accepted posts
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Jacobi Fields in Machine Learning
Jacobi fields are a concept from differential geometry that describe how neighboring geodesics on a curved manifold deviate from one another. This post provides an intuitive int...
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Fewer Edges, Faster Protein Graph Learning
Protein graphs should not be constructed blindly based on spatial proximity: they must reflect directed, geometrically viable chemistry. We introduce Angle Rewiring, a biologica...
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When the k-NN Metric Breaks: A Geometric Phase Transition in Local Density Estimation
LOF operates on the k-NN graph metric — a non-Euclidean structure that breaks under contamination. We show LOF undergoes a sharp phase transition at c*≈k/n: below it, near-perfe...
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Crystalite: A Lightweight Transformer for Efficient Crystal Modeling
Crystalite is a lightweight diffusion Transformer for crystal generation and crystal structure prediction. This post covers its chemistry-aware atom encoding, geometry-aware att...
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To Augment or Not to Augment? Diagnosing Distributional Symmetry Breaking
Many popular ML datasets are heavily canonicalized — objects almost always appear in the same orientation. We measure this with a simple classifier test, showing theoretically t...
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4-Dimensional Objects as a Tool to Study Symmetry Learning in Humans and Machines
We propose four-dimensional Shepard-Metzler shapes as a tool to study symmetry learning in humans and machines.
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Blowup and Blowdown in Deep Learning: Tracking Symmetry Breaking with Algebraic Geometry
We propose algebraic-geometric indicators to track how deep networks simultaneously expand representation dimension (blowup) and break input symmetries (blowdown) during trainin...
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TOPOS: Topological Optimal-transport Partitioned Operator Solver
Neural operators have emerged as a powerful approach in scientific machine learning, enabling resolution-invariant mappings across infinite-dimensional function spaces for appli...
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Graph Mamba - Rethinking Graph Learning
Graph Mamba replaces message passing by turning local subgraphs into token sequences processed by selective state space models. We explain the idea with an interactive Cora demo...
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Symmetry Increase and Equivariant Feature Selection
This blog shows that symmetric inputs can induce representation degeneration due to the algebraic structure of the feature space itself, leading to loss of discriminative power,...
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The Role of Directionality in Graph Neural Networks
We investigate how graph directionality may influence GNN performance across homophilic and heterophilic benchmarks. By controlling for directionality, we observe performance ch...