5 papers
Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation
Alberto Foresti, Ivan Butakov, Alexander Tolmachev +3
Mutual information (MI) estimation is a central problem in machine learning and statistics; however, existing benchmarks typically evaluate estimators on simplified, low-dimensiona…
Reducing the upper bound for the Borsuk number in to 8
Alexander Tolmachev, Vsevolod Voronov
The Borsuk number of -dimensional Euclidean space is the smallest integer such that any set of unit diameter can be partitioned in…
GAS: Improving Discretization of Diffusion ODEs via Generalized Adversarial Solver
Aleksandr Oganov, Ilya Bykov, Eva Neudachina +7
While diffusion models achieve state-of-the-art generation quality, they still suffer from computationally expensive sampling. Recent works address this issue with gradient-based o…
On lower bounds of the density of planar periodic sets without unit distances
Alexander Tolmachev
Determining the maximal density of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds f…
Optimal partitions of the flat torus into parts of smaller diameter
Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov
We consider the problem of partitioning a two-dimensional flat torus into sets in order to minimize the maximal diameter of a part. For we give numerical…