Related papers: Learning proofs for the classification of nilpoten…

Deep networks are successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are usually much less suited for semi-supervised problems because of…

Machine Learning approaches are good in solving problems that have less information. In most cases, the software domain problems characterize as a process of learning that depend on the various circumstances and changes accordingly. A…

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…

In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

Artificial intelligence and machine learning paves the way to achieve greater technical feats. In this endeavor to hone these techniques, quantum machine learning is budding to serve as an important tool. Using the techniques of deep…

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

We show that every finite group $G$ of size at least $3$ has a nilpotent subgroup of class at most $2$ and size at least $|G|^{1/32\log\log|G|}$. This answers a question of Pyber, and is essentially best possible.

One emerging application of machine learning methods is the inference of galaxy cluster masses. In this note, machine learning is used to directly combine five simulated multiwavelength measurements in order to find cluster masses. This is…

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…

These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…

We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.

Using Machine Learning systems in the real world can often be problematic, with inexplicable black-box models, the assumed certainty of imperfect measurements, or providing a single classification instead of a probability distribution. This…

We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…

In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.

Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…

The aim of this paper is to present a complete description of the structure of finite subsets with small doubling property in ordered nilpotent groups of class 2.

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…

Learning to rank is a rare technology compared with other techniques such as deep neural networks. The number of experts in the field is roughly 1/6 of the number of professionals in deep learning. Being an effective ranking methodology,…

We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…