Related papers: Learning proofs for the classification of nilpoten…
Neural networks have been successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are more difficult to train successfully for semi-supervised…
In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…
The method for a problem solution of expenditures reduction of computing resources and time is developed at a pattern recognition, with the way of construction of the minimum tests sets or separate minimum tests on Boolean matrixes is…
Classification may not be reliable for several reasons: noise in the data, insufficient input information, overlapping distributions and sharp definition of classes. Faced with several possibilities neural network may in such cases still be…
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices…
In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.
The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability…
Deep learning methodologies have been employed in several different fields, with an outstanding success in image recognition applications, such as material quality control, medical imaging, autonomous driving, etc. Deep learning models rely…
Given a finite group $G$, we denote by $\nu(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $\nu(G)>1/12,$ then $G$ is solvable.
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
We study the structure of nilpotent subsemigroups in the semigroup $M(n,\mathbb{F})$ of all $n\times n$ matrices over a field, $\mathbb{F}$, with respect to the operation of the usual matrix multiplication. We describe the maximal…
There is general consensus that learning representations is useful for a variety of reasons, e.g. efficient use of labeled data (semi-supervised learning), transfer learning and understanding hidden structure of data. Popular techniques for…
Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is…
Let $G$ be a unitriangular matrix group of nilpotency class at most ten. We show that the Identity Problem (does a semigroup contain the identity matrix?) and the Group Problem (is a semigroup a group?) are decidable in polynomial time for…
The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the…
Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…
The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup…
Quantum Computing and especially Quantum Machine Learning, in a short period of time, has gained a lot of interest through research groups around the world. This can be seen in the increasing number of proposed models for pattern…
Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…
We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal…