Yevgeny Liokumovich

works on

high-dimensional manifolds 1 language models 1 representation learning 1 residual stream analysis 1 sky map decoding 1

From the 1 of 5 linked papers with an AI index.

collaborators

5 papers

cs.LG2026

Sky sphere representation in language models

Aleksandr Berdnikov, Yevgeny Liokumovich

The paper investigates whether large language models (~100B parameters) contain a decodable representation of the night sky map within their residual streams, showing that most exa…

math.DG2025

On the existence of minimal Heegaard surfaces

Daniel Ketover, Yevgeny Liokumovich, Antoine Song

Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$ -manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or i…

math.DG2025

The Smale conjecture and min-max theory

Daniel Ketover, Yevgeny Liokumovich

We give a new proof of the Smale conjecture for $RP^{3}$ and all lens spaces using minimal surfaces and min-max theory. For $RP^{3}$ , the conjecture was first proved…

math.DG2025

Length of a closed geodesic in 3-manifolds of positive scalar curvature

Yevgeny Liokumovich, Davi Maximo, Regina Rotman

Let $M$ be a closed $3$ -dimensional Riemannian manifold with positive scalar curvature, $R_{g} \geq 6$ . We show that $M$ contains a non-trivial closed geodesic of length less than $2…

math.DG2025

Parametric inequalities and Weyl law for the volume spectrum

Larry Guth, Yevgeny Liokumovich

We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities:…