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Transformer-based Super-Resolution (SR) models have recently advanced image reconstruction quality, yet challenges remain due to computational complexity and an over-reliance on large patch sizes, which constrain fine-grained detail enhancement. In this work, we propose TaylorIR to address these limitations by utilizing a patch size of 1x1, enabling pixel-level processing in any transformer-based SR model. To address the significant computational demands under the traditional self-attention mechanism, we employ the TaylorShift attention mechanism, a memory-efficient alternative based on Taylor series expansion, achieving full token-to-token interactions with linear complexity. Experimental results demonstrate that our approach achieves new state-of-the-art SR performance while reducing memory consumption by up to 60% compared to traditional self-attention-based transformers.

We show simplified DPS-QKD using a SiN micro-ring resonator operated at 852 nm. A raw-key rate of up to 25.3 kb/s is reached at a QBER suitable for secure-key extraction. Short-reach QKD operation is maintained for zero-touch link layouts with C-band telecom fiber.

Causal structures play a central role in world models that flexibly adapt to changes in the environment. While recent works motivate the benefits of discovering local causal graphs for dynamics modelling, in this work we demonstrate that accurately capturing these relationships in complex settings remains challenging for the current state-of-the-art. To remedy this shortcoming, we postulate that sparsity is a critical ingredient for the discovery of such local causal structures. To this end we present the SPARse TrANsformer World model (SPARTAN), a Transformer-based world model that learns local causal structures between entities in a scene. By applying sparsity regularisation on the attention pattern between object-factored tokens, SPARTAN identifies sparse local causal models that accurately predict future object states. Furthermore, we extend our model to capture sparse interventions with unknown targets on the dynamics of the environment. This results in a highly interpretable world model that can efficiently adapt to changes. Empirically, we evaluate SPARTAN against the current state-of-the-art in object-centric world models on observation-based environments and demonstrate that our model can learn accurate local causal graphs and achieve significantly improved few-shot adaptation to changes in the dynamics of the environment as well as robustness against removing irrelevant distractors.

In this paper, we study vanishing of Fourier coefficients of holomorphic $\eta$-quotients. We investigate examples of two different types: the first one involves integral weight CM newforms, while the second one involves half-integral weight $\eta$-quotients associated with sums of squares and Hurwitz class numbers.

We propose a simple methodology to approximate functions with given asymptotic behavior by specifically constructed terms and an unconstrained deep neural network (DNN). The methodology we describe extends to various asymptotic behaviors and multiple dimensions and is easy to implement. In this work we demonstrate it for linear asymptotic behavior in one-dimensional examples. We apply it to function approximation and regression problems where we measure approximation of only function values (``Vanilla Machine Learning''-VML) or also approximation of function and derivative values (``Differential Machine Learning''-DML) on several examples. We see that enforcing given asymptotic behavior leads to better approximation and faster convergence., Comment: 24 Pages

Latent Video Diffusion Models can easily deceive casual observers and domain experts alike thanks to the produced image quality and temporal consistency. Beyond entertainment, this creates opportunities around safe data sharing of fully synthetic datasets, which are crucial in healthcare, as well as other domains relying on sensitive personal information. However, privacy concerns with this approach have not fully been addressed yet, and models trained on synthetic data for specific downstream tasks still perform worse than those trained on real data. This discrepancy may be partly due to the sampling space being a subspace of the training videos, effectively reducing the training data size for downstream models. Additionally, the reduced temporal consistency when generating long videos could be a contributing factor. In this paper, we first show that training privacy-preserving models in latent space is computationally more efficient and generalize better. Furthermore, to investigate downstream degradation factors, we propose to use a re-identification model, previously employed as a privacy preservation filter. We demonstrate that it is sufficient to train this model on the latent space of the video generator. Subsequently, we use these models to evaluate the subspace covered by synthetic video datasets and thus introduce a new way to measure the faithfulness of generative machine learning models. We focus on a specific application in healthcare echocardiography to illustrate the effectiveness of our novel methods. Our findings indicate that only up to 30.8% of the training videos are learned in latent video diffusion models, which could explain the lack of performance when training downstream tasks on synthetic data., Comment: 8 pages, 5 tables, 6 figures

As Artificial Intelligence (AI) systems increasingly influence decision-making across various fields, the need to attribute responsibility for undesirable outcomes has become essential, though complicated by the complex interplay between humans and AI. Existing attribution methods based on actual causality and Shapley values tend to disproportionately blame agents who contribute more to an outcome and rely on real-world measures of blameworthiness that may misalign with responsible AI standards. This paper presents a causal framework using Structural Causal Models (SCMs) to systematically attribute responsibility in human-AI systems, measuring overall blameworthiness while employing counterfactual reasoning to account for agents' expected epistemic levels. Two case studies illustrate the framework's adaptability in diverse human-AI collaboration scenarios.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Recent advances in artificial intelligence (AI) have produced systems capable of increasingly sophisticated performance on cognitive tasks. However, AI systems still struggle in critical ways: unpredictable and novel environments (robustness), lack of transparency in their reasoning (explainability), challenges in communication and commitment (cooperation), and risks due to potential harmful actions (safety). We argue that these shortcomings stem from one overarching failure: AI systems lack wisdom. Drawing from cognitive and social sciences, we define wisdom as the ability to navigate intractable problems - those that are ambiguous, radically uncertain, novel, chaotic, or computationally explosive - through effective task-level and metacognitive strategies. While AI research has focused on task-level strategies, metacognition - the ability to reflect on and regulate one's thought processes - is underdeveloped in AI systems. In humans, metacognitive strategies such as recognizing the limits of one's knowledge, considering diverse perspectives, and adapting to context are essential for wise decision-making. We propose that integrating metacognitive capabilities into AI systems is crucial for enhancing their robustness, explainability, cooperation, and safety. By focusing on developing wise AI, we suggest an alternative to aligning AI with specific human values - a task fraught with conceptual and practical difficulties. Instead, wise AI systems can thoughtfully navigate complex situations, account for diverse human values, and avoid harmful actions. We discuss potential approaches to building wise AI, including benchmarking metacognitive abilities and training AI systems to employ wise reasoning. Prioritizing metacognition in AI research will lead to systems that act not only intelligently but also wisely in complex, real-world situations., Comment: 26 pages, 1 figure, 2 tables

Undulators are X-ray sources widely used in synchrotron storage rings and free-electron laser facilities. With the commercial availability of low-temperature superconductors, a new type of undulator was born, the superconducting undulator (SCU). In this context, the industrial cooperation between the Karlsruhe Institute of Technology and Bilfinger Nuclear and Energy Transition GmbH started more than 15 years ago. Since then, many projects have been successfully completed, leading to the production of the world's leading full-scale commercial SCUs based on conduction cooling. Starting with the SCU15, the first of its kind installed SCU providing light to a beamline, followed by the SCU20 installed and still in operation at the Karlsruhe Research Accelerator. The successful realisation of such SCUs has required the simultaneous development of appropriate measurement facilities such as CASPER I and CASPER II.

The magnetic chemically peculiar Ap stars exhibit an extreme spread of rotational velocities, the reason of which is not well understood. Ap stars with rotational periods of 50 days or longer are know as super-slowly rotating Ap (ssrAp) stars. Photometrically variable Ap stars are commonly termed alpha2 Canum Venaticorum (ACV) variables. Our study aims at enlarging the sample of known ssrAp stars using data from the Zwicky Transient Facility (ZTF) survey to enable more robust and significant statistical studies of these objects. Using selection criteria based on the known characteristics of ACV variables, candidate stars were gleaned from the ZTF catalogues of periodic and suspected variable stars and from ZTF raw data. ssrAp stars were identified from this list via their characteristic photometric properties, Delta a photometry, and spectral classification. The final sample consists of 70 new ssrAp stars, which mostly exhibit rotational periods between 50 and 200 days. The object with the longest period has a rotational period of 2551.7 days. We present astrophysical parameters and a Hertzsprung-Russell diagram for the complete sample of known ssrAp stars. With very few exceptions, the ssrAp stars are grouped in the middle of the main sequence with ages in excess of 150 Myr. ZTF J021309.72+582827.7 was identified as a possible binary star harbouring an Ap star and a cool component, possibly shrouded in dust. With our study, we enlarge the sample of known ssrAp stars by about 150%, paving the way for more in-depth statistical studies., Comment: 21 pages, 6 figures, accepted for Astronomy & Astrophysics

We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be used during applications of the MINRES and GMRES algorithms and analyze their properties. We adapt several concepts originating in the field of multigrid methods, obtaining a variety of problem-adapted multi-level methods. We analyze the complexity of all algorithms, and derive a number of results on eigenvalues of the preconditioned system and convergence of iterative methods. We validate our theoretical findings through a range of numerical experiments., Comment: 37 pages

Recent advances in machine learning are transforming medical image analysis, particularly in cancer detection and classification. Techniques such as deep learning, especially convolutional neural networks (CNNs) and vision transformers (ViTs), are now enabling the precise analysis of complex histopathological images, automating detection, and enhancing classification accuracy across various cancer types. This study focuses on osteosarcoma (OS), the most common bone cancer in children and adolescents, which affects the long bones of the arms and legs. Early and accurate detection of OS is essential for improving patient outcomes and reducing mortality. However, the increasing prevalence of cancer and the demand for personalized treatments create challenges in achieving precise diagnoses and customized therapies. We propose a novel hybrid model that combines convolutional neural networks (CNN) and vision transformers (ViT) to improve diagnostic accuracy for OS using hematoxylin and eosin (H&E) stained histopathological images. The CNN model extracts local features, while the ViT captures global patterns from histopathological images. These features are combined and classified using a Multi-Layer Perceptron (MLP) into four categories: non-tumor (NT), non-viable tumor (NVT), viable tumor (VT), and none-viable ratio (NVR). Using the Cancer Imaging Archive (TCIA) dataset, the model achieved an accuracy of 99.08%, precision of 99.10%, recall of 99.28%, and an F1-score of 99.23%. This is the first successful four-class classification using this dataset, setting a new benchmark in OS research and offering promising potential for future diagnostic advancements.

Semiconducting CrSBr is a layered A-type antiferromagnet, with individual layers antiferromagnetically coupled along the stacking direction. Due to its unique orthorhombic crystal structure, CrSBr exhibits highly anisotropic mechanical and optoelectronic properties acting itself as a quasi-1D material. CrSBr demonstrates complex coupling phenomena involving phonons, excitons, magnons, and polaritons. Here we show through polarization-resolved resonant Raman scattering the intricate interaction between the vibrational and electronic properties of CrSBr. For samples spanning from few-layer to bulk thickness, we observe that the polarization of the A$_g^2$ Raman mode can be rotated by 90 degrees, shifting from alignment with the crystallographic a (intermediate magnetic) axis to the b (easy magnetic) axis, depending on the excitation energy. In contrast, the A$_g^1$ and A$_g^3$ modes consistently remain polarized along the b axis, regardless of the laser energy used. We access real and imaginary parts of the Raman tensor in our analysis, uncovering resonant electron-phonon coupling., Comment: Main text + Supplementary Information

We give the first parallel algorithm with optimal $\tilde{O}(m)$ work for the classical problem of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In graphs without negative edges, Dijkstra's algorithm solves the Single-Source Shortest Paths (SSSP) problem with optimal $\tilde O(m)$ work, but is inherently sequential. A recent breakthrough by Bernstein, Nanongkai, Wulff-Nilsen; FOCS '22 achieves the same for general graphs. Parallel shortest path algorithms are more difficult and have been intensely studied for decades. Only very recently, multiple lines of research culminated in parallel algorithms with optimal work $\tilde O(m)$ for various restricted settings, such as approximate or exact algorithms for directed or undirected graphs without negative edges. For general graphs, the best known algorithm by [shvinkumar, Bernstein, Cao, Grunau, Haeupler, Jiang, Nanongkai, Su; ESA '24 still requires $m^{1+o(1)}$ work. This paper presents a randomized parallel algorithm for SSSP in general graphs with near-linear work $\tilde O(m)$ and state-of-the-art span $n^{1/2 + o(1)}$. We follow a novel bottom-up approach leading to a particularly clean and simple algorithm. Our algorithm can be seen as a \emph{near-optimal parallel black-box reduction} from SSSP in general graphs to graphs without negative edges. In contrast to prior works, the reduction in this paper is both parallel and essentially without overhead, only affecting work and span by polylogarithmic factors., Comment: To appear at SOSA 2025

This extended abstract describes the challenges in implementing recommender systems for digital archives in the humanities, focusing on Monasterium.net, a platform for historical legal documents. We discuss three key aspects: (i) the unique characteristics of so-called charters as items for recommendation, (ii) the complex multi-stakeholder environment, and (iii) the distinct information-seeking behavior of scholars in the humanities. By examining these factors, we aim to contribute to the development of more effective and tailored recommender systems for (digital) humanities research., Comment: Presented at AltRecSys 2024: The First Workshop on Alternative, Unexpected, and Critical Ideas in Recommendation, October 18, 2024, co-located with the ACM Conference on Recommender Systems 2024 (RecSys 2024), Bari, Italy

We present synthetic light curves and spectra from three-dimensional (3D) Monte Carlo radiative transfer simulations based on a 3D core-collapse supernova explosion model of an ultra-stripped $3.5\,\mathrm{M}_{\odot}$ progenitor. Our calculations predict a fast and faint transient with $\Delta m_{15} \sim 1\texttt{-} 2\,\mathrm{mag}$ and peak bolometric luminosity between $-15.3\,\mathrm{mag}$ and $-16.4\,\mathrm{mag}$. Due to a large-scale unipolar asymmetry in the distribution of $^{56}\mathrm{Ni}$, there is a pronounced viewing-angle dependence with about $1\,\mathrm{mag}$ difference between the directions of highest and lowest luminosity. The predicted spectra for this rare class of explosions do not yet match any observed counterpart. They are dominated by prominent Mg~II lines, but features from O, C, Si, and Ca are also found. In particular, the O~I line at \wl{7}{774} appears as a blended feature together with Mg~II emission. Our model is not only faster and fainter than the observed Ib/c supernova population, but also shows a correlation between higher peak luminosity and larger $\Delta m_{15}$ that is not present in observational samples. A possible explanation is that the unusually small ejecta mass of our model accentuates the viewing-angle dependence of the photometry. We suggest that the viewing-angle dependence of the photometry may be used to constrain asymmetries in explosion models of more typical stripped-envelope supernova progenitors in future., Comment: 13 pages, 18 figures, submitted to MNRAS

Inferring atmospheric properties of exoplanets from observed spectra is key to understanding their formation, evolution, and habitability. Since traditional Bayesian approaches to atmospheric retrieval (e.g., nested sampling) are computationally expensive, a growing number of machine learning (ML) methods such as neural posterior estimation (NPE) have been proposed. We seek to make ML-based atmospheric retrieval (1) more reliable and accurate with verified results, and (2) more flexible with respect to the underlying neural networks and the choice of the assumed noise models. First, we adopt flow matching posterior estimation (FMPE) as a new ML approach to atmospheric retrieval. FMPE maintains many advantages of NPE, but provides greater architectural flexibility and scalability. Second, we use importance sampling (IS) to verify and correct ML results, and to compute an estimate of the Bayesian evidence. Third, we condition our ML models on the assumed noise level of a spectrum (i.e., error bars), thus making them adaptable to different noise models. Both our noise level-conditional FMPE and NPE models perform on par with nested sampling across a range of noise levels when tested on simulated data. FMPE trains about 3 times faster than NPE and yields higher IS efficiencies. IS successfully corrects inaccurate ML results, identifies model failures via low efficiencies, and provides accurate estimates of the Bayesian evidence. FMPE is a powerful alternative to NPE for fast, amortized, and parallelizable atmospheric retrieval. IS can verify results, thus helping to build confidence in ML-based approaches, while also facilitating model comparison via the evidence ratio. Noise level conditioning allows design studies for future instruments to be scaled up, for example, in terms of the range of signal-to-noise ratios., Comment: Accepted for publication in Astronomy & Astrophysics

We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a Lipschitz-continuous prehistory. The paramount feature is a reduction of the differential equation to a fixed point problem that admits a unique solution appealing to the contraction mapping principle. The use of exponentially weighted Sobolev spaces in this endeavor proves to be as powerful as for ordinary differential equations without delay. Our result includes a blow-up criterium for global existence of solutions. The discussion of well-posedness is concluded by new results covering continuous dependence on initial prehistories and on the right-hand sides.

Strongly correlated insulators, such as Mott or charge-transfer insulators, exhibit a strong temperature dependence in their resistivity. Consequently, self-heating effects can lead to electrothermal instabilities in planar thin film devices of these materials. When the electrical bias current exceeds a device-specific threshold, the device can switch from a high- to a low-resistance state through the formation of metallic filaments. However, since the current and temperature redistribution effects that create these filaments are sustained by local Joule heating, a reduction of the bias current below a second (lower) threshold leads to the disappearance of filaments, and the device switches back into the high-resistance state. Hence, electrothermal resistive switching is usually volatile. Here, on the contrary, we report on non-volatile resistive switching in a planar $\mathrm{NdNiO}_3$ thin-film device. By combining electrical transport measurements with optical wide-field microscopy, we provide evidence for a metallic filament that persists even after returning the bias current to zero. We attribute this effect to the pronounced hysteresis between the cooling and heating branches in the resistance vs. temperature dependence of the device. At least one hundred intermediate resistance states can be prepared, which are persistent as long as the base temperature is kept constant. Further, the switching process is non-destructive, and thermal cycling can reset the device to its pristine state., Comment: 10 pages, 5 figures

This paper presents a novel learning-based approach for online estimation of maximal safe sets for local motion planning tasks in mobile robotics. We leverage the idea of hypernetworks to achieve good generalization properties and real-time performance simultaneously. As the source of supervision, we employ the Hamilton-Jacobi (HJ) reachability analysis, allowing us to consider general nonlinear dynamics and arbitrary constraints. We integrate our model into a model predictive control (MPC) local planner as a safety constraint and compare the performance with relevant baselines in realistic 3D simulations for different environments and robot dynamics. The results show the advantages of our approach in terms of a significantly higher success rate: 2 to 18 percent over the best baseline, while achieving real-time performance.

When validated neural networks (NNs) are pruned (and retrained) before deployment, it is desirable to prove that the new NN behaves equivalently to the (original) reference NN. To this end, our paper revisits the idea of differential verification which performs reasoning on differences between NNs: On the one hand, our paper proposes a novel abstract domain for differential verification admitting more efficient reasoning about equivalence. On the other hand, we investigate empirically and theoretically which equivalence properties are (not) efficiently solved using differential reasoning. Based on the gained insights, and following a recent line of work on confidence-based verification, we propose a novel equivalence property that is amenable to Differential Verification while providing guarantees for large parts of the input space instead of small-scale guarantees constructed w.r.t. predetermined input points. We implement our approach in a new tool called VeryDiff and perform an extensive evaluation on numerous old and new benchmark families, including new pruned NNs for particle jet classification in the context of CERN's LHC where we observe median speedups >300x over the State-of-the-Art verifier alpha,beta-CROWN., Comment: 47 pages (main paper has 16 pages); 8 figures

Scanning Electron Microscopes (SEMs) are widely renowned for their ability to analyze the surface structures of microscopic objects, offering the capability to capture highly detailed, yet only grayscale, images. To create more expressive and realistic illustrations, these images are typically manually colorized by an artist with the support of image editing software. This task becomes highly laborious when multiple images of a scanned object require colorization. We propose facilitating this process by using the underlying 3D structure of the microscopic scene to propagate the color information to all the captured images, from as little as one colorized view. We explore several scene representation techniques and achieve high-quality colorized novel view synthesis of a SEM scene. In contrast to prior work, there is no manual intervention or labelling involved in obtaining the 3D representation. This enables an artist to color a single or few views of a sequence and automatically retrieve a fully colored scene or video. Project page: https://ronly2460.github.io/ArCSEM, Comment: presented and published at AI for Visual Arts Workshop and Challenges (AI4VA) in conjunction with European Conference on Computer Vision (ECCV) 2024, Milano, Italy

The rise of social media has amplified the spread of fake news, now further complicated by large language models (LLMs) like ChatGPT, which ease the generation of highly convincing, error-free misinformation, making it increasingly challenging for the public to discern truth from falsehood. Traditional fake news detection methods relying on linguistic cues also becomes less effective. Moreover, current detectors primarily focus on binary classification and English texts, often overlooking the distinction between machine-generated true vs. fake news and the detection in low-resource languages. To this end, we updated detection schema to include machine-generated news with focus on the Urdu language. We further propose a hierarchical detection strategy to improve the accuracy and robustness. Experiments show its effectiveness across four datasets in various settings.

We investigate the existence of solutions of reversible and irreversible port-Hamiltonian systems. To this end, we utilize the associated exergy, a function that is composed of the system's Hamiltonian and entropy, to prove global existence in time for bounded control functions. The results are then leveraged to prove existence of solutions of energy- and entropy-optimal control problems. Last, we explore model predictive control tailored to irreversible port-Hamiltonian systems by means of a numerical case study with a heat exchanger network., Comment: 24 pages, 6 figures

In contrast to the traditional principle of periodic sensing neuromorphic engineering pursues a paradigm shift towards bio-inspired event-based sensing, where events are primarily triggered by a change in the perceived stimulus. We show in a rigorous mathematical way that information encoding by means of Threshold-Based Representation based on either Leaky Integrate-and-Fire (LIF) or Send-on-Delta (SOD) is linked to an analog-to-spike conversion that guarantees maximum sparsity while satisfying an approximation condition based on the Alexiewicz norm.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less., Comment: To appear in KDIR 2024

While Dijkstra's algorithm has near-optimal time complexity for the problem of finding the shortest $st$-path, in practice, other algorithms are often superior on huge graphs. A prominent such example is the bidirectional search, which executes Dijkstra's algorithm from both endpoints in parallel and stops when these executions meet. In this paper, we give a strong theoretical justification for the use of such bidirectional search algorithms. We prove that for weighted multigraphs, both directed and undirected, a careful implementation of bidirectional search is instance-optimal with respect to the number of edges it explores. That is, we prove that no correct algorithm can outperform our implementation of bidirectional search on any single instance by more than a constant factor. For unweighted graphs, we show that bidirectional search is instace-optimal up to a factor of $O(\Delta)$ where $\Delta$ is the maximum degree of the graph. We also show that this is the best possible., Comment: To appear at SOSA 2025

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem of extracting relevant context information from long sequences in NLP and realistic scenes in CV. A classical neural network component, a Multi-Layer Perceptron (MLP), complements the attention mechanism. Its necessity is frequently justified by its capability of modeling nonlinear relationships. However, the attention mechanism itself is nonlinear through its internal use of similarity measures. A possible hypothesis is that this nonlinearity is sufficient for modeling typical application problems. As the MLPs usually contain the most trainable parameters of the whole model, their omission would substantially reduce the parameter set size. Further components can also be reorganized to reduce the number of parameters. Under some conditions, query and key matrices can be collapsed into a single matrix of the same size. The same is true about value and projection matrices, which can also be omitted without eliminating the substance of the attention mechanism. Initially, the similarity measure was defined asymmetrically, with peculiar properties such as that a token is possibly dissimilar to itself. A possible symmetric definition requires only half of the parameters. We have laid the groundwork by testing widespread CV benchmarks: MNIST and CIFAR-10. The tests have shown that simplified transformer architectures (a) without MLP, (b) with collapsed matrices, and (c) symmetric similarity matrices exhibit similar performance as the original architecture, saving up to 90% of parameters without hurting the classification performance., Comment: 8 pages, to appear in KDIR2024

Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to problems that are more complex than the ones on which they have been trained. Empirical investigations of such questions are impeded by two major flaws of current evaluations: (i) much of the evaluation data is contaminated, in the sense that it has already been seen during training, and (ii) benchmark datasets do not capture how problem proofs may be arbitrarily complex in various ways. As a step towards addressing these issues, we present a framework for evaluating LLMs on problems with arbitrarily complex arithmetic proofs, called MathGAP. MathGAP generates problems that follow fixed proof specifications -- along with chain-of-thought reasoning annotations -- enabling systematic studies on generalization with respect to arithmetic proof complexity. We apply MathGAP to analyze how in-context learning interacts with generalization to problems that have more complex proofs. We find that among the models tested, most show a significant decrease in performance as proofs get deeper and wider. This effect is more pronounced in complex, nonlinear proof structures, which are challenging even for GPT-4o. Surprisingly, providing in-context examples from the same distribution as the test set is not always beneficial for performance. In particular, zero-shot prompting as well as demonstrating a diverse range of examples that are less complex than the test data sometimes yield similar or higher accuracies., Comment: Preprint

The settling behavior of sediment aggregates is a critical factor influencing the transport of fine-grained sediments in riverine and marine environments. Due to the small size and fragile structure of cohesive sediment aggregates, direct measurement of their porosity and permeability is challenging. While porosity is often estimated using settling velocity relations, permeability is frequently overlooked. This study examines the impact of considering non-negligible permeability on the properties of flocs. We compare aggregate properties by calibrating experimental data to two settling models in a dilute regime: one assumes a fractal structure of aggregates and neglects permeability, while the other assumes constant porosity and permeability. Our results demonstrate that both models describe the experimental data of highly porous aggregates with similar accuracy. We further investigate aggregate dynamics in more complex flow conditions using numerical simulations employing a volume penalization method to geometrically resolve flocs. We compare the behavior of permeable and impermeable flocs in dense suspension regimes and during dilute settling in density-stratified environments. Our findings reveal that permeability significantly influences settling dynamics in complex scenarios and should be considered when determining aggregate properties.

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to existing classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively, as the modulation can be directly implemented with real devices with a finite digital resolution. However, the experimental demonstrations until now only calculated key rates in the asymptotic regime. To be used in cryptographic applications, a QKD system has to generate keys with composable security in the finite-size regime. In this paper, we present a CV QKD system using discrete modulation that is especially designed for urban atmospheric channels. For this, we use polarization encoding to cope with the turbulent but non-birefringent atmosphere. This will allow to expand CV QKD networks beyond the existing fiber backbone. In a first laboratory demonstration, we implemented a novel type of security proof allowing to calculate composable finite-size key rates against i.i.d. collective attacks without any Gaussian assumptions. We applied the full QKD protocol including a QRNG, error correction and privacy amplification to extract secret keys. In particular, we studied the impact of frame errors on the actual key generation.

In this paper we study sign changes of an infinite class of $\eta$-quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.

The multiplicities of positive and negative pions, kaons and unidentified hadrons produced in deep-inelastic scattering are measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the fraction of the virtual-photon energy transferred to the final-state hadron $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam of both electric charges and a liquid hydrogen target. These measurements cover the kinematic domain with photon virtuality $Q^2 > 1$ (GeV/$c)^2$, $0.004 < x < 0.4$, $0.1 < y < 0.7$ and $0.2 < z < 0.85$, in accordance with the kinematic domain used in earlier published COMPASS multiplicity measurements with an isoscalar target. The calculation of radiative corrections was improved by using the Monte Carlo generator DJANGOH, which results in up to 12\% larger corrections in the low-$x$ region., Comment: 19 pages, 29 figures

A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known to be at most logarithmic in the number of candidates. We study the case of elections where voters and candidates are located in a $2$-dimensional space with preferences based upon proximity voting. Our main result is that the Condorcet dimension is at most $3$, under both the Manhattan norm and the infinity norm, natural measures in electoral systems., Comment: 9 pages

The rise of Large Language Models (LLMs) has revolutionized natural language processing across numerous languages and tasks. However, evaluating LLM performance in a consistent and meaningful way across multiple European languages remains challenging, especially due to the scarcity of language-parallel multilingual benchmarks. We introduce a multilingual evaluation approach tailored for European languages. We employ translated versions of five widely-used benchmarks to assess the capabilities of 40 LLMs across 21 European languages. Our contributions include examining the effectiveness of translated benchmarks, assessing the impact of different translation services, and offering a multilingual evaluation framework for LLMs that includes newly created datasets: EU20-MMLU, EU20-HellaSwag, EU20-ARC, EU20-TruthfulQA, and EU20-GSM8K. The benchmarks and results are made publicly available to encourage further research in multilingual LLM evaluation.

Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a versatile variant of the balanced transport problem and its entropic regularization can be solved with an adapted Sinkhorn algorithm. However, it is a priori unclear how to apply domain decomposition to unbalanced problems since the independence of the cell problems is lost. In this article we show how this difficulty can be overcome at a theoretical and practical level and demonstrate with experiments that domain decomposition is also viable and efficient on large unbalanced entropic transport problems., Comment: Added acknowledgements

In the study of reading, eye-tracking technology offers unique insights into the time-course of how individuals extract information from text. A significant hurdle in using multi-line paragraph stimuli is the need to align eye gaze position with the correct line. This is made more difficult by positional noise in the eye-tracking data, primarily due to vertical drift, and often necessitates manual intervention. Such manual correction is labor-intensive, subjective, and limits the scalability of research efforts. As a result, automated solutions are desirable, especially those that do not require extensive technical skills and still allow close control over the outcome. To address this, we introduce GazeGenie: a comprehensive software solution designed specifically for researchers in eye-tracking studies on multi-line reading. Accessible via an intuitive web browser-based user interface and easily installed using Docker, GazeGenie streamlines the entire data processing pipeline from parsing fixations from raw data to calculation of word and sentence-based measures based on cleaned and drift-corrected fixations. The software's core features include the recently introduced Dual Input Stream Transformer (DIST) model and various classical algorithms all of which can be combined within a Wisdom of the Crowds (WOC) approach to enhance accuracy in fixation line-assignment. By providing an all-in-one solution for researchers, we hope to make automated fixation alignment more accessible, reducing researchers' reliance on manual intervention in vertical fixation alignment. This should lead to more accurate, efficient, and reproducible analyses of multi-line eye-movement data and pave the way to enabling larger scale studies to be carried out., Comment: This work has been submitted to the Springer Behavior Research Methods for possible publication

Autonomous systems, like vehicles or robots, require reliable, accurate, fast, resource-efficient, scalable, and low-latency trajectory predictions to get initial knowledge about future locations and movements of surrounding objects for safe human-machine interaction. Furthermore, they need to know the uncertainty of the predictions for risk assessment to provide safe path planning. This paper presents a lightweight method to address these requirements, combining Long Short-Term Memory and Mixture Density Networks. Our method predicts probability distributions, including confidence level estimations for positional uncertainty to support subsequent risk management applications and runs on a low-power embedded platform. We discuss essential requirements for human trajectory prediction in autonomous vehicle applications and demonstrate our method's performance using multiple traffic-related datasets. Furthermore, we explain reliability and sharpness metrics and show how important they are to guarantee the correctness and robustness of a model's predictions and uncertainty assessments. These essential evaluations have so far received little attention for no good reason. Our approach focuses entirely on real-world applicability. Verifying prediction uncertainties and a model's reliability are central to autonomous real-world applications. Our framework and code are available at: https://github.com/kav-institute/mdn_trajectory_forecasting.

ECG-gated cine imaging in breath-hold enables high-quality diagnostics in most patients, arrhythmia and inability to hold breath, however, can severely corrupt outcomes. Real-time cardiac MRI in free-breathing leverages robust and faster investigations regardless of these confounding factors. With the need for sufficient acceleration, adequate reconstruction methods, which transfer data into high quality images, are required. Undersampled spiral real-time acquisitions in free-breathing were conducted in a study with 16 healthy volunteers and 5 patients. Image reconstructions were performed using a novel score-based diffusion model, as well as a variational network and different compressed sensing approaches. The techniques were compared by means of an expert reader study, by calculating scalar metrics and difference images with respect to a segmented reference, and by a Bland-Altman analysis of cardiac functional parameters. In participants with irregular RR-cycles, spiral real-time acquisitions showed superior image quality with respect to the clinical reference standard. Reconstructions using the diffusion model, the variational network and l1-wavelets offered an overall comparable image quality, however sharpness was slightly increased by the diffusion approach. While slightly larger ejection fractions for the real-time acquisitions were exhibited with a bias of 1.6% for healthy subjects, differences in the data acquisition procedure resulted in uncertainties of 7.4%. The proposed real-time technique enables free-breathing acquisitions of spatio-temporal images with high-quality, covering the entire heart in less than one minute. Evaluation of the ejection fractions using the segmented reference can be significantly corrupted due to arrhythmias and averaging effects. Prolonged inference times of the diffusion model represent the main obstacle to overcome for clinical translation., Comment: 29 pages, 8 figures

We present a set of eight fallback simulations of zero-metallicity progenitors with masses between $60 M_\odot$ and $95 M_\odot$. The simulations are computed in 2D with the general relativistic CoCoNuT-FMT code for the first few seconds after black hole formation, and then mapped to the Newtonian code Prometheus for long-duration simulations beyond shock breakout. All simulations produce successful explosions with final energies ranging from $0.41 \times 10^{51}$ erg to $2.5 \times 10^{51}$ erg and black hole masses from $20.7 M_\odot$ to $34.4 M_\odot$. Explosion energies and remnant masses do not vary monotonically with progenitor mass, but the mass cuts cluster near the outer edge of the helium core. A supplementary model with decreased neutrino heating provides a tentative indication that successful explosions require the shock to reach the sonic point in the infall profile by the time of black hole formation. The propagation of the shock to the surface is only approximately captured by proposed shock invariants, but these may still be sufficient to extrapolate the final black hole mass from the first seconds of evolution. We also discuss potential multi-messenger signatures of the predicted fallback explosions. The enrichment of the ejecta in intermediate mass and iron-group elements varies considerably and is non-neligible for the more powerful explosions. Low-level neutrino emission after black hole formation from these very massive progenitors may be detectable in the case of a Galactic event., Comment: 20 pages, 15 figures, submitted to MNRAS

Although powerful for image generation, consistent and controllable video is a longstanding problem for diffusion models. Video models require extensive training and computational resources, leading to high costs and large environmental impacts. Moreover, video models currently offer limited control of the output motion. This paper introduces a novel approach to video generation by augmenting image diffusion models to create sequential animation frames while maintaining fine detail. These techniques can be applied to existing image models without training any video parameters (zero-shot) by altering the input noise in a latent diffusion model. Two complementary methods are presented. Noise crystallization ensures consistency but is limited to large movements due to reduced latent embedding sizes. Liquid noise trades consistency for greater flexibility without resolution limitations. The core concepts also allow other applications such as relighting, seamless upscaling, and improved video style transfer. Furthermore, an exploration of the VAE embedding used for latent diffusion models is performed, resulting in interesting theoretical insights such as a method for human-interpretable latent spaces.

It is proven that in the universal splitexact equivariant algebraic $KK$-theory for algebras, the $K$-theory groups coincide with classical $K$-theory in the sense of Phillips. This partially answers a question raised by Kasparov.

Considering turbulence is crucial to understanding clouds. However, covering all scales involved in the turbulent mixing of clouds with their environment is computationally challenging, urging the development of simpler models to represent some of the processes involved. By using full direct numerical simulations as a reference, this study compares several statistical approaches for representing small-scale turbulent mixing. All models use a comparable Lagrangian representation of cloud microphysics, and simulate the same cases of cloud-edge mixing, covering different ambient humidities and turbulence intensities. It is demonstrated that all statistical models represent the evolution of thermodynamics successfully, but not all models capture the changes in cloud microphysics (cloud droplet number concentration, droplet mean radius, and spectral width). Implications of these results for using the presented models as subgrid-scale schemes are discussed.

Generative models lack rigorous statistical guarantees for their outputs and are therefore unreliable in safety-critical applications. In this work, we propose Sequential Conformal Prediction for Generative Models (SCOPE-Gen), a sequential conformal prediction method producing prediction sets that satisfy a rigorous statistical guarantee called conformal admissibility control. This guarantee states that with high probability, the prediction sets contain at least one admissible (or valid) example. To this end, our method first samples an initial set of i.i.d. examples from a black box generative model. Then, this set is iteratively pruned via so-called greedy filters. As a consequence of the iterative generation procedure, admissibility of the final prediction set factorizes as a Markov chain. This factorization is crucial, because it allows to control each factor separately, using conformal prediction. In comparison to prior work, our method demonstrates a large reduction in the number of admissibility evaluations during calibration. This reduction is important in safety-critical applications, where these evaluations must be conducted manually by domain experts and are therefore costly and time consuming. We highlight the advantages of our method in terms of admissibility evaluations and cardinality of the prediction sets through experiments in natural language generation and molecular graph extension tasks.

Future large tokamaks will operate at high plasma currents and high stored plasma energies. To ensure machine protection in case of a sudden loss of plasma confinement (major disruption), a large fraction of the magnetic and thermal energy must be radiated to reduce thermal loads. The disruption mitigation system for ITER is based on massive material injection in the form of shattered pellet injection (SPI). To support ITER, a versatile SPI system was installed at the tokamak ASDEX Upgrade (AUG). The AUG SPI features three independent pellet generation cells and guide tubes, and each was equipped with different shatter heads for the 2022 experimental campaign. We dedicated over 200 plasma discharges to the study of SPI plasma termination, and in this manuscript report on the results of bolometry (total radiation) analysis. The amount of neon inside the pellets is the dominant factor determining the radiated energy fraction (frad). Large and fast fragments, produced by the $12.5^\circ$ rectangular shatter head, lead to somewhat higher values of frad compared to the $25^\circ$ circular or rectangular heads. This effect is strongest for neon content of $< 4\times10^{20}$ neon atoms injected, where a higher normal velocity component (larger fragments) seems slightly beneficial. While full-sized, 8 mm diameter, pure deuterium (D2) pellets lead to a disruption, the 4 mm or shortened 8 mm pellets of pure D2 did not lead to a disruption. The disruption threshold for pure D2 is found to be around $1\times10^{22}$ deuterium molecules inside the pellet. While the radiated energy fraction of non-disruptive SPI is below 20%, this is increased to 40% during the TQ and VDE phase of the disruptive injections. For deuterium-neon-mix pellets, frad values of $< 90$% are observed, and the curve saturates around 80% for 10% neon mixed into the 8 mm pellets ($2\times10^{21}$ neon atoms)., Comment: 15 pages, 9 figures

Large Language Models (LLMs) often produce outputs that -- though plausible -- can lack consistency and reliability, particularly in ambiguous or complex scenarios. Challenges arise from ensuring that outputs align with both factual correctness and human intent. This is problematic in existing approaches that trade improved consistency for lower accuracy. To mitigate these challenges, we propose a novel game-theoretic approach to enhance consistency and reliability during the decoding stage of LLM output generation. Our method models the decoding process as a multistage Bayesian decoding game. This ensures consistency through Correctness Alignment and enhances reliability via Ambiguity Calibration. The model dynamically converges to a consensus on the most reliable outputs and distinguishes {Valid, Specious} outputs without human feedback or additional training. Our game design allows smaller models to outperform much larger models through game mechanisms (e.g., 78.1 LLaMA13B vs 76.6 PaLM540B), as well as integrating various LL strategies and models, demonstrating the potential of game-theoretic tools to improve the truthfulness and reliability of LLMs.

We review $\mathrm{Hom}$-infinite Frobenius categorification of cluster algebras with coefficients and use it to give two applications of Jensen--King--Su's Frobenius categorification of the Grassmannian: 1) we determine the $g$-vectors of the Pl\"ucker coordinates with respect to the triangular initial seed and 2) we express the $F$-polynomials associated with the Donaldson--Thomas transformation in terms of $3$-dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng., Comment: 34 pages

We propose the novel concept of anomaly-free regions (AFR) to improve anomaly detection. An AFR is a region in the data space for which it is known that there are no anomalies inside it, e.g., via domain knowledge. This region can contain any number of normal data points and can be anywhere in the data space. AFRs have the key advantage that they constrain the estimation of the distribution of non-anomalies: The estimated probability mass inside the AFR must be consistent with the number of normal data points inside the AFR. Based on this insight, we provide a solid theoretical foundation and a reference implementation of anomaly detection using AFRs. Our empirical results confirm that anomaly detection constrained via AFRs improves upon unconstrained anomaly detection. Specifically, we show that, when equipped with an estimated AFR, an efficient algorithm based on random guessing becomes a strong baseline that several widely-used methods struggle to overcome. On a dataset with a ground-truth AFR available, the current state of the art is outperformed., Comment: Accepted at the 15th IEEE International Conference on Knowledge Graph (ICKG)

Context: The details of the mass-loss process in the late stages of low- and intermediate-mass stellar evolution are not well understood, in particular its dependence on stellar parameters. Mira variables are highly suitable targets for studying this mass-loss process. Aims: We follow up on our earlier finding that a near-to-mid-infrared colour vs. pulsation period diagram shows two sequences of Miras that can be distinguished by the third dredge-up (3DUP) indicator technetium in those stars. While IR colours are good indicators of the dust mass-loss rate (MLR) from Miras, no corresponding sequences have been found using the gas MLR. However, investigations of the gas MLR have been hampered by data limitations. We aim to alleviate these limitations with new observational data. Methods: We present new optical spectra of a well-selected sample of Miras. We searched these spectra for absorption lines of Tc and other 3DUP indicators and combined our findings with gas MLRs and expansion velocities from the literature. Furthermore, we analyse WISE MIR data and compare the broadband SEDs of Miras with and without Tc. Results: We find no systematic difference in gas MLRs between Miras with and without Tc. However, the gas envelopes of Tc-poor Miras appear to have a higher expansion velocity than those of Miras with Tc. Furthermore, our analysis of the IR photometry strongly corroborates the earlier finding that Tc-poor Miras have a higher MIR emission than Tc-rich ones, by as much as a factor of two. We model the IR colours with DARWIN and stationary wind models and conclude that Miras with and without Tc have different dust content or properties. Conclusions: We discuss several hypotheses of the observations and conclude that the reduction of free oxygen by 3DUP of carbon and iron-depleted dust grains in Tc-rich stars are the most convincing explanations for our observations., Comment: 16 pages, 10 figures, accepted for publication in Astronomy & Astrophysics