A Clinically Validated Foundation Model for Comprehensive Lung Pathology Interpretation

Pathological assessment guides lung cancer diagnosis, treatment selection, and prognostic evaluation, yet current CPath approaches rely on task-specific models for isolated objectives. Although pan-cancer foundation models offer versatility, they lack subspecialty-level depth and have not been evaluated across clinical workflows or prospectively validated in real-world settings. We introduce PulmoFoundation, a multi-center, prospectively validated, randomized controlled trial (RCT)-evaluated foundation model for comprehensive lung pathology assessment across pre-operative, intra-operative, and post-operative care. Built upon Virchow2 via subspecialty-specific pretraining using ~40,000 diagnostic H&E-stained whole-slide images (WSIs), PulmoFoundation was systematically evaluated on ~26,000 WSIs across 32 clinically relevant tasks. In addition to accurately predicting molecular markers and patient survival, our model achieves clinical-grade performance in core diagnostic tasks across biopsy, frozen section, and surgical resection slides. In a registered prospective study of 1,357 patients across 11 diagnostic tasks, our model achieved an average AUC of 92.3%. Using pre-specified triage thresholds, PulmoFoundation could reduce additional second-review burden for 68.8% of biopsies and 83.0% of frozen sections, and defer 44.5% of IHC stain orders, with PPVs of 1.0, 0.991, and 0.966. Beyond prospective validation, we conducted a crossover RCT with eight pathologists, in which AI assistance improved diagnostic accuracy across 4,928 case-reader pairs (91.7% w/ AI vs. 83.8% w/o AI). AI assistance also reduced median diagnostic time by 19.6%, increased diagnostic confidence by 8.7%, and improved inter-rater agreement from moderate (kappa = 0.56) to substantial (kappa = 0.76). Together, these evaluations support PulmoFoundation as a clinically validated decision-support system for lung pathology.

Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment. To bridge this gap, we conduct an analysis from an optimization perspective and formalize the intrinsic relationship among data symmetry priors, model equivariance, and generalization capability. Specifically, we propose for the first time a quantifiable definition of non strict symmetry at the dataset level (rather than sample level) and use it as a constraint to formulate the restoration inverse problem. We then show that the equivariance for restoration models can be naturally derived from this inverse problems incorporated the proposed symmetry constraints, and that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk. Guided by these insights, we propose a Sample Adaptive Equivariant Network that uses a hypernetwork and transformation learnable equivariant convolutions to dynamically align with each sample's inherent symmetry. Extensive experiments on super resolution, denoising, and deraining validate our theoretical findings and show significant superiority over standard baselines and traditional equivariant models. Our code and supplementary material are available at https://github.com/tanfy929/SA-Conv.

Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors

Image-to-image translation (I2I) is a fundamental task in computer vision, focused on mapping an input image from a source domain to a corresponding image in a target domain while preserving domain-invariant features and adapting domain-specific attributes. Despite the remarkable success of deep learning-based I2I approaches, the lack of paired data and unsupervised learning framework still hinder their effectiveness. In this work, we address the challenge by incorporating transformation symmetry priors into image-to-image translation networks. Specifically, we introduce rotation group equivariant convolutions to achieve rotation equivariant I2I framework, a novel contribution, to the best of our knowledge, along this research direction. This design ensures the preservation of rotation symmetry, one of the most intrinsic and domain-invariant properties of natural and scientific images, throughout the network. Furthermore, we conduct a systematic study on image symmetry priors on real dataset and propose a novel transformation learnable equivariant convolutions (TL-Conv) that adaptively learns transformation groups, enhancing symmetry preservation across diverse datasets. We also provide a theoretical analysis of the equivariance error of TL-Conv, proving that it maintains exact equivariance in continuous domains and provide a bound for the error in discrete cases. Through extensive experiments across a range of I2I tasks, we validate the effectiveness and superior performance of our approach, highlighting the potential of equivariant networks in enhancing generation quality and its broad applicability. Our code is available at https://github.com/tanfy929/Equivariant-I2I

Rotation Equivariant Mamba for Vision Tasks

Rotation equivariance constitutes one of the most general and crucial structural priors for visual data, yet it remains notably absent from current Mamba-based vision architectures. Despite the success of Mamba in natural language processing and its growing adoption in computer vision, existing visual Mamba models fail to account for rotational symmetry in their design. This omission renders them inherently sensitive to image rotations, thereby constraining their robustness and cross-task generalization. To address this limitation, we propose to incorporate rotation symmetry, a universal and fundamental geometric prior in images, into Mamba-based architectures. Specifically, we introduce EQ-VMamba, the first rotation equivariant visual Mamba architecture for vision tasks. The core components of EQ-VMamba include a carefully designed rotation equivariant cross-scan strategy and group Mamba blocks. Moreover, we provide a rigorous theoretical analysis of the intrinsic equivariance error, demonstrating that the proposed architecture enforces end-to-end rotation equivariance throughout the network. Extensive experiments across multiple benchmarks - including high-level image classification task, mid-level semantic segmentation task, and low-level image super-resolution task - demonstrate that EQ-VMamba achieves superior or competitive performance compared to non-equivariant baselines, while requiring approximately 50% fewer parameters. These results indicate that embedding rotation equivariance not only effectively bolsters the robustness of visual Mamba models against rotation transformations, but also enhances overall performance with significantly improved parameter efficiency. Code is available at https://github.com/zhongchenzhao/EQ-VMamba.

Vanilla Group Equivariant Vision Transformer: Simple and Effective

Incorporating symmetry priors as inductive biases to design equivariant Vision Transformers (ViTs) has emerged as a promising avenue for enhancing their performance. However, existing equivariant ViTs often struggle to balance performance with equivariance, primarily due to the challenge of achieving holistic equivariant modifications across the diverse modules in ViTs-particularly in harmonizing the Self-Attention mechanism with Patch Embedding. To address this, we propose a straightforward framework that systematically renders key ViT components, including patch embedding, self-attention, positional encodings, and Down/Up-Sampling, equivariant, thereby constructing ViTs with guaranteed equivariance. The resulting architecture serves as a plug-and-play replacement that is both theoretically grounded and practically versatile, scaling seamlessly even to Swin Transformers. Extensive experiments demonstrate that our equivariant ViTs consistently improve performance and data efficiency across a wide spectrum of vision tasks.

Rotation Equivariant Arbitrary-scale Image Super-Resolution

The arbitrary-scale image super-resolution (ASISR), a recent popular topic in computer vision, aims to achieve arbitrary-scale high-resolution recoveries from a low-resolution input image. This task is realized by representing the image as a continuous implicit function through two fundamental modules, a deep-network-based encoder and an implicit neural representation (INR) module. Despite achieving notable progress, a crucial challenge of such a highly ill-posed setting is that many common geometric patterns, such as repetitive textures, edges, or shapes, are seriously warped and deformed in the low-resolution images, naturally leading to unexpected artifacts appearing in their high-resolution recoveries. Embedding rotation equivariance into the ASISR network is thus necessary, as it has been widely demonstrated that this enhancement enables the recovery to faithfully maintain the original orientations and structural integrity of geometric patterns underlying the input image. Motivated by this, we make efforts to construct a rotation equivariant ASISR method in this study. Specifically, we elaborately redesign the basic architectures of INR and encoder modules, incorporating intrinsic rotation equivariance capabilities beyond those of conventional ASISR networks. Through such amelioration, the ASISR network can, for the first time, be implemented with end-to-end rotational equivariance maintained from input to output. We also provide a solid theoretical analysis to evaluate its intrinsic equivariance error, demonstrating its inherent nature of embedding such an equivariance structure. The superiority of the proposed method is substantiated by experiments conducted on both simulated and real datasets. We also validate that the proposed framework can be readily integrated into current ASISR methods in a plug \& play manner to further enhance their performance.

DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction

Dynamic Magnetic Resonance Imaging (MRI) exhibits transformation symmetries, including spatial rotation symmetry within individual frames and temporal symmetry along the time dimension. Explicit incorporation of these symmetry priors in the reconstruction model can significantly improve image quality, especially under aggressive undersampling scenarios. Recently, Equivariant convolutional neural network (ECNN) has shown great promise in exploiting spatial symmetry priors. However, existing ECNNs critically fail to model temporal symmetry, arguably the most universal and informative structural prior in dynamic MRI reconstruction. To tackle this issue, we propose a novel Deep Unrolling Network with Spatiotemporal Rotation Equivariance (DUN-SRE) for Dynamic MRI Reconstruction. The DUN-SRE establishes spatiotemporal equivariance through a (2+1)D equivariant convolutional architecture. In particular, it integrates both the data consistency and proximal mapping module into a unified deep unrolling framework. This architecture ensures rigorous propagation of spatiotemporal rotation symmetry constraints throughout the reconstruction process, enabling more physically accurate modeling of cardiac motion dynamics in cine MRI. In addition, a high-fidelity group filter parameterization mechanism is developed to maintain representation precision while enforcing symmetry constraints. Comprehensive experiments on Cardiac CINE MRI datasets demonstrate that DUN-SRE achieves state-of-the-art performance, particularly in preserving rotation-symmetric structures, offering strong generalization capability to a broad range of dynamic MRI reconstruction tasks.

A Regularization-Guided Equivariant Approach for Image Restoration

Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation accuracy and rely on strict symmetry assumptions that may not hold in practice. These limitations pose a significant drawback for image restoration tasks, which demands high accuracy and precise symmetry representation. To address these challenges, we propose a rotation-equivariant regularization strategy that adaptively enforces the appropriate symmetry constraints on the data while preserving the network's representational accuracy. Specifically, we introduce EQ-Reg, a regularizer designed to enhance rotation equivariance, which innovatively extends the insights of data-augmentation-based and equivariant-based methodologies. This is achieved through self-supervised learning and the spatial rotation and cyclic channel shift of feature maps deduce in the equivariant framework. Our approach firstly enables a non-strictly equivariant network suitable for image restoration, providing a simple and adaptive mechanism for adjusting equivariance based on task. Extensive experiments across three low-level tasks demonstrate the superior accuracy and generalization capability of our method, outperforming state-of-the-art approaches.

Rotation-Equivariant Self-Supervised Method in Image Denoising

Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely more on the prior embedded in deep networks themselves. As a result, most of the self-supervised methods are designed with Convolution Neural Networks (CNNs) architectures, which well capture one of the most important image prior, translation equivariant prior. Inspired by the great success achieved by the introduction of translational equivariance, in this paper, we explore the way to further incorporate another important image prior. Specifically, we first apply high-accuracy rotation equivariant convolution to self-supervised image denoising. Through rigorous theoretical analysis, we have proved that simply replacing all the convolution layers with rotation equivariant convolution layers would modify the network into its rotation equivariant version. To the best of our knowledge, this is the first time that rotation equivariant image prior is introduced to self-supervised image denoising at the network architecture level with a comprehensive theoretical analysis of equivariance errors, which offers a new perspective to the field of self-supervised image denoising. Moreover, to further improve the performance, we design a new mask mechanism to fusion the output of rotation equivariant network and vanilla CNN-based network, and construct an adaptive rotation equivariant framework. Through extensive experiments on three typical methods, we have demonstrated the effectiveness of the proposed method.

Continuous Filtered Backprojection by Learnable Interpolation Network

Accurate reconstruction of computed tomography (CT) images is crucial in medical imaging field. However, there are unavoidable interpolation errors in the backprojection step of the conventional reconstruction methods, i.e., filtered-back-projection based methods, which are detrimental to the accurate reconstruction. In this study, to address this issue, we propose a novel deep learning model, named Leanable-Interpolation-based FBP or LInFBP shortly, to enhance the reconstructed CT image quality, which achieves learnable interpolation in the backprojection step of filtered backprojection (FBP) and alleviates the interpolation errors. Specifically, in the proposed LInFBP, we formulate every local piece of the latent continuous function of discrete sinogram data as a linear combination of selected basis functions, and learn this continuous function by exploiting a deep network to predict the linear combination coefficients. Then, the learned latent continuous function is exploited for interpolation in backprojection step, which first time takes the advantage of deep learning for the interpolation in FBP. Extensive experiments, which encompass diverse CT scenarios, demonstrate the effectiveness of the proposed LInFBP in terms of enhanced reconstructed image quality, plug-and-play ability and generalization capability.