NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture, which limits their capacity to fully capture heterogeneous features and complex system dependencies. This constraint poses a bottleneck for large-scale PDE pre-training based on neural operators. To address these challenges, we propose a large-scale PDE pre-trained neural operator based on a nested Mixture-of-Experts (MoE) framework. In particular, the image-level MoE is designed to capture global dependencies, while the token-level Sub-MoE focuses on local dependencies. Our model can selectively activate the most suitable expert networks for a given input, thereby enhancing generalization and transferability. We conduct large-scale pre-training on twelve PDE datasets from diverse sources and successfully transfer the model to downstream tasks. Extensive experiments demonstrate the effectiveness of our approach.

Adversarial Examples Detection with Enhanced Image Difference Features based on Local Histogram Equalization

Deep Neural Networks (DNNs) have recently made significant progress in many fields. However, studies have shown that DNNs are vulnerable to adversarial examples, where imperceptible perturbations can greatly mislead DNNs even if the full underlying model parameters are not accessible. Various defense methods have been proposed, such as feature compression and gradient masking. However, numerous studies have proven that previous methods create detection or defense against certain attacks, which renders the method ineffective in the face of the latest unknown attack methods. The invisibility of adversarial perturbations is one of the evaluation indicators for adversarial example attacks, which also means that the difference in the local correlation of high-frequency information in adversarial examples and normal examples can be used as an effective feature to distinguish the two. Therefore, we propose an adversarial example detection framework based on a high-frequency information enhancement strategy, which can effectively extract and amplify the feature differences between adversarial examples and normal examples. Experimental results show that the feature augmentation module can be combined with existing detection models in a modular way under this framework. Improve the detector's performance and reduce the deployment cost without modifying the existing detection model.

Adversarial Example Defense via Perturbation Grading Strategy

Deep Neural Networks have been widely used in many fields. However, studies have shown that DNNs are easily attacked by adversarial examples, which have tiny perturbations and greatly mislead the correct judgment of DNNs. Furthermore, even if malicious attackers cannot obtain all the underlying model parameters, they can use adversarial examples to attack various DNN-based task systems. Researchers have proposed various defense methods to protect DNNs, such as reducing the aggressiveness of adversarial examples by preprocessing or improving the robustness of the model by adding modules. However, some defense methods are only effective for small-scale examples or small perturbations but have limited defense effects for adversarial examples with large perturbations. This paper assigns different defense strategies to adversarial perturbations of different strengths by grading the perturbations on the input examples. Experimental results show that the proposed method effectively improves defense performance. In addition, the proposed method does not modify any task model, which can be used as a preprocessing module, which significantly reduces the deployment cost in practical applications.