6 papers
Intrinsic Geometry Matching: learning observation-equivariant process geometry
Manuel Lecha, Michael Bronstein, Iolo Jones
Real data are often arbitrary, indirect observations of an unknown underlying process, and those observations can distort its geometry. Existing geometric methods equip data with t…
Riemannian Metric Matching for Scalable Geometric Modeling of Distributions
Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst +2
High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly wit…
Why Are DMD Students Lazy? Understanding the Copying Behavior in Few-Step Distillation
Shucheng Li, Iolo Jones, Alexander Tong +1
Distribution Matching Distillation (DMD) compresses pretrained diffusion models into efficient few-step generators by aligning their noised distributions across all scales. In prin…
Carré du champ flow matching: better quality-generalisation tradeoff in generative models
Jacob Bamberger, Iolo Jones, Dennis Duncan +3
Deep generative models often face a fundamental tradeoff: high sample quality can come at the cost of memorisation, where the model reproduces training data rather than generalisin…
Manifold Diffusion Geometry: Curvature, Tangent Spaces, and Dimension
Iolo Jones
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian…
Algebraic Dynamical Systems in Machine Learning
Iolo Jones, Jerry Swan, Jeffrey Giansiracusa
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a…