Fourier Neural Operators for Non-Markovian Processes:Approximation Theorems and Experiments

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror padding, enabling it to handle non-periodic inputs. We rigorously prove that MFNOs can approximate solutions of path-dependent stochastic differential equations and Lipschitz transformations of fractional Brownian motions to an arbitrary degree of accuracy. Our theoretical analysis builds on Wong--Zakai type theorems and various approximation techniques. Empirically, the MFNO exhibits strong resolution generalization--a property rarely seen in standard architectures such as LSTMs, TCNs, and DeepONet. Furthermore, our model achieves performance that is comparable or superior to these baselines while offering significantly faster sample path generation than classical numerical schemes.

MedErr-CT: A Visual Question Answering Benchmark for Identifying and Correcting Errors in CT Reports

Computed Tomography (CT) plays a crucial role in clinical diagnosis, but the growing demand for CT examinations has raised concerns about diagnostic errors. While Multimodal Large Language Models (MLLMs) demonstrate promising comprehension of medical knowledge, their tendency to produce inaccurate information highlights the need for rigorous validation. However, existing medical visual question answering (VQA) benchmarks primarily focus on simple visual recognition tasks, lacking clinical relevance and failing to assess expert-level knowledge. We introduce MedErr-CT, a novel benchmark for evaluating medical MLLMs' ability to identify and correct errors in CT reports through a VQA framework. The benchmark includes six error categories - four vision-centric errors (Omission, Insertion, Direction, Size) and two lexical error types (Unit, Typo) - and is organized into three task levels: classification, detection, and correction. Using this benchmark, we quantitatively assess the performance of state-of-the-art 3D medical MLLMs, revealing substantial variation in their capabilities across different error types. Our benchmark contributes to the development of more reliable and clinically applicable MLLMs, ultimately helping reduce diagnostic errors and improve accuracy in clinical practice. The code and datasets are available at https://github.com/babbu3682/MedErr-CT.

Rationale-aware Autonomous Driving Policy utilizing Safety Force Field implemented on CARLA Simulator

Despite the rapid improvement of autonomous driving technology in recent years, automotive manufacturers must resolve liability issues to commercialize autonomous passenger car of SAE J3016 Level 3 or higher. To cope with the product liability law, manufacturers develop autonomous driving systems in compliance with international standards for safety such as ISO 26262 and ISO 21448. Concerning the safety of the intended functionality (SOTIF) requirement in ISO 26262, the driving policy recommends providing an explicit rational basis for maneuver decisions. In this case, mathematical models such as Safety Force Field (SFF) and Responsibility-Sensitive Safety (RSS) which have interpretability on decision, may be suitable. In this work, we implement SFF from scratch to substitute the undisclosed NVIDIA's source code and integrate it with CARLA open-source simulator. Using SFF and CARLA, we present a predictor for claimed sets of vehicles, and based on the predictor, propose an integrated driving policy that consistently operates regardless of safety conditions it encounters while passing through dynamic traffic. The policy does not have a separate plan for each condition, but using safety potential, it aims human-like driving blended in with traffic flow.