艾希施泰滕-英戈尔施塔特天主教大学

Kolmogorov–Arnold Networks (KANs) have recently emerged as a structured alternative to standard MLPs, yet a principled theory for their training dynamics, generalization, and privacy properties remains limited. In this paper, we analyze gradient descent (GD) for training two-layer KANs and derive general bounds that characterize their training dynamics, generalization, and utility under differential privacy (DP). As a concrete instantiation, we specialize our analysis to logistic loss under an NTK-separable assumption, where we show that polylogarithmic network width suffices for GD to achieve an optimization rate of order 1/T and a generalization rate of order 1/n, with T denoting the number of GD iterations and n the sample size. In the private setting, we characterize the noise required for (ε,δ)-DP and obtain a utility bound of order √(d)/(nε) (with d the input dimension), matching the classical lower bound for general convex Lipschitz problems. Our results imply that polylogarithmic width is not only sufficient but also necessary under differential privacy, revealing a qualitative gap between non-private (sufficiency only) and private (necessity also emerges) training regimes. Experiments further illustrate how these theoretical insights can guide practical choices, including network width selection and early stopping.

Floodplains are dynamic ecosystems that provide a multitude of ecosystem services (ES), yet they have historically been managed primarily for a limited set of human benefits, often at the expense of biodiversity and multi-functionality. This review synthesises current knowledge in ES and the multi-functionality of floodplains. It further highlights the potential of Nature-based Solutions (NbS) to restore and enhance floodplain multi-functionality and ES through ecologically sound and socially inclusive approaches. Focusing on non-monetary ES assessment tools, such as the RESI and IDES frameworks, the study synthesises lessons from three European case studies (Danube River Basin, River Nebel in Germany and Koviljsko-Petrovaradinski Rit in Serbia). These case studies demonstrate the application of ES indices at basin, regional and local scales for prioritisation, restoration evaluation and stakeholder-informed decision-making. We further discuss trade-offs and synergies amongst ES and highlight participatory approaches that integrate stakeholder perspectives in NbS design and implementation. This review underscores the importance of multi-scale assessments in implementing sustainable floodplain management strategies and supports decision-makers in applying NbS for resilient landscapes that balance ecological, social and economic benefits. Highlights Floodplain restorations are Nature-based solutions enhancing many ecosystem services; Non-monetary assessments of ES allow for consistent evaluation of multi-functionality across scales; Case studies reveal trade-offs between regulating and provisioning ES, emphasising the need for integrated floodplain management; Integration of stakeholders into Nature-based solution planning will increase their acceptance and maximise the benefit for nature and society; ES mapping and multi-functionality metrics at multiple scales offer strategic tools for implementing EU biodiversity and climate strategies, including the 2024 Nature Restoration Law.

Multiverse analysis offers a comprehensive response to a core vulnerability in empirical research: the uncertainty of scientific conclusions arising from defensible yet flexible data-processing and -analysis decisions. By systematically mapping and computing all or a sample of all plausible data-processing pipelines, multiverse analysis reports the robustness of findings across analytical flexibility and increases transparency in the research process. As its adoption grows across disciplines, so too does the need for clarity on how to design, report, and interpret multiverse results responsibly. In this article, we provide interdisciplinary guidance on key procedural considerations, including defensibility and equivalence evaluations, preregistration, and computational demands. We aim to harmonize terminology, promote best practices, and foster conceptual cohesion across fields, supported by reference to domain-specific resources when appropriate. By doing so, we contribute to the broader movement toward more robust, reproducible, and transparent science, one that not only reports results but also interrogates the analytical pipelines that produce them.

We establish the first population risk bounds for Kolmogorov-Arnold Networks (KANs) trained by mini-batch SGD with gradient clipping, covering non-private SGD as well as differentially private SGD (DP-SGD) with Gaussian perturbations that interpolate between independent and temporally correlated noise. This setting is substantially closer to practice than prior KAN theory along two axes: training is by mini-batch SGD, the standard recipe for modern networks, rather than full-batch gradient descent (GD); and correlated-noise mechanisms have empirically shown a more favorable privacy-utility tradeoff than independent-noise mechanisms. Our results cover the corresponding full-batch GD and independent-noise DP-GD results for KANs by Wang et al. (2026), while yielding sharper fixed-second-layer specializations. The technical core is a new analysis route for correlated-noise DP training in the non-convex regime. Temporal dependence breaks the conditional-centering structure underlying standard one-step SGD arguments, and the projection step obstructs the exact cancellation structure of correlated perturbations. We address these difficulties through an auxiliary unprojected dynamics, a shifted iterate that absorbs the current noise perturbation, and a high-probability bootstrap certifying projection inactivity. Combining this optimization analysis with a stability-based generalization argument yields the stated population risk bounds. To the best of our knowledge, this is the first optimization and population risk analysis of a correlated-noise mechanism for DP training beyond convex learning, in particular for neural networks.

BACKGROUND: Germany is a popular destination for international students. However, little is known about their mental health issues. Further, there is limited research in European countries investigating risk and protective factors for acculturative stress and mental health issues among international student samples. This study aimed to investigate the prevalence of depression, anxiety and acculturative stress among international students in Germany. Further, we examined the association of possible protective and risk factors with these outcome variables. METHODS: A total of 327 international students in Germany completed an online survey. Standardised measures for depression (PHQ-9), anxiety (GAD-7), and acculturative stress were used. Hierarchical regression analyses were employed to assess the impact of demographic factors, psychological variables, and coping strategies on mental health outcomes. RESULTS: The prevalence of depression and anxiety was high among international students (46.5% and 46.8%, respectively). A substantial proportion of the sample (31.2%) reported suicidal ideation or thoughts of self-harm. Further, international students in our study reported moderate acculturative stress. Mindfulness, different sources of social support, self-efficacy, optimism and acceptance were protective factors against depression, anxiety or acculturative stress. However, less than half of our sample was well supported by university facilities. A few demographic variables (gender, graduation, education, home country) were related to higher acculturative stress and anxiety. Acculturative stress was a significant predictor of depression and anxiety. CONCLUSION: Our findings highlight the importance of addressing mental health issues among international students. The results suggest that universities may consider providing adequate psychological services and strengthening institutional support for international students.