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We present a method, which allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we propose to use a scoring function which chooses the most promising data. To further reduce the complexity of the approximation, we restrict our considerations to the set of closed-loop reachable states. That is, the approximating function only has to be accurate within this set. This makes our method especially suited for systems, where the set of initial conditions is small. In order to guarantee safety and high performance of the designed approximated controller, we use reachability analysis based on Monte Carlo methods.

In this paper we present a hybrid method for the automatic detection of dermatological pathologies in medical reports. We use a large language model combined with medical ontologies to predict, given a first appointment or follow-up medical report, the pathology a person may suffer from. The results show that teaching the model to learn the type, severity and location on the body of a dermatological pathology as well as in which order it has to learn these three features significantly increases its accuracy. The article presents the demonstration of state-of-the-art results for classification of medical texts with a precision of 0.84, micro and macro F1-score of 0.82 and 0.75, and makes both the method and the dataset used available to the community. -- En este art\'iculo presentamos un m\'etodo h\'ibrido para la detecci\'on autom\'atica de patolog\'ias dermatol\'ogicas en informes m\'edicos. Usamos un modelo de lenguaje amplio en espa\~nol combinado con ontolog\'ias m\'edicas para predecir, dado un informe m\'edico de primera cita o de seguimiento, la patolog\'ia del paciente. Los resultados muestran que el tipo, la gravedad y el sitio en el cuerpo de una patolog\'ia dermatol\'ogica, as\'i como en qu\'e orden tiene un modelo que aprender esas tres caracter\'isticas, aumentan su precisi\'on. El art\'iculo presenta la demostraci\'on de resultados comparables al estado del arte de clasificaci\'on de textos m\'edicos con una precisi\'on de 0.84, micro y macro F1-score de 0.82 y 0.75, y deja a disposici\'on de la comunidad tanto el m\'etodo como el conjunto de datos utilizado., Comment: 22 pages, in Spanish language, 6 figures, Proceedings of the 40th venue of the SEPLN

Recent advances in large language models have enabled the creation of highly effective chatbots, which may serve as a platform for targeted advertising. This paper investigates the risks of personalizing advertising in chatbots to their users. We developed a chatbot that embeds personalized product advertisements within LLM responses, inspired by similar forays by AI companies. Our benchmarks show that ad injection impacted certain LLM attribute performance, particularly response desirability. We conducted a between-subjects experiment with 179 participants using chabots with no ads, unlabeled targeted ads, and labeled targeted ads. Results revealed that participants struggled to detect chatbot ads and unlabeled advertising chatbot responses were rated higher. Yet, once disclosed, participants found the use of ads embedded in LLM responses to be manipulative, less trustworthy, and intrusive. Participants tried changing their privacy settings via chat interface rather than the disclosure. Our findings highlight ethical issues with integrating advertising into chatbot responses

Simple data augmentation techniques, such as rotations and flips, are widely used to enhance the generalization power of computer vision models. However, these techniques often fail to modify high-level semantic attributes of a class. To address this limitation, researchers have explored generative augmentation methods like the recently proposed DA-Fusion. Despite some progress, the variations are still largely limited to textural changes, thus falling short on aspects like varied viewpoints, environment, weather conditions, or even class-level semantic attributes (eg, variations in a dog's breed). To overcome this challenge, we propose DIAGen, building upon DA-Fusion. First, we apply Gaussian noise to the embeddings of an object learned with Textual Inversion to diversify generations using a pre-trained diffusion model's knowledge. Second, we exploit the general knowledge of a text-to-text generative model to guide the image generation of the diffusion model with varied class-specific prompts. Finally, we introduce a weighting mechanism to mitigate the impact of poorly generated samples. Experimental results across various datasets show that DIAGen not only enhances semantic diversity but also improves the performance of subsequent classifiers. The advantages of DIAGen over standard augmentations and the DA-Fusion baseline are particularly pronounced with out-of-distribution samples., Comment: Accepted for publication in GCPR 2024

The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain adjacency relation. This problem is PSPACE-complete in general. The concept of the dominating set is known to be quite useful for analyzing wireless networks, social networks, and sensor networks. We develop an approach to solve the dominating set reconfiguration problem based on Answer Set Programming (ASP). Our declarative approach relies on a high-level ASP encoding, and both the grounding and solving tasks are delegated to an ASP-based combinatorial reconfiguration solver. To evaluate the effectiveness of our approach, we conduct experiments on a newly created benchmark set.

We are interested in automating reasoning with and about study regulations, catering to various stakeholders, ranging from administrators, over faculty, to students at different stages. Our work builds on an extensive analysis of various study programs at the University of Potsdam. The conceptualization of the underlying principles provides us with a formal account of study regulations. In particular, the formalization reveals the properties of admissible study plans. With these at end, we propose an encoding of study regulations in Answer Set Programming that produces corresponding study plans. Finally, we show how this approach can be extended to a generic user interface for exploring study plans., Comment: To appear in Theory and Practise of Logic Programming

Slot attention aims to decompose an input image into a set of meaningful object files (slots). These latent object representations enable various downstream tasks. Yet, these slots often bind to object parts, not objects themselves, especially for real-world datasets. To address this, we introduce Guided Latent Slot Diffusion - GLASS, an object-centric model that uses generated captions as a guiding signal to better align slots with objects. Our key insight is to learn the slot-attention module in the space of generated images. This allows us to repurpose the pre-trained diffusion decoder model, which reconstructs the images from the slots, as a semantic mask generator based on the generated captions. GLASS learns an object-level representation suitable for multiple tasks simultaneously, e.g., segmentation, image generation, and property prediction, outperforming previous methods. For object discovery, GLASS achieves approx. a +35% and +10% relative improvement for mIoU over the previous state-of-the-art (SOTA) method on the VOC and COCO datasets, respectively, and establishes a new SOTA FID score for conditional image generation amongst slot-attention-based methods. For the segmentation task, GLASS surpasses SOTA weakly-supervised and language-based segmentation models, which were specifically designed for the task., Comment: Project Page: https://guided-sa.github.io

Attribution maps are one of the most established tools to explain the functioning of computer vision models. They assign importance scores to input features, indicating how relevant each feature is for the prediction of a deep neural network. While much research has gone into proposing new attribution methods, their proper evaluation remains a difficult challenge. In this work, we propose a novel evaluation protocol that overcomes two fundamental limitations of the widely used incremental-deletion protocol, i.e., the out-of-domain issue and lacking inter-model comparisons. This allows us to evaluate 23 attribution methods and how eight different design choices of popular vision models affect their attribution quality. We find that intrinsically explainable models outperform standard models and that raw attribution values exhibit a higher attribution quality than what is known from previous work. Further, we show consistent changes in the attribution quality when varying the network design, indicating that some standard design choices promote attribution quality.

This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular components for data loading and processing, as well as model training, optimization, and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBenchmarkX is that it allows for the transformation and lifting between topological domains. This enables, for example, to obtain richer data representations and more fine-grained analyses by mapping the topology and features of a graph to higher-order topological domains such as simplicial and cell complexes. The range of applicability of TopoBenchmarkX is demonstrated by benchmarking several TDL architectures for various tasks and datasets.

Residual connections and normalization layers have become standard design choices for graph neural networks (GNNs), and were proposed as solutions to the mitigate the oversmoothing problem in GNNs. However, how exactly these methods help alleviate the oversmoothing problem from a theoretical perspective is not well understood. In this work, we provide a formal and precise characterization of (linearized) GNNs with residual connections and normalization layers. We establish that (a) for residual connections, the incorporation of the initial features at each layer can prevent the signal from becoming too smooth, and determines the subspace of possible node representations; (b) batch normalization prevents a complete collapse of the output embedding space to a one-dimensional subspace through the individual rescaling of each column of the feature matrix. This results in the convergence of node representations to the top-$k$ eigenspace of the message-passing operator; (c) moreover, we show that the centering step of a normalization layer -- which can be understood as a projection -- alters the graph signal in message-passing in such a way that relevant information can become harder to extract. We therefore introduce a novel, principled normalization layer called GraphNormv2 in which the centering step is learned such that it does not distort the original graph signal in an undesirable way. Experimental results confirm the effectiveness of our method.

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise., Comment: 30 pages, 10 figures, comments welcome

Graph neural networks (GNNs) have emerged as powerful tools for processing relational data in applications. However, GNNs suffer from the problem of oversmoothing, the property that the features of all nodes exponentially converge to the same vector over layers, prohibiting the design of deep GNNs. In this work we study oversmoothing in graph convolutional networks (GCNs) by using their Gaussian process (GP) equivalence in the limit of infinitely many hidden features. By generalizing methods from conventional deep neural networks (DNNs), we can describe the distribution of features at the output layer of deep GCNs in terms of a GP: as expected, we find that typical parameter choices from the literature lead to oversmoothing. The theory, however, allows us to identify a new, nonoversmoothing phase: if the initial weights of the network have sufficiently large variance, GCNs do not oversmooth, and node features remain informative even at large depth. We demonstrate the validity of this prediction in finite-size GCNs by training a linear classifier on their output. Moreover, using the linearization of the GCN GP, we generalize the concept of propagation depth of information from DNNs to GCNs. This propagation depth diverges at the transition between the oversmoothing and non-oversmoothing phase. We test the predictions of our approach and find good agreement with finite-size GCNs. Initializing GCNs near the transition to the non-oversmoothing phase, we obtain networks which are both deep and expressive.

We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi graph, and consecutively augment the graph with cells for each dimension with a specified probability. As the number of possible cells increases combinatorially -- e.g., 2-cells can be represented as cycles, or permutations -- we derive an approximate sampling algorithm for this model limited to two-dimensional abstract cell complexes. Since there is a large variance in the number of simple cycles on graphs drawn from the same configuration of ER, we also provide an efficient method to approximate that number, which is of independent interest. Moreover, it enables us to specify the expected number of 2-cells of each boundary length we want to sample. We provide some initial analysis into the properties of random CCs drawn from this model. We further showcase practical applications for our random CCs as null models, and in the context of (random) liftings of graphs to cell complexes. Both the sampling and cycle count estimation algorithms are available in the package `py-raccoon` on the Python Packaging Index., Comment: 10 pages, 8 figures (plus appendix). For evaluation code, see https://github.com/josefhoppe/random-abstract-cell-complexes

A long-standing challenge in developing machine learning approaches has been the lack of high-quality labeled data. Recently, models trained with purely synthetic data, here termed synthetic clones, generated using large-scale pre-trained diffusion models have shown promising results in overcoming this annotation bottleneck. As these synthetic clone models progress, they are likely to be deployed in challenging real-world settings, yet their suitability remains understudied. Our work addresses this gap by providing the first benchmark for three classes of synthetic clone models, namely supervised, self-supervised, and multi-modal ones, across a range of robustness measures. We show that existing synthetic self-supervised and multi-modal clones are comparable to or outperform state-of-the-art real-image baselines for a range of robustness metrics - shape bias, background bias, calibration, etc. However, we also find that synthetic clones are much more susceptible to adversarial and real-world noise than models trained with real data. To address this, we find that combining both real and synthetic data further increases the robustness, and that the choice of prompt used for generating synthetic images plays an important part in the robustness of synthetic clones., Comment: Accepted at CVPR 2024 Workshop: SyntaGen-Harnessing Generative Models for Synthetic Visual Datasets. Project page at https://synbenchmark.github.io/SynCloneBenchmark Comments: Fix typo in Fig. 1

We draw on the Protection Motivation Theory (PMT) to design nudges that encourage users to change breached passwords. Our online experiment ($n$=$1,386$) compared the effectiveness of a threat appeal (highlighting negative consequences of breached passwords) and a coping appeal (providing instructions on how to change the breached password) in a 2x2 factorial design. Compared to the control condition, participants receiving the threat appeal were more likely to intend to change their passwords, and participants receiving both appeals were more likely to end up changing their passwords; both comparisons have a small effect size. Participants' password change behaviors are further associated with other factors such as their security attitudes (SA-6) and time passed since the breach, suggesting that PMT-based nudges are useful but insufficient to fully motivate users to change their passwords. Our study contributes to PMT's application in security research and provides concrete design implications for improving compromised credential notifications., Comment: Manuscript under review at ACM Transactions on Computer-Human Interaction

We propose Large Neighborhood Prioritized Search (LNPS) for solving combinatorial optimization problems in Answer Set Programming (ASP). LNPS is a metaheuristic that starts with an initial solution and then iteratively tries to find better solutions by alternately destroying and prioritized searching for a current solution. Due to the variability of neighborhoods, LNPS allows for flexible search without strongly depending on the destroy operators. We present an implementation of LNPS based on ASP. The resulting heulingo solver demonstrates that LNPS can significantly enhance the solving performance of ASP for optimization. Furthermore, we establish the competitiveness of our LNPS approach by empirically contrasting it to (adaptive) large neighborhood search., Comment: 11 pages

We construct unitary irreducible representation of the de Sitter group, that forms the basis for the study of $dS_{d+1}$ QFT. Using the intertwining kernel analysis, we discuss bosonic symmetric tensor, and fermionic higher-spinors. Particular care is given to the structure and construction of exceptional series and fermionic operators. We discuss the discrete series, and explain how and why the exceptional series give rise to seemingly non-invariant correlators in de Sitter. Using tools from Clifford analysis, we show that for $d>3$, there are no exceptional fermionic representations, and so no unitary (higher)-gravitino fields. We also consider the structure of representations for $d=3$ and $d=2$, as relevant for the study of $dS_4$, the only space allowing for unitary gravitino and its generalisation, and of $dS_3$., Comment: 50 pages, 1 fig., many diagrams

Unsupervised semantic segmentation aims to automatically partition images into semantically meaningful regions by identifying global semantic categories within an image corpus without any form of annotation. Building upon recent advances in self-supervised representation learning, we focus on how to leverage these large pre-trained models for the downstream task of unsupervised segmentation. We present PriMaPs - Principal Mask Proposals - decomposing images into semantically meaningful masks based on their feature representation. This allows us to realize unsupervised semantic segmentation by fitting class prototypes to PriMaPs with a stochastic expectation-maximization algorithm, PriMaPs-EM. Despite its conceptual simplicity, PriMaPs-EM leads to competitive results across various pre-trained backbone models, including DINO and DINOv2, and across different datasets, such as Cityscapes, COCO-Stuff, and Potsdam-3. Importantly, PriMaPs-EM is able to boost results when applied orthogonally to current state-of-the-art unsupervised semantic segmentation pipelines. Code is available at https://github.com/visinf/primaps., Comment: Published in TMLR (September 2024) | OpenReview: see https://openreview.net/forum?id=UawaTQzfwy | Project Page: see https://visinf.github.io/primaps/ | Code: see https://github.com/visinf/primaps

The need for compliant and proprioceptive actuators has grown more evident in pursuing more adaptable and versatile robotic systems. Hydraulically Amplified Self-Healing Electrostatic (HASEL) actuators offer distinctive advantages with their inherent softness and flexibility, making them promising candidates for various robotic tasks, including delicate interactions with humans and animals, biomimetic locomotion, prosthetics, and exoskeletons. This has resulted in a growing interest in the capacitive self-sensing capabilities of HASEL actuators to create miniature displacement estimation circuitry that does not require external sensors. However, achieving HASEL self-sensing for actuation frequencies above 1 Hz and with miniature high-voltage power supplies has remained limited. In this paper, we introduce the F-HASEL actuator, which adds an additional electrode pair used exclusively for capacitive sensing to a Peano-HASEL actuator. We demonstrate displacement estimation of the F-HASEL during high-frequency actuation up to 20 Hz and during external loading using miniaturized circuitry comprised of low-cost off-the-shelf components and a miniature high-voltage power supply. Finally, we propose a circuitry to estimate the displacement of multiple F-HASELs and demonstrate it in a wearable application to track joint rotations of a virtual reality user in real-time., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hypergraphs and simplicial complexes. While the increased expressivity of these models can indeed lead to a better classification performance and a more faithful representation of the underlying system, the computational cost of these higher-order models can increase dramatically. To this end, we here explore a simplicial complex neural network learning architecture based on random walks and fast 1D convolutions (SCRaWl), in which we can adjust the increase in computational cost by varying the length and number of random walks considered while accounting for higher-order relationships. Importantly, due to the random walk-based design, the expressivity of the proposed architecture is provably incomparable to that of existing message-passing simplicial neural networks. We empirically evaluate SCRaWl on real-world datasets and show that it outperforms other simplicial neural networks.

Video frame interpolation, the task of synthesizing new frames in between two or more given ones, is becoming an increasingly popular research target. However, the current evaluation of frame interpolation techniques is not ideal. Due to the plethora of test datasets available and inconsistent computation of error metrics, a coherent and fair comparison across papers is very challenging. Furthermore, new test sets have been proposed as part of method papers so they are unable to provide the in-depth evaluation of a dedicated benchmarking paper. Another severe downside is that these test sets violate the assumption of linearity when given two input frames, making it impossible to solve without an oracle. We hence strongly believe that the community would greatly benefit from a benchmarking paper, which is what we propose. Specifically, we present a benchmark which establishes consistent error metrics by utilizing a submission website that computes them, provides insights by analyzing the interpolation quality with respect to various per-pixel attributes such as the motion magnitude, contains a carefully designed test set adhering to the assumption of linearity by utilizing synthetic data, and evaluates the computational efficiency in a coherent manner., Comment: http://sniklaus.com/vfibench

Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are based on the algebraic representation of graphs via matrices such as the graph Laplacian, or on associated graph embeddings. Such embeddings associate to each node a set of coordinates in a vector space, a representation which can then be employed for learning tasks such as the classification or alignment of the nodes of the graph. As the geometric picture provided by embedding methods enables the use of a multitude of methods developed for vector space data, embeddings have thus gained interest both from a theoretical as well as a practical perspective. Inspired by trace-optimization problems, often encountered in the analysis of graph-based data, here we present a method to derive ellipsoidal embeddings of the nodes of a graph, in which each node is assigned a set of coordinates on the surface of a hyperellipsoid. Our method may be seen as an alternative to popular spectral embedding techniques, to which it shares certain similarities we discuss. To illustrate the utility of the embedding we conduct a case study in which we analyse synthetic and real world networks with modular structure, and compare the results obtained with known methods in the literature., Comment: 29 pages, 6 figures. A few typos corrected

We present alternative approaches to routing and scheduling in Answer Set Programming (ASP), and explore them in the context of Multi-agent Path Finding. The idea is to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents. This also abolishes the need for fixed upper bounds on the length of plans. The trade-off for this avoidance is that (parts of) temporal trajectories must be acyclic, since multiple occurrences of the same action or fluent cannot be distinguished anymore. While this approach provides an interesting alternative for modeling routing, it is without alternative for scheduling since fine-grained timings cannot be represented in ASP in a feasible way. This is different for partial orders that can be efficiently handled by external means such as acyclicity and difference constraints. We formally elaborate upon this idea and present several resulting ASP encodings. Finally, we demonstrate their effectiveness via an empirical analysis.

Autonomous spacecraft control via Shielded Deep Reinforcement Learning (SDRL) has become a rapidly growing research area. However, the construction of shields and the definition of tasking remains informal, resulting in policies with no guarantees on safety and ambiguous goals for the RL agent. In this paper, we first explore the use of formal languages, namely Linear Temporal Logic (LTL), to formalize spacecraft tasks and safety requirements. We then define a manner in which to construct a reward function from a co-safe LTL specification automatically for effective training in SDRL framework. We also investigate methods for constructing a shield from a safe LTL specification for spacecraft applications and propose three designs that provide probabilistic guarantees. We show how these shields interact with different policies and the flexibility of the reward structure through several experiments., Comment: 9 pages, 2 figures, 2 tables, ACC 2024

Privacy policies are crucial for informing users about data practices, yet their length and complexity often deter users from reading them. In this paper, we propose an automated approach to identify and visualize data practices within privacy policies at different levels of detail. Leveraging crowd-sourced annotations from the ToS;DR platform, we experiment with various methods to match policy excerpts with predefined data practice descriptions. We further conduct a case study to evaluate our approach on a real-world policy, demonstrating its effectiveness in simplifying complex policies. Experiments show that our approach accurately matches data practice descriptions with policy excerpts, facilitating the presentation of simplified privacy information to users.

We present a global fit of neutral-current elastic (NCE) neutrino-scattering data and parity-violating electron-scattering (PVES) data with the goal of determining the strange quark contribution to the vector and axial form factors of the proton. Previous fits of this form included data from a variety of PVES experiments (PVA4, HAPPEx, G0, SAMPLE) and the NCE neutrino and anti-neutrino data from BNL E734. These fits did not constrain the strangeness contribution to the axial form factor $G_A^s(Q^2)$ at low $Q^2$ very well because there was no NCE data for $Q^2<0.45$ GeV$^2$. Our new fit includes for the first time MiniBooNE NCE data from both neutrino and anti-neutrino scattering; this experiment used a hydrocarbon target and so a model of the neutrino interaction with the carbon nucleus was required. Three different nuclear models have been employed: a relativistic Fermi gas model, the SuperScaling Approximation model, and a spectral function model. We find a tremendous improvement in the constraint of $G_A^s(Q^2)$ at low $Q^2$ compared to previous work, although more data is needed from NCE measurements that focus on exclusive single-proton final states, for example from MicroBooNE., Comment: Revised in light of referee comments; now accepted for publication in Physical Review D

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field., Comment: Proceedings of the 41st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/.

The representation of a dynamic problem in ASP usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today's ASP solvers is conflict-driven constraint learning. Our question is now whether a constraint learned for particular time steps can be generalized and reused at other time stamps, and ultimately whether this enhances the overall solver performance on temporal problems. Knowing full well the domain of time, we study conditions under which learned dynamic constraints can be generalized. We propose a simple translation of the original logic program such that, for the translated programs, the learned constraints can be generalized to other time points. Additionally, we identify a property of temporal problems that allows us to generalize all learned constraints to all time steps. It turns out that this property is satisfied by many planning problems. Finally, we empirically evaluate the impact of adding the generalized constraints to an ASP solver. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: 41 pages, 2 figures, Under consideration in Theory and Practice of Logic Programming (TPLP)

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric, and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added., Comment: arXiv admin note: text overlap with arXiv:2304.14778

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive representations of graphs as Gaussian mixture models, fitted to distributions of sampled node embeddings over the same space. The Wasserstein distance between these Gaussian mixture distributions then yields an interpretable and easily computable distance measure, which can further be tailored for the comparison at hand by choosing appropriate embeddings. We propose two embeddings for this framework and show that under certain assumptions about the shape of the resulting Gaussian mixture components, further computational improvements of this Wasserstein distance can be achieved. An empirical validation of our findings on synthetic data and real-world Functional Brain Connectivity networks shows promising performance compared to existing embedding methods.

Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least $k$ points, thereby providing a $k$-anonymity type disclosure guarantee for each point in the dataset. Previous algorithms for univariate microaggregation had a $O(k n)$ time complexity. By rephrasing microaggregation as an instance of the concave least weight subsequence problem, in this work we provide improved algorithms that provide an optimal univariate microaggregation on sorted data in $O(n)$ time and space. We further show that our algorithms work not only for sum of squares cost functions, as typically considered, but seamlessly extend to many other cost functions used for univariate microaggregation tasks. In experiments we show that the presented algorithms lead to real world performance improvements.

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling problem -- learning convenient representations of the gravitational potential from position and acceleration data. These PINN gravity models, or PINN-GMs, have demonstrated advantages in model compactness, robustness to noise, and sample efficiency when compared to popular alternatives; however, further investigation has revealed various failure modes for these and other machine learning gravity models which this manuscript aims to address. Specifically, this paper introduces the third generation Physics-Informed Neural Network Gravity Model (PINN-GM-III) which includes design changes that solve the problems of feature divergence, bias towards low-altitude samples, numerical instability, and extrapolation error. Six evaluation metrics are proposed to expose these past pitfalls and illustrate the PINN-GM-III's robustness to them. This study concludes by evaluating the PINN-GM-III modeling accuracy on a heterogeneous density asteroid, and comparing its performance to other analytic and machine learning gravity models., Comment: 40 pages, 10 figures, submitted to The Journal of Astronautical Sciences

The Casas--Alvero conjecture predicts that every univariate polynomial $f$ over a field $K$ of characteristic zero having a common factor with each of its derivatives $H_i(f)$ is a power of a linear polynomial. Let $f=x^d+a_1x^{d-1}+\cdots+a_1x \in K[a_1,\ldots,a_{d-1}][x]$ and let $R_i = Res(f,H_i(f))\in K[a_1,\ldots,a_{d-1}]$ be the resultant of $f$ and $H_i(f)$, $i \in \{1,\ldots,d-1\}$. The Casas-Alvero Conjecture is equivalent to saying that $R_1,\ldots,R_{d-1}$ are ``independent'' in a certain sense, namely that the height $ht(R_1,\ldots,R_{d-1})=d-1$ in $K[a_1,\ldots,a_{d-1}]$. In this paper we prove a very partial result in this direction : if $i \in \{d-3,d-2,d-1\}$ then $R_i \notin \sqrt{(R_1,\ldots,\breve{R_i},\ldots,R_{d-1}}$., Comment: arXiv admin note: text overlap with arXiv:2307.05997

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.

We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary conformal field theory with an exactly marginal coupling corresponding to the strength of the interaction between the photon and the matter degrees of freedom. In part one of this project, we present three results. We show how the Maxwell equations put severe constraints on boundary three-point functions involving two currents and a symmetric traceless tensor. We use semi-definite programming to show that any three dimensional conformal field theory with a global U(1) symmetry must have a spin two gap less than about 1.05. Finally, combining a numerical bound on an OPE coefficient and some Ward identities involving the current and the displacement operator, we bound the displacement operator two-point function above. This upper bound also constrains a boundary contribution to the anomaly in the trace of the stress tensor for these types of theories., Comment: 33 pages + appendices, 8 figures

The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis. Recently, the Hodge Laplacian has come into focus as a generalisation of the ordinary Laplacian for higher-order graph models such as simplicial and cellular complexes. Akin to the traditional analysis of graph Laplacians, many authors analyse the smallest eigenvalues of the Hodge Laplacian, which are connected to important topological properties such as homology. However, small eigenvalues of the Hodge Laplacian can carry different information depending on whether they are related to curl or gradient eigenmodes, and thus may not be comparable. We therefore introduce the notion of persistent eigenvector similarity and provide a method to track individual harmonic, curl, and gradient eigenvectors/-values through the so-called persistence filtration, leveraging the full information contained in the Hodge-Laplacian spectrum across all possible scales of a point cloud. Finally, we use our insights (a) to introduce a novel form of Hodge spectral clustering and (b) to classify edges and higher-order simplices based on their relationship to the smallest harmonic, curl, and gradient eigenvectors., Comment: 5 pages, 4 figures, comments welcome

The process of developing control functions for embedded systems is resource-, time-, and data-intensive, often resulting in sub-optimal cost and solutions approaches. Reinforcement Learning (RL) has great potential for autonomously training agents to perform complex control tasks with minimal human intervention. Due to costly data generation and safety constraints, however, its application is mostly limited to purely simulated domains. To use RL effectively in embedded system function development, the generated agents must be able to handle real-world applications. In this context, this work focuses on accelerating the training process of RL agents by combining Transfer Learning (TL) and X-in-the-Loop (XiL) simulation. For the use case of transient exhaust gas re-circulation control for an internal combustion engine, use of a computationally cheap Model-in-the-Loop (MiL) simulation is made to select a suitable algorithm, fine-tune hyperparameters, and finally train candidate agents for the transfer. These pre-trained RL agents are then fine-tuned in a Hardware-in-the-Loop (HiL) system via TL. The transfer revealed the need for adjusting the reward parameters when advancing to real hardware. Further, the comparison between a purely HiL-trained and a transferred agent showed a reduction of training time by a factor of 5.9. The results emphasize the necessity to train RL agents with real hardware, and demonstrate that the maturity of the transferred policies affects both training time and performance, highlighting the strong synergies between TL and XiL simulation.

Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend (implicitly) on a chosen metric, which is typically agnostically chosen as the standard Euclidean metric on $\mathbb{R}^n$. Recent work has tried to uncover the 'true' metric on the point cloud using distance-to-measure functions, in order to obtain more meaningful persistent homology results. Here we propose an alternative look at this problem: we posit that information on the point cloud is lost when restricting persistent homology to a single (correct) distance function. Instead, we show how by varying the distance function on the underlying space and analysing the corresponding shifts in the persistence diagrams, we can extract additional topological and geometrical information. Finally, we numerically show that non-isotropic persistent homology can extract information on orientation, orientational variance, and scaling of randomly generated point clouds with good accuracy and conduct some experiments on real-world data., Comment: 30 pages, 17 figures, comments welcome!