Zobrazeno 1 - 10
of 2 713
pro vyhledávání: '"Krotov, A."'
Autor:
Krotov, Denis S.
For the Hamming graph $H(n,q)$, where a $q$ is a constant prime power and $n$ grows, we construct perfect colorings without non-essential arguments such that $n$ depends exponentially on the off-diagonal part of the quotient matrix. In particular, we
Externí odkaz:
http://arxiv.org/abs/2412.04461
We characterize mixed-level orthogonal arrays it terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer-Friedman (BF) bound for pure-level orthogonal arrays. For the case when the numbers of levels are pow
Externí odkaz:
http://arxiv.org/abs/2411.16559
Autor:
Goryainov, Sergey, Krotov, Denis
In Cayley graphs on the additive group of a small vector space over GF$(q)$, $q=2,3$, we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the same field. The existence of a CR code in such Cayley graph $G$ implie
Externí odkaz:
http://arxiv.org/abs/2411.09698
Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require storing ea
Externí odkaz:
http://arxiv.org/abs/2410.24153
Autor:
Achilli, Beatrice, Ventura, Enrico, Silvestri, Gianluigi, Pham, Bao, Raya, Gabriel, Krotov, Dmitry, Lucibello, Carlo, Ambrogioni, Luca
Generative diffusion processes are state-of-the-art machine learning models deeply connected with fundamental concepts in statistical physics. Depending on the dataset size and the capacity of the network, their behavior is known to transition from a
Externí odkaz:
http://arxiv.org/abs/2410.08727
The growth of deep learning (DL) relies heavily on huge amounts of labelled data for tasks such as natural language processing and computer vision. Specifically, in image-to-text or image-to-image pipelines, opinion (sentiment) may be inadvertently l
Externí odkaz:
http://arxiv.org/abs/2409.09560
We define a triangle design as a partition of the set of $2$-dimensional subspaces of an $n$-dimensional vector space into triangles, where a triangle consists of three subspaces with the trivial, $0$-dimensional, intersection and $1$-dimensional mut
Externí odkaz:
http://arxiv.org/abs/2407.19157
Large Language Models (LLMs) struggle to handle long input sequences due to high memory and runtime costs. Memory-augmented models have emerged as a promising solution to this problem, but current methods are hindered by limited memory capacity and r
Externí odkaz:
http://arxiv.org/abs/2402.13449
Autor:
Krotov, Denis S.
We solve several first questions in the table of small parameters of completely regular (CR) codes in Hamming graphs $H(n,q)$. The most uplifting result is the existence of a $\{13,6,1;1,6,9\}$-CR code in $H(n,2)$, $n\ge 13$. We also establish the no
Externí odkaz:
http://arxiv.org/abs/2312.08360
Autor:
Krotov, Denis S., Mogilnykh, Ivan Yu.
Additive one-weight codes over a finite field of non-prime order are equivalent to special subspace coverings of the points of projective space, which we call multispreads. The current paper is devoted to the characterization of the parameters of mul
Externí odkaz:
http://arxiv.org/abs/2312.07883