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Melanie Weber

@mweber.bsky.social
44 followers 9 following 11 posts

Assistant Professor @Harvard. Previously Hooke Research Fellow @Oxford and PhD @Princeton. Studying Geometry and Machine Learning.

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Melanie Weber @mweber.bsky.social · 02/03/2026
Can we reconstruct heterogeneous protein conformations from cryo-EM data while respecting molecular geometry? We present a geometry-aware framework that leverages graph-based representations and exhibits high reconstruction accuracy. arxiv.org/pdf/2602.21915
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Melanie Weber @mweber.bsky.social · 15/01/2026
Can GNNs color graphs? We study GNN-based neural algorithmic reasoning for approximate k-coloring, introducing differentiable objectives and recursive warm starts that allow GNNs to outperform classical methods at scale. Led by Knut Vanderbush. Details here: arxiv.org/pdf/2601.05137
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Melanie Weber @mweber.bsky.social · 03/11/2025
How can we reliably optimize on manifolds learned from data? We present an iso-Riemannian optimization framework that overcomes challenges of classical methods, and allows for interpretable clustering and efficient inverse problem solving, even in high dimensions. Lead:@WillemDiepev1. bit.ly/4hG5Seh
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Melanie Weber @mweber.bsky.social · 17/10/2025
How does neural feature geometry evolve during training? Modeling feature spaces as geometric graphs, we show that nonlinear activations drive transformations resembling Ricci flow, revealing how class structure emerges and suggesting geometry-informed training principles. arxiv.org/abs/2509.22362
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Melanie Weber @mweber.bsky.social · 05/09/2025
Convexity verification is central to optimization in ML and data science. We introduce a framework for testing geodesic convexity in nonlinear programs on geometric domains. Julia implementation available to leverage certificates in applications. Led by Andrew Cheng, Vaibhav Dixit. bit.ly/3HIlkJu
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Melanie Weber @mweber.bsky.social · 28/08/2025
Single-cell data reveals developmental hierarchies, but common embeddings distort them. We present Contrastive Poincaré Maps, a self-supervised hyperbolic encoder that preserves hierarchies, scales efficiently, and uncovers lineage across datasets. Lead: @nithyabhasker.bsky.social 🧬 bit.ly/4211hMY
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Melanie Weber @mweber.bsky.social · 16/04/2025
Community detection is a classical graph learning task. Our new JMLR paper shows how discrete Ricci curvature and geometric flows unveil (mixed) communities and studies relations between the curvature of a graph and its dual. w\ Yu Tian, Zach Lubberts: www.jmlr.org/papers/v26/2...
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Melanie Weber @mweber.bsky.social · 21/02/2025
Hypergraphs naturally parametrize higher-order relations.Yet GNNs on hypergraph expansions often outperform specialized topological models. We show that adding hypergraph-level encodings yields significant performance and expressivity gains.w/ Raphael Pellegrin, Lukas Fesser arxiv.org/pdf/2502.09570
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