5 problems

Let $X$ be the data manifold formed by a collection of token embeddings in a $1536$-dimensional embedding space, and let $N$ denote the number of sampled token embeddings. Full-dim…

Let $c{lambda}$ and $c{phi}$ be regularly varying random variables, with tail exponents $calpha$ and $cbeta$, respectively. Let $A$ and $B$ be random matrices in general position,…

Let ${\mathsf{lPCA}}\xspace$ denote a local principal component analysis estimator that infers the dimension of the tangent plane, and let ${\mathsf{MLE}}\xspace$ denote a parametr…

Intrinsic-dimension conjecture. The optimal value of $k$ is related to the intrinsic dimension of the data distribution, even when the distribution is not strictly supported on a l…

The Paris-14E Parc Montsouris dataset consists of daily average temperatures organized into patterns, and the Grassberger–Procaccia approach estimates intrinsic dimension from the…