arXiv:2603.03804v1 Announce Type: cross Abstract: Central Bank Digital Currency (CBDCs) are becoming a new digital financial tool aimed at financial inclusion, increased monetary stability, and improved efficiency of payment systems, as they are issued by central banks. One of the most important aspects is that the CBDC must offer secure offline payment methods to users, allowing them to retain cash-like access without violating Anti-Money Laundering and Counter-terrorism Financing (AML/CFT) rules. The offline CBDC ecosystems will provide financial inclusion, empower underserved communities, and ensure equitable access to digital payments, even in connectivity-poor remote locations. With the rapid growth of Internet of Things (IoT) devices in our everyday lives, they are capable of performing secure digital transactions. Integrating offline CBDC payment with IoT devices enables seamless, automated payment without internet connectivity. However, IoT devices face special challenges due to their resource-constrained nature. This makes it difficult to include features such as double-spending prevention, privacy preservation, low-computation operation, and digital identity management. The work proposes a privacy-preserving offline CBDC model with integrated secure elements (SEs), zero-knowledge proofs (ZKPs), and intermittent synchronisation to conduct offline payments on IoT hardware. The proposed model is based on recent improvements in offline CBDC prototypes, regulations and cryptographic design choices such as hybrid architecture that involves using combination of online and offline payment in IoT devices using secure hardware with lightweight zero-knowledge proof cryptographic algorithm.

arXiv:2602.07970v3 Announce Type: replace-cross Abstract: Partial Differential Equations are precise in modelling the physical, biological and graphical phenomena. However, the numerical methods suffer from the curse of dimensionality, high computation costs and domain-specific discretization. We aim to explore pros and cons of different PDE solvers, and apply them to specific scientific simulation problems, including forwarding solution, inverse problems and equations discovery. In particular, we extend the recent CNF (NeurIPS 2023) framework solver to coupled and non-linear settings, together with down-stream applications. The outcomes include implementation of selected methods, self-tuning techniques, evaluation on benchmark problems and a comprehensive survey of neural PDE solvers and scientific simulation applications.

arXiv:2603.02948v1 Announce Type: cross Abstract: Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling approach is proposed, which relies on the use of Domain-aware Fourier Features (DaFFs) for the positional encoding of the input space. These features encapsulate all the domain-specific characteristics, such as the geometry and boundary conditions, and unlike Random Fourier Features (RFFs), eliminate the need for explicit boundary condition loss terms and loss balancing schemes, while simplifying the optimization process and reducing the computational cost associated with training. We further develop an LRP-based explainability framework tailored to PINNs, enabling the extraction of relevance attribution scores for the input space. It is demonstrated that PINN-DaFFs achieve orders-of-magnitude lower errors and allow faster convergence compared to vanilla PINNs and RFFs-based PINNs. Furthermore, LRP analysis reveals that the proposed leads to more physically consistent feature attributions, while PINN-RFFs and vanilla PINNs display more scattered and less physics-relevant patterns. These results demonstrate that DaFFs not only enhance PINNs' accuracy and efficiency but also improve interpretability, laying the ground for more robust and informative physics-informed learning.

arXiv:2602.19517v2 Announce Type: replace Abstract: We introduce CFE-Bench (Classroom Final Exam), a multimodal benchmark for evaluating the reasoning capabilities of large language models across more than 20 STEM domains. CFE-Bench is curated from repeatedly used, authentic university homework and exam problems, paired with reference solutions provided by course instructors. CFE-Bench remains challenging for frontier models: the newly released Gemini-3.1-pro-preview achieves 59.69% overall accuracy, while the second-best model, Gemini-3-flash-preview, reaches 55.46%, leaving substantial room for improvement. Beyond aggregate scores, we conduct a diagnostic analysis by decomposing instructor reference solutions into structured reasoning flows. We find that while frontier models often answer intermediate sub-questions correctly, they struggle to reliably derive and maintain correct intermediate states throughout multi-step solutions. We further observe that model-generated solutions typically contain more reasoning steps than instructor solutions, indicating lower step efficiency and a higher risk of error accumulation. Data and code are available at https://github.com/Analogy-AI/CFE_Bench.