Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs

Partial differential equations (PDEs) are widely used to model complex physical systems, but solving them efficiently remains a significant challenge. Recently, Transformers have emerged as the preferred architecture for PDEs due to their ability to capture intricate dependencies. However, they struggle with representing continuous dynamics and long-range interactions. To overcome these limitations, we introduce the Mamba Neural Operator (MNO), a novel framework that enhances neural operator-based techniques for solving PDEs. MNO establishes a formal theoretical connection between structured state-space models (SSMs) and neural operators, offering a unified structure that can adapt to diverse architectures, including Transformer-based models. By leveraging the structured design of SSMs, MNO captures long-range dependencies and continuous dynamics more effectively than traditional Transformers. Through extensive analysis, we show that MNO significantly boosts the expressive power and accuracy of neural operators, making it not just a complement but a superior framework for PDE-related tasks, bridging the gap between efficient representation and accurate solution approximation.

Explicit Differentiable Slicing and Global Deformation for Cardiac Mesh Reconstruction

Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired as 2D slices that are sparsely sampled and noisy, and mesh reconstruction on such data is a challenging task. Traditional voxel-based approaches rely on pre- and post-processing that compromises image fidelity, while mesh-level deep learning approaches require mesh annotations that are difficult to get. Therefore, direct cross-domain supervision from 2D images to meshes is a key technique for advancing 3D learning in medical imaging, but it has not been well-developed. While there have been attempts to approximate the optimized meshes' slicing, few existing methods directly use 2D slices to supervise mesh reconstruction in a differentiable manner. Here, we propose a novel explicit differentiable voxelization and slicing (DVS) algorithm that allows gradient backpropagation to a mesh from its slices, facilitating refined mesh optimization directly supervised by the losses defined on 2D images. Further, we propose an innovative framework for extracting patient-specific left ventricle (LV) meshes from medical images by coupling DVS with a graph harmonic deformation (GHD) mesh morphing descriptor of cardiac shape that naturally preserves mesh quality and smoothness during optimization. Experimental results demonstrate that our method achieves state-of-the-art performance in cardiac mesh reconstruction tasks from CT and MRI, with an overall Dice score of 90% on multi-datasets, outperforming existing approaches. The proposed method can further quantify clinically useful parameters such as ejection fraction and global myocardial strains, closely matching the ground truth and surpassing the traditional voxel-based approach in sparse images.

Learning Task-Specific Sampling Strategy for Sparse-View CT Reconstruction

Sparse-View Computed Tomography (SVCT) offers low-dose and fast imaging but suffers from severe artifacts. Optimizing the sampling strategy is an essential approach to improving the imaging quality of SVCT. However, current methods typically optimize a universal sampling strategy for all types of scans, overlooking the fact that the optimal strategy may vary depending on the specific scanning task, whether it involves particular body scans (e.g., chest CT scans) or downstream clinical applications (e.g., disease diagnosis). The optimal strategy for one scanning task may not perform as well when applied to other tasks. To address this problem, we propose a deep learning framework that learns task-specific sampling strategies with a multi-task approach to train a unified reconstruction network while tailoring optimal sampling strategies for each individual task. Thus, a task-specific sampling strategy can be applied for each type of scans to improve the quality of SVCT imaging and further assist in performance of downstream clinical usage. Extensive experiments across different scanning types provide validation for the effectiveness of task-specific sampling strategies in enhancing imaging quality. Experiments involving downstream tasks verify the clinical value of learned sampling strategies, as evidenced by notable improvements in downstream task performance. Furthermore, the utilization of a multi-task framework with a shared reconstruction network facilitates deployment on current imaging devices with switchable task-specific modules, and allows for easily integrate new tasks without retraining the entire model.

CT-SDM: A Sampling Diffusion Model for Sparse-View CT Reconstruction across All Sampling Rates

Sparse views X-ray computed tomography has emerged as a contemporary technique to mitigate radiation dose. Because of the reduced number of projection views, traditional reconstruction methods can lead to severe artifacts. Recently, research studies utilizing deep learning methods has made promising progress in removing artifacts for Sparse-View Computed Tomography (SVCT). However, given the limitations on the generalization capability of deep learning models, current methods usually train models on fixed sampling rates, affecting the usability and flexibility of model deployment in real clinical settings. To address this issue, our study proposes a adaptive reconstruction method to achieve high-performance SVCT reconstruction at any sampling rate. Specifically, we design a novel imaging degradation operator in the proposed sampling diffusion model for SVCT (CT-SDM) to simulate the projection process in the sinogram domain. Thus, the CT-SDM can gradually add projection views to highly undersampled measurements to generalize the full-view sinograms. By choosing an appropriate starting point in diffusion inference, the proposed model can recover the full-view sinograms from any sampling rate with only one trained model. Experiments on several datasets have verified the effectiveness and robustness of our approach, demonstrating its superiority in reconstructing high-quality images from sparse-view CT scans across various sampling rates.

Enhancing Transferability of Adversarial Attacks with GE-AdvGAN+: A Comprehensive Framework for Gradient Editing

Transferable adversarial attacks pose significant threats to deep neural networks, particularly in black-box scenarios where internal model information is inaccessible. Studying adversarial attack methods helps advance the performance of defense mechanisms and explore model vulnerabilities. These methods can uncover and exploit weaknesses in models, promoting the development of more robust architectures. However, current methods for transferable attacks often come with substantial computational costs, limiting their deployment and application, especially in edge computing scenarios. Adversarial generative models, such as Generative Adversarial Networks (GANs), are characterized by their ability to generate samples without the need for retraining after an initial training phase. GE-AdvGAN, a recent method for transferable adversarial attacks, is based on this principle. In this paper, we propose a novel general framework for gradient editing-based transferable attacks, named GE-AdvGAN+, which integrates nearly all mainstream attack methods to enhance transferability while significantly reducing computational resource consumption. Our experiments demonstrate the compatibility and effectiveness of our framework. Compared to the baseline AdvGAN, our best-performing method, GE-AdvGAN++, achieves an average ASR improvement of 47.8. Additionally, it surpasses the latest competing algorithm, GE-AdvGAN, with an average ASR increase of 5.9. The framework also exhibits enhanced computational efficiency, achieving 2217.7 FPS, outperforming traditional methods such as BIM and MI-FGSM. The implementation code for our GE-AdvGAN+ framework is available at https://github.com/GEAdvGANP

Enhancing Adversarial Attacks via Parameter Adaptive Adversarial Attack

In recent times, the swift evolution of adversarial attacks has captured widespread attention, particularly concerning their transferability and other performance attributes. These techniques are primarily executed at the sample level, frequently overlooking the intrinsic parameters of models. Such neglect suggests that the perturbations introduced in adversarial samples might have the potential for further reduction. Given the essence of adversarial attacks is to impair model integrity with minimal noise on original samples, exploring avenues to maximize the utility of such perturbations is imperative. Against this backdrop, we have delved into the complexities of adversarial attack algorithms, dissecting the adversarial process into two critical phases: the Directional Supervision Process (DSP) and the Directional Optimization Process (DOP). While DSP determines the direction of updates based on the current samples and model parameters, it has been observed that existing model parameters may not always be conducive to adversarial attacks. The impact of models on adversarial efficacy is often overlooked in current research, leading to the neglect of DSP. We propose that under certain conditions, fine-tuning model parameters can significantly enhance the quality of DSP. For the first time, we propose that under certain conditions, fine-tuning model parameters can significantly improve the quality of the DSP. We provide, for the first time, rigorous mathematical definitions and proofs for these conditions, and introduce multiple methods for fine-tuning model parameters within DSP. Our extensive experiments substantiate the effectiveness of the proposed P3A method. Our code is accessible at: https://anonymous.4open.science/r/P3A-A12C/

Diff3Dformer: Leveraging Slice Sequence Diffusion for Enhanced 3D CT Classification with Transformer Networks

The manifestation of symptoms associated with lung diseases can vary in different depths for individual patients, highlighting the significance of 3D information in CT scans for medical image classification. While Vision Transformer has shown superior performance over convolutional neural networks in image classification tasks, their effectiveness is often demonstrated on sufficiently large 2D datasets and they easily encounter overfitting issues on small medical image datasets. To address this limitation, we propose a Diffusion-based 3D Vision Transformer (Diff3Dformer), which utilizes the latent space of the Diffusion model to form the slice sequence for 3D analysis and incorporates clustering attention into ViT to aggregate repetitive information within 3D CT scans, thereby harnessing the power of the advanced transformer in 3D classification tasks on small datasets. Our method exhibits improved performance on two different scales of small datasets of 3D lung CT scans, surpassing the state of the art 3D methods and other transformer-based approaches that emerged during the COVID-19 pandemic, demonstrating its robust and superior performance across different scales of data. Experimental results underscore the superiority of our proposed method, indicating its potential for enhancing medical image classification tasks in real-world scenarios.

Low-rank based motion correction followed by automatic frame selection in DT-CMR

Motivation: Post-processing of in-vivo diffusion tensor CMR (DT-CMR) is challenging due to the low SNR and variation in contrast between frames which makes image registration difficult, and the need to manually reject frames corrupted by motion. Goals: To develop a semi-automatic post-processing pipeline for robust DT-CMR registration and automatic frame selection. Approach: We used low intrinsic rank averaged frames as the reference to register other low-ranked frames. A myocardium-guided frame selection rejected the frames with signal loss, through-plane motion and poor registration. Results: The proposed method outperformed our previous noise-robust rigid registration on helix angle data quality and reduced negative eigenvalues in healthy volunteers.

MoreHopQA: More Than Multi-hop Reasoning

Most existing multi-hop datasets are extractive answer datasets, where the answers to the questions can be extracted directly from the provided context. This often leads models to use heuristics or shortcuts instead of performing true multi-hop reasoning. In this paper, we propose a new multi-hop dataset, MoreHopQA, which shifts from extractive to generative answers. Our dataset is created by utilizing three existing multi-hop datasets: HotpotQA, 2WikiMultihopQA, and MuSiQue. Instead of relying solely on factual reasoning, we enhance the existing multi-hop questions by adding another layer of questioning that involves one, two, or all three of the following types of reasoning: commonsense, arithmetic, and symbolic. Our dataset is created through a semi-automated process, resulting in a dataset with 1,118 samples that have undergone human verification. We then use our dataset to evaluate five different large language models: Mistral 7B, Gemma 7B, Llama 3 (8B and 70B), and GPT-4. We also design various cases to analyze the reasoning steps in the question-answering process. Our results show that models perform well on initial multi-hop questions but struggle with our extended questions, indicating that our dataset is more challenging than previous ones. Our analysis of question decomposition reveals that although models can correctly answer questions, only a portion - 38.7% for GPT-4 and 33.4% for Llama3-70B - achieve perfect reasoning, where all corresponding sub-questions are answered correctly. Evaluation code and data are available at https://github.com/Alab-NII/morehopqa

Groupwise Deformable Registration of Diffusion Tensor Cardiovascular Magnetic Resonance: Disentangling Diffusion Contrast, Respiratory and Cardiac Motions

Diffusion tensor based cardiovascular magnetic resonance (DT-CMR) offers a non-invasive method to visualize the myocardial microstructure. With the assumption that the heart is stationary, frames are acquired with multiple repetitions for different diffusion encoding directions. However, motion from poor breath-holding and imprecise cardiac triggering complicates DT-CMR analysis, further challenged by its inherently low SNR, varied contrasts, and diffusion-induced textures. Our solution is a novel framework employing groupwise registration with an implicit template to isolate respiratory and cardiac motions, while a tensor-embedded branch preserves diffusion contrast textures. We've devised a loss refinement tailored for non-linear least squares fitting and low SNR conditions. Additionally, we introduce new physics-based and clinical metrics for performance evaluation. Access code and supplementary materials at: https://github.com/Mobbyjj/DTCMRRegistration