30 citations · 95 across the 24 of their papers we have counts for
25 papers
Growth in noncommutative algebras and entropy in derived categories
Dmitri Piontkovski
A noncommutative projective variety is defined, after Artin and Zhang, by a graded coherent algebra A, where the category of coherent sheaves is the quotient qgr(A) of the category…
Multilinear nilalgebras and the Jacobian theorem
Dmitri Piontkovski
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states…
Degree of freedom count in linear gauge invariant PDE systems
Simon Lyakhovich, Dmitri Piontkovski
We consider not necessarily Lagrangian partial linear differential equations (PDE) with constant coefficients. Einstein proposed a definition of the"strength" of such a field theor…
Betti numbers of attention graphs is all you really need
Laida Kushnareva, Dmitri Piontkovski, Irina Piontkovskaya
We apply methods of topological analysis to the attention graphs, calculated on the attention heads of the BERT model ( arXiv:1810.04805v2 ). Our research shows that the classifier…
Acceptability Judgements via Examining the Topology of Attention Maps
Daniil Cherniavskii, Eduard Tulchinskii, Vladislav Mikhailov +7
The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acce…
Bernstein algebras that are algebraic and the Kurosh problem
Dmitri Piontkovski, Fouad Zitan
We study the class of Bernstein algebras that are algebraic, in the sense that each element generates a finite-dimensional subalgebra. Every Bernstein algebra has a maximal algebra…