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.

KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts, they often lack stability, interpretability, and scalability in regimes dominated by broadband or continuous spectra. Koopman-based approaches provide a principled linear perspective on nonlinear dynamics, but existing methods rely on restrictive finite-dimensional assumptions or explicit spectral parameterizations that degrade in high-dimensional settings. Against these issues, we introduce KoopGen, a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators. By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation while enforcing exact operator-theoretic constraints during learning. Across systems ranging from nonlinear oscillators to high-dimensional chaotic and spatiotemporal dynamics, KoopGen improves prediction accuracy and stability, while clarifying which components of continuous-spectrum dynamics admit interpretable and learnable representations.

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.

Improving Memory Efficiency for Training KANs via Meta Learning

Inspired by the Kolmogorov-Arnold representation theorem, KANs offer a novel framework for function approximation by replacing traditional neural network weights with learnable univariate functions. This design demonstrates significant potential as an efficient and interpretable alternative to traditional MLPs. However, KANs are characterized by a substantially larger number of trainable parameters, leading to challenges in memory efficiency and higher training costs compared to MLPs. To address this limitation, we propose to generate weights for KANs via a smaller meta-learner, called MetaKANs. By training KANs and MetaKANs in an end-to-end differentiable manner, MetaKANs achieve comparable or even superior performance while significantly reducing the number of trainable parameters and maintaining promising interpretability. Extensive experiments on diverse benchmark tasks, including symbolic regression, partial differential equation solving, and image classification, demonstrate the effectiveness of MetaKANs in improving parameter efficiency and memory usage. The proposed method provides an alternative technique for training KANs, that allows for greater scalability and extensibility, and narrows the training cost gap with MLPs stated in the original paper of KANs. Our code is available at https://github.com/Murphyzc/MetaKAN.

Towards Prospective Medical Image Reconstruction via Knowledge-Informed Dynamic Optimal Transport

Medical image reconstruction from measurement data is a vital but challenging inverse problem. Deep learning approaches have achieved promising results, but often requires paired measurement and high-quality images, which is typically simulated through a forward model, i.e., retrospective reconstruction. However, training on simulated pairs commonly leads to performance degradation on real prospective data due to the retrospective-to-prospective gap caused by incomplete imaging knowledge in simulation. To address this challenge, this paper introduces imaging Knowledge-Informed Dynamic Optimal Transport (KIDOT), a novel dynamic optimal transport framework with optimality in the sense of preserving consistency with imaging physics in transport, that conceptualizes reconstruction as finding a dynamic transport path. KIDOT learns from unpaired data by modeling reconstruction as a continuous evolution path from measurements to images, guided by an imaging knowledge-informed cost function and transport equation. This dynamic and knowledge-aware approach enhances robustness and better leverages unpaired data while respecting acquisition physics. Theoretically, we demonstrate that KIDOT naturally generalizes dynamic optimal transport, ensuring its mathematical rationale and solution existence. Extensive experiments on MRI and CT reconstruction demonstrate KIDOT's superior performance.

Adaptive Implicit-Based Deep Learning Channel Estimation for 6G Communications

With the widespread deployment of fifth-generation (5G) wireless networks, research on sixth-generation (6G) technology is gaining momentum. Artificial Intelligence (AI) is anticipated to play a significant role in 6G, particularly through integration with the physical layer for tasks such as channel estimation. Considering resource limitations in real systems, the AI algorithm should be designed to have the ability to balance the accuracy and resource consumption according to the scenarios dynamically. However, conventional explicit multilayer-stacked Deep Learning (DL) models struggle to adapt due to their heavy reliance on the structure of deep neural networks. This article proposes an adaptive Implicit-layer DL Channel Estimation Network (ICENet) with a lightweight framework for vehicle-to-everything communications. This novel approach balances computational complexity and channel estimation accuracy by dynamically adjusting computational resources based on input data conditions, such as channel quality. Unlike explicit multilayer-stacked DL-based channel estimation models, ICENet offers a flexible framework, where specific requirements can be achieved by adaptively changing the number of iterations of the iterative layer. Meanwhile, ICENet requires less memory while maintaining high performance. The article concludes by highlighting open research challenges and promising future research directions.

GMapLatent: Geometric Mapping in Latent Space

Cross-domain generative models based on encoder-decoder AI architectures have attracted much attention in generating realistic images, where domain alignment is crucial for generation accuracy. Domain alignment methods usually deal directly with the initial distribution; however, mismatched or mixed clusters can lead to mode collapse and mixture problems in the decoder, compromising model generalization capabilities. In this work, we innovate a cross-domain alignment and generation model that introduces a canonical latent space representation based on geometric mapping to align the cross-domain latent spaces in a rigorous and precise manner, thus avoiding mode collapse and mixture in the encoder-decoder generation architectures. We name this model GMapLatent. The core of the method is to seamlessly align latent spaces with strict cluster correspondence constraints using the canonical parameterizations of cluster-decorated latent spaces. We first (1) transform the latent space to a canonical parameter domain by composing barycenter translation, optimal transport merging and constrained harmonic mapping, and then (2) compute geometric registration with cluster constraints over the canonical parameter domains. This process realizes a bijective (one-to-one and onto) mapping between newly transformed latent spaces and generates a precise alignment of cluster pairs. Cross-domain generation is then achieved through the aligned latent spaces embedded in the encoder-decoder pipeline. Experiments on gray-scale and color images validate the efficiency, efficacy and applicability of GMapLatent, and demonstrate that the proposed model has superior performance over existing models.

TelOps: AI-driven Operations and Maintenance for Telecommunication Networks

Telecommunication Networks (TNs) have become the most important infrastructure for data communications over the last century. Operations and maintenance (O&M) is extremely important to ensure the availability, effectiveness, and efficiency of TN communications. Different from the popular O&M technique for IT systems (e.g., the cloud), artificial intelligence for IT Operations (AIOps), O&M for TNs meets the following three fundamental challenges: topological dependence of network components, highly heterogeneous software, and restricted failure data. This article presents TelOps, the first AI-driven O&M framework for TNs, systematically enhanced with mechanism, data, and empirical knowledge. We provide a comprehensive comparison between TelOps and AIOps, and conduct a proof-of-concept case study on a typical O&M task (failure diagnosis) for a real industrial TN. As the first systematic AI-driven O&M framework for TNs, TelOps opens a new door to applying AI techniques to TN automation.

Review of Mathematical Optimization in Federated Learning

Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed datasets while satisfying a variety of privacy and system constraints.Different from conventional distributed optimization methods, FL needs to address several specific issues (e.g., non-i.i.d. data distributions and differential private noises), which pose a set of new challenges in the problem formulation, algorithm design, and convergence analysis. In this paper, we will systematically review existing FL optimization research including their assumptions, formulations, methods, and theoretical results. Potential future directions are also discussed.