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We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism $(X,S)\twoheadrightarrow(Y,T)$, we can establish emulation by a cascade product (subsemigroup of the wreath product): $(X,S)\hookrightarrow (Y,T)\wr (Z,U)$. The dependent component $(Z,U)$ contains the kernel of the morphism, the information lost in the map. The implementation complements the existing tools for the holonomy decomposition algorithm. It gives an incremental method to get a coarser decomposition when computing the complete skeleton for holonomy is not feasible. Here, we describe a simplified and generalized algorithm for the lemma and compare it to the holonomy method. Incidentally, the kernel-based method could be the easiest way of understanding the hierarchical decompositions of transformation semigroups and thus the celebrated Krohn-Rhodes theory., Comment: 13 pages, 3 figures, v2: clarifications and added example computer algebra session; final version will be published elsewhere

Training summarization models requires substantial amounts of training data. However for less resourceful languages like Hungarian, openly available models and datasets are notably scarce. To address this gap our paper introduces HunSum-2 an open-source Hungarian corpus suitable for training abstractive and extractive summarization models. The dataset is assembled from segments of the Common Crawl corpus undergoing thorough cleaning, preprocessing and deduplication. In addition to abstractive summarization we generate sentence-level labels for extractive summarization using sentence similarity. We train baseline models for both extractive and abstractive summarization using the collected dataset. To demonstrate the effectiveness of the trained models, we perform both quantitative and qualitative evaluation. Our dataset, models and code are publicly available, encouraging replication, further research, and real-world applications across various domains.

Data augmentation methods for neural machine translation are particularly useful when limited amount of training data is available, which is often the case when dealing with low-resource languages. We introduce a novel augmentation method, which generates new sentences by swapping objects and subjects across bisentences. This is performed simultaneously based on the dependency parse trees of the source and target sentences. We name this method TreeSwap. Our results show that TreeSwap achieves consistent improvements over baseline models in 4 language pairs in both directions on resource-constrained datasets. We also explore domain-specific corpora, but find that our method does not make significant improvements on law, medical and IT data. We report the scores of similar augmentation methods and find that TreeSwap performs comparably. We also analyze the generated sentences qualitatively and find that the augmentation produces a correct translation in most cases. Our code is available on Github.

In this paper we deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$, with replacement, define the same inner right translation of $S$. We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two., Comment: 16 pages

We present a generic framework for data augmentation via dependency subtree swapping that is applicable to machine translation. We extract corresponding subtrees from the dependency parse trees of the source and target sentences and swap these across bisentences to create augmented samples. We perform thorough filtering based on graphbased similarities of the dependency trees and additional heuristics to ensure that extracted subtrees correspond to the same meaning. We conduct resource-constrained experiments on 4 language pairs in both directions using the IWSLT text translation datasets and the Hunglish2 corpus. The results demonstrate consistent improvements in BLEU score over our baseline models in 3 out of 4 language pairs. Our code is available on GitHub.

A novel stochastic optimization method called MAC was suggested. The method is based on the calculation of the objective function at several random points and then an empirical expected value and an empirical covariance matrix are calculated. The empirical expected value is proven to converge to the optimum value of the problem. The MAC algorithm was encoded in Matlab and the code was tested on 20 test problems. Its performance was compared with those of the interior point method (Matlab name: fmincon), simplex, pattern search (PS), simulated annealing (SA), particle swarm optimization (PSO), and genetic algorithm (GA) methods. The MAC method failed two test functions and provided inaccurate results on four other test functions. However, it provided accurate results and required much less CPU time than the widely used optimization methods on the other 14 test functions.

We introduce HunSum-1: a dataset for Hungarian abstractive summarization, consisting of 1.14M news articles. The dataset is built by collecting, cleaning and deduplicating data from 9 major Hungarian news sites through CommonCrawl. Using this dataset, we build abstractive summarizer models based on huBERT and mT5. We demonstrate the value of the created dataset by performing a quantitative and qualitative analysis on the models' results. The HunSum-1 dataset, all models used in our experiments and our code are available open source.

In this paper we study semigroups satisfying the identity $aba=ab$., Comment: 18 pages

AI engines utilizing deep learning neural networks provide excellent tools for analyzing traditional board games. Here we are interested in gaining new insights into the ancient game of Go. For that purpose, we need to define new numerical measures based on the raw output of the engines. In this paper, we develop a numerical tool for automated move-by-move performance evaluation in a context-sensitive manner and for recognizing game features. We measure the urgency of a move by the cost of passing, which is the score value difference between the current configuration of stones and after a hypothetical pass in the same board position. Here we investigate the properties of this measure and describe some applications., Comment: 10 pages, 3 figures, final version will be published elsewhere

We train Transformer-based neural machine translation models for Hungarian-English and English-Hungarian using the Hunglish2 corpus. Our best models achieve a BLEU score of 40.0 on HungarianEnglish and 33.4 on English-Hungarian. Furthermore, we present results on an ongoing work about syntax-based augmentation for neural machine translation. Both our code and models are publicly available.

I train models for the task of neural machine translation for English-Hungarian and Hungarian-English, using the Hunglish2 corpus. The main contribution of this work is evaluating different data augmentation methods during the training of NMT models. I propose 5 different augmentation methods that are structure-aware, meaning that instead of randomly selecting words for blanking or replacement, the dependency tree of sentences is used as a basis for augmentation. I start my thesis with a detailed literature review on neural networks, sequential modeling, neural machine translation, dependency parsing and data augmentation. After a detailed exploratory data analysis and preprocessing of the Hunglish2 corpus, I perform experiments with the proposed data augmentation techniques. The best model for Hungarian-English achieves a BLEU score of 33.9, while the best model for English-Hungarian achieves a BLEU score of 28.6.

Designing complex architectures has been an essential cogwheel in the revolution deep learning has brought about in the past decade. When solving difficult problems in a datadriven manner, a well-tried approach is to take an architecture discovered by renowned deep learning scientists as a basis (e.g. Inception) and try to apply it to a specific problem. This might be sufficient, but as of now, achieving very high accuracy on a complex or yet unsolved task requires the knowledge of highly-trained deep learning experts. In this work, we would like to contribute to the area of Automated Machine Learning (AutoML), specifically Neural Architecture Search (NAS), which intends to make deep learning methods available for a wider range of society by designing neural topologies automatically. Although several different approaches exist (e.g. gradient-based or evolutionary algorithms), our focus is on one of the most promising research directions, reinforcement learning. In this scenario, a recurrent neural network (controller) is trained to create problem-specific neural network architectures (child). The validation accuracies of the child networks serve as a reward signal for training the controller with reinforcement learning. The basis of our proposed work is Efficient Neural Architecture Search (ENAS), where parameter sharing is applied among the child networks. ENAS, like many other RL-based algorithms, emphasize the learning of child networks as increasing their convergence result in a denser reward signal for the controller, therefore significantly reducing training times. The controller was originally trained with REINFORCE. In our research, we propose to modify this to a more modern and complex algorithm, PPO, which has demonstrated to be faster and more stable in other environments. Then, we briefly discuss and evaluate our results.

Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a controlled condition. In dynamical systems theory, such change points are known as bifurcations and lie on a function of the controlled condition called the bifurcation diagram. In this work, we propose a gradient-based approach for inferring the parameters of differential equations that produce a user-specified bifurcation diagram. The cost function contains an error term that is minimal when the model bifurcations match the specified targets and a bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes. The gradients can be computed without the need to differentiate through the operations of the solver that was used to compute the diagram. We demonstrate parameter inference with minimal models which explore the space of saddle-node and pitchfork diagrams and the genetic toggle switch from synthetic biology. Furthermore, the cost landscape allows us to organise models in terms of topological and geometric equivalence.

We present an approach for automatic punctuation restoration with BERT models for English and Hungarian. For English, we conduct our experiments on Ted Talks, a commonly used benchmark for punctuation restoration, while for Hungarian we evaluate our models on the Szeged Treebank dataset. Our best models achieve a macro-averaged $F_1$-score of 79.8 in English and 82.2 in Hungarian. Our code is publicly available., Comment: 11 pages, 6 figures, source code at https://github.com/attilanagy234/neural-punctuator

The widespread availability of superhuman AI engines is changing how we play the ancient game of Go. The open-source software packages developed after the AlphaGo series shifted focus from producing strong playing entities to providing tools for analyzing games. Here we describe two ways of how the innovations of the second generation engines (e.g.~score estimates, variable komi) can be used for defining new metrics that help deepen our understanding of the game. First, we study how much information the search component contributes in addition to the raw neural network policy output. This gives an intrinsic strength measurement for the neural network. Second, we define the effect of a move by the difference in score estimates. This gives a fine-grained, move-by-move performance evaluation of a player. We use this in combating the new challenge of detecting online cheating., Comment: 16 pages, 12 figures, accepted for CANDAR 2020, The Eighth International Symposium on Computing and Networking, Naha, Okinawa, Japan, November 24-27, 2020; final version will be published in IEEE Xplore

Measuring the distance between two bacterial genomes under the inversion process is usually done by assuming all inversions to occur with equal probability. Recently, an approach to calculating inversion distance using group theory was introduced, and is effective for the model in which only very short inversions occur. In this paper, we show how to use the group-theoretic framework to establish minimal distance for any weighting on the set of inversions, generalizing previous approaches. To do this we use the theory of rewriting systems for groups, and exploit the Knuth--Bendix algorithm, the first time this theory has been introduced into genome rearrangement problems. The central idea of the approach is to use existing group theoretic methods to find an initial path between two genomes in genome space (for instance using only short inversions), and then to deform this path to optimality using a confluent system of rewriting rules generated by the Knuth--Bendix algorithm., Comment: 15 pages, 4 figures. To appear in Frontiers in Genetics: Evolution and Population Genetics, in a special issue on Algebraic and Geometric Phylogenetics

The new coronavirus disease 2019 (COVID-19) has been emerged as a rapidly spreading pandemic. The disease is thought to spread mainly from person-to-person through respiratory droplets produced when an infected person coughs, sneezes, or talks. The pathogen of COVID-19 is the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It infects the cells binding to the angiotensin-converting enzyme 2 receptor (ACE2) which is expressed by cells throughout the airways as targets for cellular entry. Although the majority of persons infected with SARS-CoV-2 experience symptoms of mild upper respiratory tract infection, in some people infections of the peripheral airways result in severe, potentially fatal pneumonia. However, the induction of COVID-19 pneumonia requires that SARS-CoV-2 reaches the peripheral airways. While huge efforts have been made to understand the spread of the disease as well as the pathogenesis following cellular entry, much less attention is paid how SARS-CoV-2 from the environment reach the receptors of the target cells. The aim of the present study is to characterize the deposition distribution of SARS-CoV-2 in the airways upon exposure to cough-generated aerosol. For this purpose, the Stochastic Lung Deposition Model has been applied. Aerosol size distribution and breathing parameters were taken from the literature supposing normal breathing through the nose. We found that the probability of direct infection of the peripheral airways due to inhalation of aerosol generated by a bystander cough is very low. As the number of pathogens deposited in the extrathoracic airways is ~10 times higher than in the peripheral airways, we concluded that in most cases COVID-19 pneumonia must be preceded by SARS-CoV-2 infection of the upper airways. Our results suggest that without the enhancement of viral load in the upper airways, COVID-19 would be much less dangerous..., Comment: 10 pages, 5 figures

In this paper we give a subdirect decomposition of semigroups $({\mathfrak F}(S); \circ )$, where $S$ is a semigroup, ${\mathfrak F}(S)$ is the set of all fuzzy sets in $S$, and the operation $\circ$ on ${\mathfrak F}(S)$ is defined by the following way: for $f, g\in {\mathfrak F}(S)$ and $s\in S$, $(f\circ g)(s)=\vee _{{x, y\in S}\atop{s=xy}}(f(x)\wedge g(y))$ if $s\in S^2$, and $(f\circ g)(s)=0$ otherwise., Comment: 11 pages

Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and Philosophy itself. Their unified essence is having a shared understanding of the world helped by off-loading our cognitive efforts to suitable languages., Comment: v4 some clarifications

L. Lov\'asz and B. Szegedy proved in 2006 that the limits of convergent graph sequences can be described by measurable symmetric functions $W: [0, 1]\times [0, 1]\to [0, 1]$ called graphons. In our present paper we investigate the structure of the set of all graphons within the semigroup $(\mathfrak{F}([0, 1]^2); \circ)$ of all fuzzy subsets of the unit square $[0,1]^2=[0, 1]\times [0, 1]$, where the operation $\circ$ is defined by: for every $f, g\in \mathfrak{F}([0,1]^2)$ and every $s\in [0,1]^2$, $(f\circ g)(s)=\vee_{x\in [0,1]^2}(f(x)\wedge g(s))$., Comment: 8 pages