Related papers: Algebraic methods for solving recognition problems…
We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
In recent years, the interest in interpretable classification models has grown. One of the proposed ways to improve the interpretability of a rule-based classification model is to use sets (unordered collections) of rules, instead of lists…
Along with the proliferation of digital data collected using sensor technologies and a boost of computing power, Deep Learning (DL) based approaches have drawn enormous attention in the past decade due to their impressive performance in…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain examples of such numeral systems are considered. In addition,…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
The cross-depiction problem is that of recognising visual objects regardless of whether they are photographed, painted, drawn, etc. It is a potentially significant yet under-researched problem. Emulating the remarkable human ability to…
One-class recognition is traditionally approached either as a representation learning problem or a feature modeling problem. In this work, we argue that both of these approaches have their own limitations; and a more effective solution can…
To coordinate with other agents in its environment, an agent needs models of what the other agents are trying to do. When communication is impossible or expensive, this information must be acquired indirectly via plan recognition. Typical…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Machine Learning produces efficient decision and prediction models based on input-output data only. Such models have the form of decision trees or neural nets and are far from transparent analytical models, based on mathematical formulas.…
In this paper, we present a new kind of learning implementation to recognize the patterns using the concept of Mirroring Neural Network (MNN) which can extract information from distinct sensory input patterns and perform pattern recognition…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…
Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…
Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations…
In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…