 14/12/2024
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!
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Motonobu Kanagawa @motonobu-kanagawa.bsky.social · 17/11/2024
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
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