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Cross-entropy (CE) loss is the de-facto standard for training deep neural networks to perform classification. However, CE-trained deep neural networks struggle with robustness and generalisation issues. To alleviate these issues, we propose high error margin (HEM) loss, a variant of multi-class margin loss that overcomes the training issues of other margin-based losses. We evaluate HEM extensively on a range of architectures and datasets. We find that HEM loss is more effective than cross-entropy loss across a wide range of tasks: unknown class rejection, adversarial robustness, learning with imbalanced data, continual learning, and semantic segmentation (a pixel-level classification task). Despite all training hyper-parameters being chosen for CE loss, HEM is inferior to CE only in terms of clean accuracy and this difference is insignificant. We also compare HEM to specialised losses that have previously been proposed to improve performance on specific tasks. LogitNorm, a loss achieving state-of-the-art performance on unknown class rejection, produces similar performance to HEM for this task, but is much poorer for continual learning and semantic segmentation. Logit-adjusted loss, designed for imbalanced data, has superior results to HEM for that task, but performs more poorly on unknown class rejection and semantic segmentation. DICE, a popular loss for semantic segmentation, is inferior to HEM loss on all tasks, including semantic segmentation. Thus, HEM often out-performs specialised losses, and in contrast to them, is a general-purpose replacement for CE loss., Comment: Code: https://codeberg.org/mwspratling/HEMLoss

We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in $\mathbb{R}^n$. The extremal properties of interest are the expected values of the maximum and minimum surface area among facets. We determine the asymptotic growth in every fixed dimension, up to absolute constants.

In this second part we study first the group $Aut_{\mathbb{Q}}(S)$ of numerically trivial automorphisms of a properly elliptic surface $S$, that is, of a minimal surface with Kodaira dimension $\kappa(S)=1$, in the case $\chi(S) \geq 1$. Our first surprising result is that, against what has been believed for over 40 years, we have nontrivial such groups for $p_g(S) >0$. Indeed, we show even that there is no absolute upper bound for their cardinalities $|Aut_{\mathbb{Q}}(S)|$. At any rate, we give explicit and almost sharp upper bounds for $|Aut_{\mathbb{Q}}(S)|$ in terms of the numerical invariants of $S$, as $\chi(S)$, the irregularity $q(S)$, and the bigenus $P_2(S)$. Moreover, we come quite close to a complete description of the possible groups $Aut_{\mathbb{Q}}(S)$, and we give an effective criterion for surfaces to have trivial $Aut_{\mathbb{Q}}(S)$. Our second surprising results concern the group $Aut_{\mathbb{Z}}(S)$ of cohomologically trivial automorphisms; we are able to give the explicit upper bounds for $|Aut_{\mathbb{Z}}(S)|$ in special cases: $9$ when $p_g(S) =0$, and the sharp upper bound $3$ when $S$ (i.e., the pluricanonical elliptic fibration) is isotrivial. We produce also non isotrivial examples where $Aut_{\mathbb{Z}}(S)$ is a cyclic group of order $2$ or $3$., Comment: 64 pages, Keywords: Compact K\"ahler manifolds, algebraic surfaces, elliptic surfaces, automorphisms, cohomologically trivial automorphisms, numerically trivial automorphisms, Enriques--Kodaira classfication

Massive Open Online Courses (MOOCs) have greatly contributed to making education more accessible. However, many MOOCs maintain a rigid, one-size-fits-all structure that fails to address the diverse needs and backgrounds of individual learners. Learning path personalization aims to address this limitation, by tailoring sequences of educational content to optimize individual student learning outcomes. Existing approaches, however, often require either massive student interaction data or extensive expert annotation, limiting their broad application. In this study, we introduce a novel data-efficient framework for learning path personalization that operates without expert annotation. Our method employs a flexible recommender system pre-trained with reinforcement learning on a dataset of raw course materials. Through experiments on semi-synthetic data, we show that this pre-training stage substantially improves data-efficiency in a range of adaptive learning scenarios featuring new educational materials. This opens up new perspectives for the design of foundation models for adaptive learning., Comment: NeurIPS 2024 Workshop on Large Foundation Models for Educational Assessment (FM-Assess), Dec 2024, Vancouver, Canada

Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, I propose to base comparisons on the predictive distributions of linear readouts from intermediate representations. In Bayesian statistics, the prior predictive distribution is a full description of the inductive bias and generalization of a model, making it a great basis for comparisons. This distribution directly gives the evidence a dataset would provide in favor of the model. If we want to compare multiple models to each other, we can use a metric for probability distributions like the Jensen-Shannon distance or the total variation distance. As these are metrics, this induces pseudo-metrics for representations, which measure how well two representations could be distinguished based on a linear read out. For a linear readout with a Gaussian prior on the read-out weights and Gaussian noise, we can analytically compute the (prior and posterior) predictive distributions without approximations. These distributions depend only on the linear kernel matrix of the representations in the model. Thus, the Bayesian metrics connect linear read-out based comparisons to kernel based metrics like centered kernel alignment and representational similarity analysis. I demonstrate the new methods with deep neural networks trained on ImageNet-1k comparing them to each other and a small subset of the Natural Scenes Dataset. The Bayesian comparisons broadly agree with existing metrics, but are more stringent. Empirically, evaluations vary less across different random image samples and yield informative results with full uncertainty information. Thus the proposed Bayesian metrics nicely extend our toolkit for comparing representations.

Frontier artificial intelligence (AI) systems pose increasing risks to society, making it essential for developers to provide assurances about their safety. One approach to offering such assurances is through a safety case: a structured, evidence-based argument aimed at demonstrating why the risk associated with a safety-critical system is acceptable. In this article, we propose a safety case template for offensive cyber capabilities. We illustrate how developers could argue that a model does not have capabilities posing unacceptable cyber risks by breaking down the main claim into progressively specific sub-claims, each supported by evidence. In our template, we identify a number of risk models, derive proxy tasks from the risk models, define evaluation settings for the proxy tasks, and connect those with evaluation results. Elements of current frontier safety techniques - such as risk models, proxy tasks, and capability evaluations - use implicit arguments for overall system safety. This safety case template integrates these elements using the Claims Arguments Evidence (CAE) framework in order to make safety arguments coherent and explicit. While uncertainties around the specifics remain, this template serves as a proof of concept, aiming to foster discussion on AI safety cases and advance AI assurance., Comment: 21 pages, 6 figures, 1 table

As frontier artificial intelligence (AI) systems become more capable, it becomes more important that developers can explain why their systems are sufficiently safe. One way to do so is via safety cases: reports that make a structured argument, supported by evidence, that a system is safe enough in a given operational context. Safety cases are already common in other safety-critical industries such as aviation and nuclear power. In this paper, we explain why they may also be a useful tool in frontier AI governance, both in industry self-regulation and government regulation. We then discuss the practicalities of safety cases, outlining how to produce a frontier AI safety case and discussing what still needs to happen before safety cases can substantially inform decisions., Comment: 25 pages, 6 figures, 5 tables

We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n=8$ is possible., Comment: 28 pages

We revisit the partial $\mathrm{C}^{1,\alpha}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the H\"older exponent $\alpha$ on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari's regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent.

Over the past year, artificial intelligence (AI) companies have been increasingly adopting AI safety frameworks. These frameworks outline how companies intend to keep the potential risks associated with developing and deploying frontier AI systems to an acceptable level. Major players like Anthropic, OpenAI, and Google DeepMind have already published their frameworks, while another 13 companies have signaled their intent to release similar frameworks by February 2025. Given their central role in AI companies' efforts to identify and address unacceptable risks from their systems, AI safety frameworks warrant significant scrutiny. To enable governments, academia, and civil society to pass judgment on these frameworks, this paper proposes a grading rubric. The rubric consists of seven evaluation criteria and 21 indicators that concretize the criteria. Each criterion can be graded on a scale from A (gold standard) to F (substandard). The paper also suggests three methods for applying the rubric: surveys, Delphi studies, and audits. The purpose of the grading rubric is to enable nuanced comparisons between frameworks, identify potential areas of improvement, and promote a race to the top in responsible AI development., Comment: 16 pages, 4 tables

The new class of compact quasi-axisymmetric stellarators with a wide range of field periods offers the unique potential to combine the advantages of the two leading magnetic confinement fusion devices, tokamaks and stellarators. Here we present the first numerical optimization of this class which has so far only been obtained analytically. Our approach finds significantly improved quasi-axisymmetric equilibria at aspect ratio $< 2.5$, resulting in no losses of alpha particles at reactor volume while also satisfying improved magnetohydrodynamic stability and a self-consistent plasma current.

In this first part we describe the group $Aut_{\mathbb{Z}}(S)$ of cohomologically trivial automorphisms of a properly elliptic surface (a minimal surface $S$ with Kodaira dimension $\kappa(S)=1$), in the initial case $ \chi(\mathcal{O}_S) =0$. In particular, in the case where $Aut_{\mathbb{Z}}(S)$ is finite, we give the upper bound 4 for its cardinality, showing more precisely that if $Aut_{\mathbb{Z}}(S)$ is nontrivial, it is one of the following groups: $\mathbb{Z}/2, \mathbb{Z}/3, (\mathbb{Z}/2)^2$. We also show with easy examples that the groups $\mathbb{Z}/2, \mathbb{Z}/3$ do effectively occur. Respectively, in the case where $Aut_{\mathbb{Z}}(S)$ is infinite, we give the sharp upper bound 2 for the number of its connected components., Comment: 49 pages, to appear in a volume of the Taiwanese Journal of Mathematics dedicated to Yurii (Gennadievich) Prokhorov on the occasion of his 60th birthday

The increasing automation of vehicles is resulting in the integration of more extensive in-vehicle sensor systems, electronic control units, and software. Additionally, vehicle-to-everything communication is seen as an opportunity to extend automated driving capabilities through information from a source outside the ego vehicle. However, the validation and verification of automated driving functions already pose a challenge due to the number of possible scenarios that can occur for a driving function, which makes it difficult to achieve comprehensive test coverage. Currently, the establishment of Safety Of The Intended Functionality ( SOTIF ) mandates the implementation of scenario-based testing. The introduction of additional external systems through vehicle-to-everything further complicates the problem and increases the scenario space. In this paper, a methodology based on state charts is proposed for modeling the interaction with external systems, which may remain as black boxes. This approach leverages the testability and coverage analysis inherent in state charts by combining them with scenario-based testing. The overall objective is to reduce the space of scenarios necessary for testing a networked driving function and to streamline validation and verification. The utilization of this approach is demonstrated using a simulated signalized intersection with a roadside unit that detects vulnerable road users., Comment: 10 pages, 5 figures, 2 figures in Appendix

Global optimization of crystal compositions is a significant yet computationally intensive method to identify stable structures within chemical space. The specific physical properties linked to a three-dimensional atomic arrangement make this an essential task in the development of new materials. We present a method that efficiently uses active learning of neural network force fields for structure relaxation, minimizing the required number of steps in the process. This is achieved by neural network force fields equipped with uncertainty estimation, which iteratively guide a pool of randomly generated candidates towards their respective local minima. Using this approach, we are able to effectively identify the most promising candidates for further evaluation using density functional theory (DFT). Our method not only reliably reduces computational costs by up to two orders of magnitude across the benchmark systems Si16 , Na8Cl8 , Ga8As8 and Al4O6 , but also excels in finding the most stable minimum for the unseen, more complex systems Si46 and Al16O24 . Moreover, we demonstrate at the example of Si16 that our method can find multiple relevant local minima while only adding minor computational effort.

Several jurisdictions are starting to regulate frontier artificial intelligence (AI) systems, i.e. general-purpose AI systems that match or exceed the capabilities present in the most advanced systems. To reduce risks from these systems, regulators may require frontier AI developers to adopt safety measures. The requirements could be formulated as high-level principles (e.g. 'AI systems should be safe and secure') or specific rules (e.g. 'AI systems must be evaluated for dangerous model capabilities following the protocol set forth in...'). These regulatory approaches, known as 'principle-based' and 'rule-based' regulation, have complementary strengths and weaknesses. While specific rules provide more certainty and are easier to enforce, they can quickly become outdated and lead to box-ticking. Conversely, while high-level principles provide less certainty and are more costly to enforce, they are more adaptable and more appropriate in situations where the regulator is unsure exactly what behavior would best advance a given regulatory objective. However, rule-based and principle-based regulation are not binary options. Policymakers must choose a point on the spectrum between them, recognizing that the right level of specificity may vary between requirements and change over time. We recommend that policymakers should initially (1) mandate adherence to high-level principles for safe frontier AI development and deployment, (2) ensure that regulators closely oversee how developers comply with these principles, and (3) urgently build up regulatory capacity. Over time, the approach should likely become more rule-based. Our recommendations are based on a number of assumptions, including (A) risks from frontier AI systems are poorly understood and rapidly evolving, (B) many safety practices are still nascent, and (C) frontier AI developers are best placed to innovate on safety practices., Comment: Forthcoming in P Hacker, A Engel, S Hammer and B Mittelstadt (eds), The Oxford Handbook on the Foundations and Regulation of Generative AI (Oxford University Press)

Frontier artificial intelligence (AI) systems could pose increasing risks to public safety and security. But what level of risk is acceptable? One increasingly popular approach is to define capability thresholds, which describe AI capabilities beyond which an AI system is deemed to pose too much risk. A more direct approach is to define risk thresholds that simply state how much risk would be too much. For instance, they might state that the likelihood of cybercriminals using an AI system to cause X amount of economic damage must not increase by more than Y percentage points. The main upside of risk thresholds is that they are more principled than capability thresholds, but the main downside is that they are more difficult to evaluate reliably. For this reason, we currently recommend that companies (1) define risk thresholds to provide a principled foundation for their decision-making, (2) use these risk thresholds to help set capability thresholds, and then (3) primarily rely on capability thresholds to make their decisions. Regulators should also explore the area because, ultimately, they are the most legitimate actors to define risk thresholds. If AI risk estimates become more reliable, risk thresholds should arguably play an increasingly direct role in decision-making., Comment: 24 pages, 6 figures, 1 table

The generation of ligands that both are tailored to a given protein pocket and exhibit a range of desired chemical properties is a major challenge in structure-based drug design. Here, we propose an in-silico approach for the $\textit{de novo}$ generation of 3D ligand structures using the equivariant diffusion model PILOT, combining pocket conditioning with a large-scale pre-training and property guidance. Its multi-objective trajectory-based importance sampling strategy is designed to direct the model towards molecules that not only exhibit desired characteristics such as increased binding affinity for a given protein pocket but also maintains high synthetic accessibility. This ensures the practicality of sampled molecules, thus maximizing their potential for the drug discovery pipeline. PILOT significantly outperforms existing methods across various metrics on the common benchmark dataset CrossDocked2020. Moreover, we employ PILOT to generate novel ligands for unseen protein pockets from the Kinodata-3D dataset, which encompasses a substantial portion of the human kinome. The generated structures exhibit predicted $IC_{50}$ values indicative of potent biological activity, which highlights the potential of PILOT as a powerful tool for structure-based drug design.

Synchrotron light source storage rings aim to maintain a continuous beam current without observable beam motion during injection. One element that paves the way to this target is the non-linear kicker (NLK). The field distribution it generates poses challenges for optimising the topping-up operation. Within this study, a reinforcement learning agent was developed and trained to optimise the NLK operation parameters. We present the models employed, the optimisation process, and the achieved results.

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism groups on any K3 surface., Comment: 41 pages, 2 figures

The grading of open-ended questions is a high-effort, high-impact task in education. Automating this task promises a significant reduction in workload for education professionals, as well as more consistent grading outcomes for students, by circumventing human subjectivity and error. While recent breakthroughs in AI technology might facilitate such automation, this has not been demonstrated at scale. It this paper, we introduce a novel automatic short answer grading (ASAG) system. The system is based on a fine-tuned open-source transformer model which we trained on large set of exam data from university courses across a large range of disciplines. We evaluated the trained model's performance against held-out test data in a first experiment and found high accuracy levels across a broad spectrum of unseen questions, even in unseen courses. We further compared the performance of our model with that of certified human domain experts in a second experiment: we first assembled another test dataset from real historical exams - the historic grades contained in that data were awarded to students in a regulated, legally binding examination process; we therefore considered them as ground truth for our experiment. We then asked certified human domain experts and our model to grade the historic student answers again without disclosing the historic grades. Finally, we compared the hence obtained grades with the historic grades (our ground truth). We found that for the courses examined, the model deviated less from the official historic grades than the human re-graders - the model's median absolute error was 44 % smaller than the human re-graders', implying that the model is more consistent than humans in grading. These results suggest that leveraging AI enhanced grading can reduce human subjectivity, improve consistency and thus ultimately increase fairness.

Verifying highly automated driving functions can be challenging, requiring identifying relevant test scenarios. Scenario-based testing will likely play a significant role in verifying these systems, predominantly occurring within simulation. In our approach, we use traffic scenes as a starting point (seed-scene) to address the individuality of various highly automated driving functions and to avoid the problems associated with a predefined test traffic scenario. Different highly autonomous driving functions, or their distinct iterations, may display different behaviors under the same operating conditions. To make a generalizable statement about a seed-scene, we simulate possible outcomes based on various behavior profiles. We utilize our lightweight simulation environment and populate it with rule-based and machine learning behavior models for individual actors in the scenario. We analyze resulting scenarios using a variety of criticality metrics. The density distributions of the resulting criticality values enable us to make a profound statement about the significance of a particular scene, considering various eventualities.

While there is extensive literature on approximation, deterministic as well as random, of general convex bodies $K$ in the symmetric difference metric, or other metrics arising from intrinsic volumes, very little is known for corresponding random results in the Hausdorff distance when the approximant $K_n$ is given by the convex hull of $n$ independent random points chosen uniformly on the boundary or in the interior of $K$. When $K$ is a polygon and the points are chosen on its boundary, we determine the exact limiting behavior of the expected Hausdorff distance between a polygon as $n\to\infty$. From this we derive the behavior of the asymptotic constant for a regular polygon in the number of vertices., Comment: 17 pages, 2 figures

We prove that there are at most $(24-r_0)$ low-degree rational curves on high-degree models of K3 surfaces with at most Du Val singularities, where $r_0$ is the number of exceptional divisors on the minimal resolution. We also provide several existence results in the above setting (i.e. for rational curves on quasi-polarized K3 surfaces), which imply that for various values of $r_0$ our bound cannot be improved., Comment: 24 pages

Process mining in healthcare presents a range of challenges when working with different types of data within the healthcare domain. There is high diversity considering the variety of data collected from healthcare processes: operational processes given by claims data, a collection of events during surgery, data related to pre-operative and post-operative care, and high-level data collections based on regular ambulant visits with no apparent events. In this case study, a data set from the last category is analyzed. We apply process-mining techniques on sparse patient heart failure data and investigate whether an information gain towards several research questions is achievable. Here, available data are transformed into an event log format, and process discovery and conformance checking are applied. Additionally, patients are split into different cohorts based on comorbidities, such as diabetes and chronic kidney disease, and multiple statistics are compared between the cohorts. Conclusively, we apply decision mining to determine whether a patient will have a cardiovascular outcome and whether a patient will die., Comment: 10 pages, 3 figures, 9 tables, 31 references

The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or $s$-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more traditional versions of functional affine surface areas as well as to the classical affine surface areas for convex bodies is discussed in detail., Comment: arXiv admin note: text overlap with arXiv:1711.11088

Generative AI is expected to have a vast, positive impact on education; however, at present, this potential has not yet been demonstrated at scale at university level. In this study, we present first evidence that generative AI can increase the speed of learning substantially in university students. We tested whether using the AI-powered teaching assistant Syntea affected the speed of learning of hundreds of distance learning students across more than 40 courses at the IU International University of Applied Sciences. Our analysis suggests that using Syntea reduced their study time substantially--by about 27\% on average--in the third month after the release of Syntea. Taken together, the magnitude of the effect and the scalability of the approach implicate generative AI as a key lever to significantly improve and accelerate learning by personalisation.

The growing interest in tin-halide semiconductors for photovoltaic applications demands an in-depth knowledge of the fundamental properties of its constituents, starting from the smallest monomers entering the initial stages of formation. In this first-principles work based on time-dependent density-functional theory, we investigate the structural, electronic, and optical properties of tin-halide molecules SnX$_n^{2-n}$, with $n=1,2,3,4$ and X = Cl, Br, I, simulating these compounds in vacuo as well as in an implicit solvent. We find that structural properties are very sensitive to the halogen species while the charge distribution is also affected by stoichiometry. The ionicity of the Sn-X bond is confirmed by the Bader charge analysis albeit charge displacement plots point to more complex metal-halide coordination. Particular focus is posed on the neutral molecules SnX$_2$, for which electronic and optical properties are discussed in detail. Band gaps and absorption onset decrease with increasing size of the halogen species and despite general common features, each molecule displays peculiar optical signatures. Our results are elaborated in the context of experimental and theoretical literature, including the more widely studied lead-halide analogs, aiming to contribute with microscopic insight to a better understanding of tin-halide perovskites.

This research explores strategies for steering the output of large language models (LLMs) towards specific styles, such as sentiment, emotion, or writing style, by adding style vectors to the activations of hidden layers during text generation. We show that style vectors can be simply computed from recorded layer activations for input texts in a specific style in contrast to more complex training-based approaches. Through a series of experiments, we demonstrate the effectiveness of activation engineering using such style vectors to influence the style of generated text in a nuanced and parameterisable way, distinguishing it from prompt engineering. The presented research constitutes a significant step towards developing more adaptive and effective AI-empowered interactive systems., Comment: Will be published as findings paper at EACL2024 - 18th Conference of the European Chapter of the Association for Computational Linguistics

Let $E$ be a totally real number field of degree $d$ and let $m \geqslant 3$ be an integer. We show that if $md \leqslant 21$ then there exists an $(m-2)$-dimensional family of complex projective $K3$ surfaces with real multiplication by $E$. Analogous results are proved for CM number fields and also for all known higher-dimensional hyperk\"ahler manifolds., Comment: 32 pages; v2: major extension covering also higher-dimensional hyperk\"ahler manifolds and possible Picard lattices

Various fields, including medical and human interaction robots, gain advantages from the development of bioinspired soft actuators. Many recently developed grippers are pneumatics that require external pressure supply systems, thereby limiting the autonomy of these robots. This necessitates the development of scalable and efficient on-board pressure generation systems. While conventional air compression systems are hard to miniaturize, thermopneumatic systems that joule-heat a transducer material to generate pressure present a promising alternative. However, the transducer materials of previously reported thermopneumatic systems demonstrate high heat capacities and limited surface area resulting in long response times and low operation frequencies. This study presents a thermopneumatic pressure generator using aerographene, a highly porous (>99.99 %) network of interconnected graphene microtubes, as lightweight and low heat capacity transducer material. An aerographene pressurizer module (AGPM) can pressurize a reservoir of 4.2 cm3 to about ~140 mbar in 50 ms. Periodic operation of the AGPM for 10 s at 0.66 Hz can further increase the pressure in the reservoir to ~360 mbar. It is demonstrated that multiple AGPMs can be operated parallelly or in series for improved performance. For example, three parallelly operated AGPMs can generate pressure pulses of ~215 mbar. Connecting AGPMs in series increases the maximum pressure achievable by the system. It is shown that three AGPMs working in series can pressurize the reservoir to ~2000 mbar in about 2.5 min. The AGPM's minimalistic design can be easily adapted to circuit boards, making the concept a promising fit for the on-board pressure supply of soft robots., Comment: Author Affiliation: Functional Nanomaterials, Department of Materials Science, Kiel University, Germany; Corresponding Authors: Dr.-Ing. Fabian Sch\"utt (fas@tf.uni-kiel.de), Prof. Dr. Rainer Adelung (ra@tf.uni-kiel.de)

The GERmanium Detector Array (GERDA) experiment operated enriched high-purity germanium detectors in a liquid argon cryostat, which contains 0.33% of $^{36}$Ar, a candidate isotope for the two-neutrino double-electron capture (2$\nu$ECEC) and therefore for the neutrinoless double-electron capture (0$\nu$ECEC). If detected, this process would give evidence of lepton number violation and the Majorana nature of neutrinos. In the radiative 0$\nu$ECEC of $^{36}$Ar, a monochromatic photon is emitted with an energy of 429.88 keV, which may be detected by the GERDA germanium detectors. We searched for the $^{36}$Ar 0$\nu$ECEC with GERDA data, with a total live time of 4.34 yr (3.08 yr accumulated during GERDA Phase II and 1.26 yr during GERDA Phase I). No signal was found and a 90% C.L. lower limit on the half-life of this process was established T$_{1/2}$ > 1.5x10$^{22}$ yr, Comment: 10 pages, 5 figures, 1 table

Difficulty adjustment in practice exercises has been shown to be beneficial for learning. However, previous research has mostly investigated close-ended tasks, which do not offer the students multiple ways to reach a valid solution. Contrary to this, in order to learn in an open-ended learning task, students need to effectively explore the solution space as there are multiple ways to reach a solution. For this reason, the effects of difficulty adjustment could be different for open-ended tasks. To investigate this, as our first contribution, we compare different methods of difficulty adjustment in a user study conducted with 86 participants. Furthermore, as the practice behavior of the students is expected to influence how well the students learn, we additionally look at their practice behavior as a post-hoc analysis. Therefore, as a second contribution, we identify different types of practice behavior and how they link to students' learning outcomes and subjective evaluation measures as well as explore the influence the difficulty adjustment methods have on the practice behaviors. Our results suggest the usefulness of taking into account the practice behavior in addition to only using the practice performance to inform adaptive intervention and difficulty adjustment methods.

We exhibit large families of K3 surfaces with real multiplication, both abstractly using lattice theory, the Torelli theorem and the surjectivity of the period map, as well as explicitly using dihedral covers and isogenies., Comment: 25pp; v2: typos corrected, exposition streamlined

As artificial intelligence (AI) models are scaled up, new capabilities can emerge unintentionally and unpredictably, some of which might be dangerous. In response, dangerous capabilities evaluations have emerged as a new risk assessment tool. But what should frontier AI developers do if sufficiently dangerous capabilities are in fact discovered? This paper focuses on one possible response: coordinated pausing. It proposes an evaluation-based coordination scheme that consists of five main steps: (1) Frontier AI models are evaluated for dangerous capabilities. (2) Whenever, and each time, a model fails a set of evaluations, the developer pauses certain research and development activities. (3) Other developers are notified whenever a model with dangerous capabilities has been discovered. They also pause related research and development activities. (4) The discovered capabilities are analyzed and adequate safety precautions are put in place. (5) Developers only resume their paused activities if certain safety thresholds are reached. The paper also discusses four concrete versions of that scheme. In the first version, pausing is completely voluntary and relies on public pressure on developers. In the second version, participating developers collectively agree to pause under certain conditions. In the third version, a single auditor evaluates models of multiple developers who agree to pause if any model fails a set of evaluations. In the fourth version, developers are legally required to run evaluations and pause if dangerous capabilities are discovered. Finally, the paper discusses the desirability and feasibility of our proposed coordination scheme. It concludes that coordinated pausing is a promising mechanism for tackling emerging risks from frontier AI models. However, a number of practical and legal obstacles need to be overcome, especially how to avoid violations of antitrust law., Comment: 24 pages, 3 figures, 1 table

Recent decisions by leading AI labs to either open-source their models or to restrict access to their models has sparked debate about whether, and how, increasingly capable AI models should be shared. Open-sourcing in AI typically refers to making model architecture and weights freely and publicly accessible for anyone to modify, study, build on, and use. This offers advantages such as enabling external oversight, accelerating progress, and decentralizing control over AI development and use. However, it also presents a growing potential for misuse and unintended consequences. This paper offers an examination of the risks and benefits of open-sourcing highly capable foundation models. While open-sourcing has historically provided substantial net benefits for most software and AI development processes, we argue that for some highly capable foundation models likely to be developed in the near future, open-sourcing may pose sufficiently extreme risks to outweigh the benefits. In such a case, highly capable foundation models should not be open-sourced, at least not initially. Alternative strategies, including non-open-source model sharing options, are explored. The paper concludes with recommendations for developers, standard-setting bodies, and governments for establishing safe and responsible model sharing practices and preserving open-source benefits where safe., Comment: Official release at https://www.governance.ai/research-paper/open-sourcing-highly-capable-foundation-models

Deep generative diffusion models are a promising avenue for 3D de novo molecular design in materials science and drug discovery. However, their utility is still limited by suboptimal performance on large molecular structures and limited training data. To address this gap, we explore the design space of E(3)-equivariant diffusion models, focusing on previously unexplored areas. Our extensive comparative analysis evaluates the interplay between continuous and discrete state spaces. From this investigation, we present the EQGAT-diff model, which consistently outperforms established models for the QM9 and GEOM-Drugs datasets. Significantly, EQGAT-diff takes continuous atom positions, while chemical elements and bond types are categorical and uses time-dependent loss weighting, substantially increasing training convergence, the quality of generated samples, and inference time. We also showcase that including chemically motivated additional features like hybridization states in the diffusion process enhances the validity of generated molecules. To further strengthen the applicability of diffusion models to limited training data, we investigate the transferability of EQGAT-diff trained on the large PubChem3D dataset with implicit hydrogen atoms to target different data distributions. Fine-tuning EQGAT-diff for just a few iterations shows an efficient distribution shift, further improving performance throughout data sets. Finally, we test our model on the Crossdocked data set for structure-based de novo ligand generation, underlining the importance of our findings showing state-of-the-art performance on Vina docking scores.