Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
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Conditions on curvature, temperature, and saddle behavior ensure polynomial mixing times for Langevin dynamics on Riemannian manifolds via a submersion relation.
Derives ODEs and explicit solutions for geodesics between full-rank matrices in deep linear network geometry and shows that certain horizontal straight lines in the invariant balanced manifold remain geodesics under Riemannian submersion.
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Patnaik-Pearson intrinsic dimension for internal representations of neural networks
Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
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Rapid mixing for Gibbs measures in Riemannian manifolds
Conditions on curvature, temperature, and saddle behavior ensure polynomial mixing times for Langevin dynamics on Riemannian manifolds via a submersion relation.
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Geodesics in the Deep Linear Network
Derives ODEs and explicit solutions for geodesics between full-rank matrices in deep linear network geometry and shows that certain horizontal straight lines in the invariant balanced manifold remain geodesics under Riemannian submersion.