Related papers: Learning proofs for the classification of nilpoten…
Around 1980 commutator theory was generalized from groups to arbitrary algebras using the socalled term condition commutator. The semigroups that are abelian with respect to this commutator were classified by Warne (1994). We study what…
We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, we demonstrate the utility of machine-learning in…
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
In many real-world scenarios, labeled data for a specific machine learning task is costly to obtain. Semi-supervised training methods make use of abundantly available unlabeled data and a smaller number of labeled examples. We propose a new…
Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Extreme Learning Machines (ELMs) have become a popular tool in the field of Artificial Intelligence due to their very high training speed and generalization capabilities. Another advantage is that they have a single hyper-parameter that…
Semi-supervised few-shot learning consists in training a classifier to adapt to new tasks with limited labeled data and a fixed quantity of unlabeled data. Many sophisticated methods have been developed to address the challenges this…
In this paper, we show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log2(n)] + m + 3)-by-(finite of order $\le$ m!). Also we show that the derived length of…
In a context of malicious software detection, machine learning (ML) is widely used to generalize to new malware. However, it has been demonstrated that ML models can be fooled or may have generalization problems on malware that has never…
While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains: The current strategies rely heavily on a huge amount of labeled data. In many real-world problems, it is not feasible to create such an…
We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.
We obtain a characterization of the binary commutator on completely simple semigroups, using their Rees matrix representation. Consequently, we prove that a regular semigroup is nilpotent (solvable) if and only if it is simple, and all its…
We present a taxonomy of research on Machine Learning (ML) applied to enhance simulations together with a catalog of some activities. We cover eight patterns for the link of ML to the simulations or systems plus three algorithmic areas:…
Quantum classification is defined as the task of predicting the associated class of an unknown quantum state drawn from an ensemble of pure states given a finite number of copies of this state. By recasting the state discrimination problem…
Machine learning-based intrusion detection requires complex models to capture patterns in high-dimensional, noisy, and class-imbalanced raw network traffic, yet deploying such models remains impractical on resource-constrained devices with…
A minimal model of polychronous groups in neural networks is presented. The model is computationally efficient and allows the study of polychronous groups independent of specific neuron models. Computational experiments were performed with…
When analyzing the behavior of machine learning algorithms, it is important to identify specific data subgroups for which the considered algorithm shows different performance with respect to the entire dataset. The intervention of domain…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…