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Structure-aware Deep Learning (2026)
Wendlinger, Lorenz
Graph structures permeate the digital landscape in explicit and implicit forms. They connect or construct artifacts by combining semantic and structural information. We also observe them in the systems designed to process this data, in their learning algorithms and the very nature of the tasks they solve. At the same time, machine learning methods are extremely data-hungry, requiring petabytes of data for training. Due to their complexity, graphs remain an under-utilized resource in this regard. Many approaches cannot incorporate them due to being fully structurally unaware or not suited to the specific flavour of graphs encountered in some domains. This disconnect is sub-optimal from an effectiveness and efficiency perspective. We present methods that extend the scope of structure-aware deep learning through structural knowledge integration and enrichment, structural performance prediction, and synergistic transfer learning. Knowledge graphs organize information and make it directly available for querying. They provide a structured inference interface for manual and automated inspection, though they can suffer from data quality issues and require careful schema design. We rephrase the reconciliation of knowledge in knowledge graphs as a link prediction task, making it tractable with adapted graph neural networks, while also benefiting conventional link prediction tasks. We further combine textual semantics and structural expression for legal reference prediction via adapted heterogeneous graph neural networks operating on complex meta-information enriched graphs. Additionally, we explore methods for the integration of intermediary expressions in strongly typed heterogeneous graphs, improving prediction via meta-path-based processing. We also develop methods for automated machine learning workflow analysis and performance prediction. This includes the learning of salient representations for management as well as improvement of workflows through automatic suggestion and refinement of components. These are then extended to the prediction of Neural Architecture Search performance prediction, including adaptation to operation-on-edge spaces. Finally, we investigate the transfer capability of pre-trained attention structures for text-based prediction tasks and find it to be both inferior to directly optimized attention masks as well as highly dependent on inherent domain knowledge. We also show that the exploitation of hierarchical task formulation can improve prediction performance through joint learning in diverse learning domains, including link prediction, performance prediction, and specialized and general argumentation mining. The dissertation contains previously published or submitted texts: Wendlinger, L., Hübscher, G., Ekelhart, A., Granitzer, M. (2022). Reconciliation of Mental Concepts with Graph Neural Networks. In: Strauss, C., Cuzzocrea, A., Kotsis, G., Tjoa, A.M., Khalil, I. (eds): Database and Expert Systems Applications. DEXA 2022. Lecture Notes in Computer Science, vol 13427, p 133-146. Springer, Cham. https://doi.org/10.1007/978-3-031-12426-6_11; Wendlinger, L., Granitzer M. (2024). Informed Heterogeneous Attention Networks for Metapath Based Learning. In: SAC '24: Proceedings of the 39th ACM/SIGAPP Symposium on Applied Computing, p 458-465, ACM, New York. https://doi.org/10.1145/3605098.3635890; Wendlinger, L., Nonn, S.A., Al Zubaer, A., Granitzer, M. (2026). The Missing Link: Joint Legal Citation Prediction Using Heterogeneous Graph Enrichment. In: Wrembel, R., Kotsis, G., Tjoa, A.M., Khalil, I. (eds) Database and Expert Systems Applications. DEXA 2025. Lecture Notes in Computer Science, vol 16047, p 197-211. Springer, Cham. https://doi.org/10.1007/978-3-032-02088-8_14; Wendlinger, L., Stier, J., Granitzer, M. (2021). Evofficient: Reproducing a Cartesian Genetic Programming Method. In: Hu, T., Lourenço, N., Medvet, E. (eds) Genetic Programming. EuroGP 2021. Lecture Notes in Computer Science, vol 12691, p 162-178. Springer, Cham. https://doi.org/10.1007/978-3-030-72812-0_11; Wendlinger, L., Berndl, E., Granitzer, M. (2021). Methods for Automatic Machine-Learning Workflow Analysis. In: Dong, Y., Kourtellis, N., Hammer, B., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track. ECML PKDD 2021. Lecture Notes in Computer Science, vol 12979, p 52-67. Springer, Cham. https://doi.org/10.1007/978-3-030-86517-7_4; Wendlinger, L., Granitzer, M., Fellicious, C. (2023). Pooling Graph Convolutional Networks for Structural Performance Prediction. In: Nicosia, G., et al. (eds) Machine Learning, Optimization, and Data Science. LOD 2022. Lecture Notes in Computer Science, vol 13811, p 1-16. Springer, Cham. https://doi.org/10.1007/978-3-031-25891-6_1; Wendlinger, L., Braun, C., Zubaer, A., Nonn, S., Großkopf, S., Fellicious, C., Granitzer, M.: On the Suitability of pre-trained foundational LLMs for Analysis in German Legal Education, submitted to the proceedings of the International Conference on Machine Learning, Optimization, and Data Science 2025, preprint published: https://doi.org/10.48550/arXiv.2412.15902; Wendlinger, L., Kuhn, R., Mitrovic, J., Granitzer, M. (2025). Joint Learning for Efficient German Argument Mining. In: 2025 IEEE 37th International Conference on Tools with Artificial Intelligence (ICTAI), Athens, Greece, 2025, p 770-777. IEEE, Los Alamitos. https://doi.org/10.1109/ICTAI66417.2025.00111.
Einbettung und Charakterisierung von aligned bar 1-visibility Graphen und outer fan free Graphen (2026)
Neuwirth, Daniel
In dieser Arbeit werden drei verschiedene Klassen von Graphen untersucht. Die Klassen sind die bar (1;1)-visibilty Graphen, die aligned bar 1-visibility Graphen und die outer fan free Graphen. Die Klassen werden durch ihre möglichen Einbettungen charakterisiert. Die Repräsentation der bar (1; j)-visibility Graphen ist, dass jeder Knoten als horizontaler Strich und jede Kante als vertikaler Strich gezeichnet wird. Eine Kante kann einen Knoten genau einmal schneiden und ein Knoten kann j-mal geschnitten werden. Wir erweitern die Ergebnisse von Dean et. al. und geben Beispiele mit einer maximalen Dichte an für bar (1; 2)-visibility, bar (1; 3)-visibility und bar (1; 4)-visibility Graphen und geben einen maximal dünnen Graphen für die Klasse der bar (1;1) visibility Graphen an. Wir zeigen, dass die Klassen der bar (1; j)-visibility Graphen für 1 < j < 1eine unendliche Hierarchie bilden. Abschließend beweisen wir, dass das Erkennungsproblem ob ein Graph eine bar (1;1)-visibility Repräsentation hat, NP-vollständig ist. Die Klasse der aligned bar 1-visibility Graphen (AB1V ) erhält man, indem man die bar (1;1)-visibility Repräsentation um 90 Grad dreht und alle Knoten verlängert, so dass diese alle mit der y-Koordinate 0 starten. Die relative Position bzgl. der x-Koordinate wird mit der t-Ordnung beschrieben und mit der r-Ordnung die relative Position bzgl. der y-Koordinate. Wir erweitern die Erkenntnisse von Felsner und Massow für die Klasse der AB1V Graphen bzgl. ihrer maximalen Dichte, der minimale Grad eines Knotens. Wir führen die Methode Pfadaddition ein, um anhand deren Abschlusseigenschaften zu unterscheiden, ob ein Graph in einer Klasse liegt oder nicht. Diese Methode nutzen wir, um die Beziehung der Klasse der AB1V Graphen mit anderen Klassen zu untersuchen. Für die Klasse der maximalen Graphen geben wir einen dünnen Graphen und eine untere Schranke bzgl. der Dichte an. Wir geben einen Algorithmus an, welcher eine Bucheinbettung aus einer AB1V Einbettung berechnet. Für die Klassen der optimalen AB1V Graphen geben wir einen Einbettungsalgorithmus an. Wir verbessern den Erkennungsalgorithmus von Felsner und Massow, ob ein Graph mit einer gegebenen t-Ordnung eine AB1V Einbettung besitzt. Für die Klasse der distinkt strong AB1V Graphen, Graphen in der jeder Knoten ein unterschiedliche r-Ordnung hat und maximal für die r-Ordnung ist, geben wir einen Algorithmus an, der in O(n6) eine mögliche Einbettung berechnet. Zum Schluss zeigen wir für diese Klasse, dass es exponentiell viele verschiedene Einbettungen gibt. Ein Graph hat eine outer fan free Einbettung, wenn alle Knoten inzident zu einer Fläche sind und keine Kante von zwei Kanten geschnitten wird, die adjazent zu einem Knoten sind. Wir untersuchen diese Klasse zuerst auf die Dichte. Weiter erforschen wir die Beziehung zwischen den Klassen der AB1V , RAC und k-planaren Graphen. Abschließend geben wir eine Reduktion von NAE-3-SAT auf das Erkennungsproblem von outer fan free Graphen an.
Multidimensional Wavelets and Neural Networks (2025)
Schiermeier, Kathrin
The construction of scaling functions and wavelets in multiple dimensions and for arbitrary scaling matrices is a challenging task entailing some complexities. Existing approaches mainly focus on the two-dimensional case using dyadic or quincunx sampling. This thesis aims to develop a method to construct multidimensional scaling and wavelet filters yielding orthogonal scaling functions and wavelets under the usage of convolutional neural networks. We start by recalling substantial fundamentals of ideals, modules, Fourier analysis, filterbanks and multiresolution analyses, where the mentioned concepts are already considered in an arbitrary dimensional setting to prepare the proof of the main result. There, we show the connection between multivariate scaling functions and multidimensional filters possessing certain properties. This enables us to construct scaling functions and corresponding wavelets by discrete filter design. Exploiting the link between the discrete wavelet decomposition, filterbanks and neural networks, we utilize the latter to do so. Being the main difficulty of this process, we especially focus on the Cohen criterion, which concerns the zeros of the Fourier transform of the scaling filter in modulus representing a multivariate trigonometric polynomial. After transferring the Bernstein inequality for univariate trigonomic polynomials to multiple dimensions, we present a method to derive a finite set of inequality constraints implying that the Cohen criterion holds true for a given multivariate cosine sum. Afterwards, we introduce neural networks and TensorFlow as the main tools to execute the described approach, formulate the described objective as an optimization problem and present some smaller numerical experiments and their results. A second objective of this thesis is the construction of filters possessing a unimodular modulation vector and therefore the ability to be completed to a perfect reconstruction filterbank. Both - the construction and the filterbank completion - can also be considered in a neural network framework as we will detail in the last section of this thesis alongside with the presentation of corresponding numerical experiments. In the context of filterbank completion, a further observation which allows to complete any given interpolatory filter to a perfect reconstruction filterbank in a very intuitive and simple way is presented. Furthermore, we explain that any given unimodular filter can be rendered interpolatory through prefiltering.
Multi-Leader Congestion Games with an Adversary (2025)
Henle, Mona
In this thesis, we introduced a congestion game with multiple leaders and a single follower (adversary) which is motivated by security applications with congestion effects. Our objective was to understand the result and the impact of selfish acting individuals in these games. In this regard, we analyzed the existence, the computation and the quality of (approximate) pure Nash equilibria. First, we observed that an exact pure Nash equilibrium always exists in the resulting strategic game among the leaders if the resource cost coefficients are identical and the underlying congestion game is a matroid congestion game. If one of these two conditions is not fulfilled, the existence of PNE is not ensured anymore in general. Consequently, we focused on approximate equilibria. For the case of symmetric singleton strategies, one of our main result established that K ≈ 1.1974, the unique solution of a cubic polynomial equation, is the smallest possible factor such that the existence of a K-approximate equilibrium is guaranteed for all instances of the game. To this end, we presented an efficient algorithm which computes a K-approximate PNE. Furthermore, we showed that the factor K is tight by providing an instance where no α-approximate PNE with α < K exists. However, for a specific symmetric singleton instance there might be a better α-approximate PNE, i.e., with α < K. A given instance could even admit an exact PNE. We provided therefore a polynomial time procedure that computes a best approximate PNE of a given instance. In particular, this procedure can verify the existence of an exact PNE in a given instance efficiently and, if it exists, can also determine the corresponding load vector. Finally, for symmetric singleton instances with two resources, we compared the total cost of a best (cheapest) and worst (most expensive) PNE to the total cost of an optimal outcome, termed by the price of stability and the price of anarchy, respectively. In particular, we verified that the PoS and the PoA are 4/3.
On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients (2025)
Ellinger, Simon
In this dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, such as the Euler-Maruyama scheme or a transformed Milstein scheme, for classes of piecewise Lipschitz continuous, Hölder continuous and Sobolev regular drift coefficients. To do this, we derive the optimal error rates for the different classes of irregular drift coefficients. Furthermore, we show that the solution of an SDE with piecewise Hölder continuous drift coefficient has a regular local density, which is used in the proofs of the lower bounds.
Asset Tokenization and Authentication in the Industrial Metaverse (2025)
Prummer, Michael
The Industrial Revolution is a crucial development step in human history that started three centuries ago and is still ongoing. It continually influences and shapes the globalized world. Today, industries account for 20% of carbon dioxide emissions worldwide and require more than a third of global energy consumption. Current problems, such as climate change, increasing waste, and pollution, require simultaneous optimization across all industrial domains, infrastructure, and systems as they depend on each other. The global industry faces the immense challenges of providing for a surging world population expected to peak in the mid-2080s with 10.4 billion people, as reported by the United Nations. Hence, industries are expected to become less resource-intensive, sustainable, and more resilient to disrupted supply chains while producing for a growing population for the next decades. The Fourth Industrial Revolution, or Industry 4.0 (I4.0), started around 2010 and is still an ongoing transformation of industrial processes towards digitalization, creating smart factories referring to the digital data integration of the entire manufacturing cycle. I4.0 is incredibly information-intensive and requires immense data to simulate and predict essential operations based on a digital shadow of the factory, a so-called digital twin. The Metaverse is considered a digitalization megatrend merging digital and physical worlds, creating immersive experiences and new opportunities for interaction and innovation across various sectors and industries. The vision of the Metaverse promotes interconnected and interoperable real-time 3D virtual worlds that can be frictionlessly traversed while sustaining ownership of one's assets under a self-sovereign identity in a decentralized environment without platform lock-ins to a specific ecosystem. Therefore, the Metaverse creates an immersive parallel reality with collective virtually shared spaces for entertainment, social interactions, education, and a new working environment. The Industrial Metaverse synthesizes Metaverse concepts with current industrial automation, such as I4.0, to deepen the digital-physical convergence by interconnecting internal and external systems to enable decision-making and predictions based on significantly broader knowledge. An Industrial Metaverse factory is entirely mirrored to integrate digital twins of all types of equipment, assets, and other entities that can communicate vertically and horizontally, as well as the knowledge about relevant external systems and industrial core sectors. Through the comprehensive data integration of the Industrial Metaverse, AI-driven applications can predict future events, reducing system and hardware failures. Furthermore, the interconnected virtual environments create a meta-ecosystem for global collaboration, providing spaces for solving complex problems such as engineering and product design tasks, simulation of product twins, and reduced development time and costs. The connected industrial ecosystems create a token-based digital economy for exchanging data, assets, and services cross-metaverse connecting isolated data silos. Sharing digital twin resources and services with other systems enables new innovative applications and growing ecosystems. The theoretical part of this thesis defines the essential characteristics and key technologies of the Industrial Metaverse to derive a reference architecture for a decentralized system of systems, outlining the fundamental Industrial Metaverse building blocks. Interoperable data exchange, access management, and system communication are critical challenges. Especially interoperability of assets such as 3D files that come in different formats and identities must be ensured to move between virtual environments. The unique fusion of technologies leverages interconnected digital twins in the context of immersion, interaction, and collaboration for secure, autonomous-governed, decentralized industrial applications. Hence, the Industrial Metaverse requires the possibility of exchanging assets, products, and services across all systems in a secure manner. Distributed ledger technology enables tamper-proof transactions of assets and value in a decentralized token economy. Therefore, we investigate the feasibility of current tokenization methods for industrial assets, in particular, Printed Circuit Board (PCB) designs and 3D models. We contribute methods to create unique fingerprints of PCB designs to enable their exchange in the token economy. We investigate how to bind files in different formats and quality representations to the same token. A robust multi-file binding based on the copper layers of a PCB design was achieved by calculating an adaptive perceptual hash of all files. The adaptive perceptual hash was evaluated against numerous tamperings of the routing layout of a PCB, showing decent resistance to layout changes. The resulting adaptive perceptual hash can be used as an additional identification attribute in a tokenized asset. Furthermore, assets must be authenticatable and verifiable by marketplaces, manufacturers, and other participants to create trust in a decentralized environment. While assets can be tampered with to manipulate, for example, cryptographic hashes that link the file to the token, perceptual hashes can compute a perceived or functional similarity of two objects instead of the plain file integrity. Without the possibility of verifying and protecting intellectual property, mass adoption of the Metaverse and Industrial Metaverse is unlikely. Therefore, we contribute to detecting tampering attacks on 3D models by introducing a 3D perceptual hash that is robust to a set of mesh manipulations, enabling the trusted exchange and authentication of 3D data in the Metaverse.
An ICT architecture for enabling ancillary services in Distributed Renewable Energy Sources based on the SGAM framework (2022)
Stocker, Armin ; Alshawish, Ali ; Bor, Martin ; Vidler, John ; Gouglidis, Antonios ; Scott, Andrew ; Marnerides, Angelos ; De Meer, Hermann ; Hutchison, David
Smart Grids are electrical grids that require a decentralised way of controlling electric power conditioning and thereby control the production and distribution of energy. Yet, the integration of Distributed Renewable Energy Sources (DRESs) in the Smart Grid introduces new challenges with regards to electrical grid balancing and storing of electrical energy, as well as additional monetary costs. Furthermore, the future smart grid also has to take over the provision of Ancillary Services (ASs). In this paper, a distributed ICT infrastructure to solve such challenges, specifically related to ASs in future Smart Grids, is described. The proposed infrastructure is developed on the basis of the Smart Grid Architecture Model (SGAM) framework, which is defined by the European Commission in Smart Grid Mandate M/490. A testbed that provides a flexible, secure, and low-cost version of this architecture, illustrating the separation of systems and responsibilities, and supporting both emulated DRESs and real hardware has been developed. The resulting system supports the integration of a variety of DRESs with a secure two-way communication channel between the monitoring and controlling components. It assists in the analysis of various inter-operabilities and in the verification of eventual system designs. To validate the system design, the mapping of the proposed architecture to the testbed is presented. Further work will help improve the architecture in two directions; first, by investigating specific-purpose use cases, instantiated using this more generic framework; and second, by investigating the effects a realistic number and variety of connected devices within different grid configurations has on the testbed infrastructure.
SAT Solving Using XOR-OR-AND Normal Forms and Cryptographic Fault Attacks (2025)
Danner, Julian
The Boolean satisfiability problem (SAT) lies at the core of computational logic and has found many applications in verification, cryptography, and artificial intelligence. While conflict-driven SAT solvers (CDCL) excel on large industrial instances, they struggle with XOR-rich instances arising frequently in cryptanalysis, due to the inefficiency of CNF encodings of linear constraints. Conversely, algebraic approaches can work with linear XOR constraints naturally but fail to scale to relevant sizes. Bridging these complementary paradigms with a focus on cryptographic problems is at the heart of this thesis. On one hand, this dissertation advances SAT solving by introducing the XOR-OR-AND normal form (XNF) as a generalization of the conjunctive normal form (CNF), where literals are replaced by XOR chains of literals. This allows for a native representation of XOR constraints. We generalize the CDCL architecture to the richer language of XNFs. The underlying reasoning based on the proof system SRES which is shown to be exponentially stronger than classical resolution. An implementation demonstrates competitive performance and often surpasses state-of-the-art algebraic and logic solvers on random and cryptographic benchmarks. Furthermore, we prove that every XNF formula can be converted in polynomial time to a formula in 2-XNF, enabling a graph-based approach similar to 2-SAT. Building on this, we propose advanced in- and pre-processing techniques, and construct a simple DPLL-based solving framework. Our implementation, 2-Xornado, outperforms modern algebraic and logic solving approaches on many random and some structured cryptographic problems. On the other hand, we apply combined algebraic and logical techniques to cryptanalysis of stream ciphers. We introduce a formal guess-and-determine (GD) framework using a logical abstraction of the information flow in the internal state. From an algebraic point of view, we can then find optimal GD attacks utilizing a Gröbner basis. As a case study, we apply this method to aid in the construction of novel fault attacks on the ciphers KCipher-2 and Enocoro-128v2. Using ad hoc methods combining algebraic and logical approaches, we show that both ciphers are vulnerable to active side-channel attacks under rather weak fault models.
Optimal convergence rates of MCMC integration for functions with unbounded second moment (2025)
Hofstadler, Julian
We study the Markov chain Monte Carlo estimator for numerical integration for func- tions that do not need to be square integrable with respect to the invariant distribution. For chains with a spectral gap we show that the absolute mean error for L^p functions, with p ∈ (1, 2), decreases like n^(1/p)−1 , which is known to be the optimal rate. This improves currently known results where an additional parameter δ > 0 appears and the convergence is of order n^((1+δ)/p)−1 .
A parameterized halting problem, Δ0 truth and the MRDP theorem (2024)
Chen, Yijia ; Müller, Moritz ; Yokoyama, Keita
We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given Δ0-formula ϕ(x); the parameter is the size of ϕ. This parameterization focusses attention on instances where n is large compared to the size of ϕ.We show unconditionally that this problem does not belong to the parameterized analogue of AC0. From this we derive that certain natural upper bounds on the complexity of our parameterized problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that IΔ0 proves the MRDP theorem in a certain weak sense.
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