Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
Laplacian eigenmaps for dimensionality reduction and data representation.Neural computation, 15(6):1373–1396
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Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
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Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs
LRD framework with Frenet, NRS, and GFMI metrics shows layer-wise structure in 31 models provides usable signal for model selection and pruning on MTEB tasks.