5 papers
Spectral embedding and the latent geometry of multipartite networks
Alexander Modell, Ian Gallagher, Joshua Cape +1
Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science…
The Origins of Representation Manifolds in Large Language Models
Alexander Modell, Patrick Rubin-Delanchy, Nick Whiteley
There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key el…
How high is `high'? Rethinking the roles of dimensionality in topological data analysis and manifold learning
Hannah Sansford, Nick Whiteley, Patrick Rubin-Delanchy
We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random functi…
Valid Conformal Prediction for Dynamic GNNs
Ed Davis, Ian Gallagher, Daniel John Lawson +1
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are p…
Statistical exploration of the Manifold Hypothesis
Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold,…