Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.

HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation

Hyperspectral image (HSI) restoration is crucial for reliable analysis, as real HSIs suffer from degradations like noise, blur, and resolution loss. However, existing models trained on source data often fail on target domains lacking clean references, a common occurrence in practice. To address this issue, we present HIR-ALIGN, a plug-and-play target-adaptive augmentation framework that enhances hyperspectral image restoration by augmenting limited training images with synthetic data that closely matches the target distribution using no extra data. It consists of three stages: (i) proxy generation, where off-the-shelf restoration models restore degraded target observations to produce semantics-preserving proxy HSIs that approximate target-domain clean images; (ii) distribution-adaptive synthesis, where a blur-robust unCLIP diffusion model generates target-aligned RGBs from proxy RGBs, with prompt conditioning and embedding-space noise initialization. Then, a warp-based spectral transfer module synthesizes HSIs by aligning each generated RGB with the proxy RGB, estimating soft patch-wise transport weights, and applying these weights and learnable local interpolation kernels to the proxy HSI; and (iii) aligned supervised finetuning, where restoration networks pretrained on the source distribution are finetuned using both the proxy HSIs and synthesized target-aligned HSIs, and are then deployed on degraded target images. We further provide theoretical analysis showing that augmentation-based finetuning can achieve lower target-domain restoration risk by jointly improving target distribution coverage and controlling spectral bias. Extensive experiments on simulated and real datasets across denoising and super-resolution tasks demonstrate that HIR-ALIGN consistently improves source-only supervised baselines, outperforming both source-only counterparts and representative unsupervised methods.

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.

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws

Emergent intelligence have played a major role in the modern AI development. While existing studies primarily rely on empirical observations to characterize this phenomenon, a rigorous theoretical framework remains underexplored. This study attempts to develop a mathematical approach to formalize emergent intelligence from the perspective of limit theory. Specifically, we introduce a performance function E(N, P, K), dependent on data size N, model size P and training steps K, to quantify intelligence behavior. We posit that intelligence emerges as a transition from finite to effectively infinite knowledge, and thus recast emergent intelligence as existence of the limit $\lim_{N,P,K \to \infty} \mathcal{E}(N,P,K)$, with emergent abilities corresponding to the limiting behavior. This limit theory helps reveal that emergent intelligence originates from the existence of a parameter-limit architecture (referred to as the limit architecture), and that emergent intelligence rationally corresponds to the learning behavior of this limit system. By introducing tools from nonlinear Lipschitz operator theory, we prove that the necessary and sufficient conditions for existence of the limit architecture. Furthermore, we derive the scaling law of foundation models by leveraging tools of Lipschitz operator and covering number. Theoretical results show that: 1) emergent intelligence is governed by three key factors-training steps, data size and the model architecture, where the properties of basic blocks play a crucial role in constructing foundation models; 2) the critical condition Lip(T)=1 for emergent intelligence provides theoretical support for existing findings. 3) emergent intelligence is determined by an infinite-dimensional system, yet can be effectively realized in practice through a finite-dimensional architecture. Our empirical results corroborate these theoretical findings.

The First Challenge on Remote Sensing Infrared Image Super-Resolution at NTIRE 2026: Benchmark Results and Method Overview

This paper presents the NTIRE 2026 Remote Sensing Infrared Image Super-Resolution (x4) Challenge, one of the associated challenges of NTIRE 2026. The challenge aims to recover high-resolution (HR) infrared images from low-resolution (LR) inputs generated through bicubic downsampling with a x4 scaling factor. The objective is to develop effective models or solutions that achieve state-of-the-art performance for infrared image SR in remote sensing scenarios. To reflect the characteristics of infrared data and practical application needs, the challenge adopts a single-track setting. A total of 115 participants registered for the competition, with 13 teams submitting valid entries. This report summarizes the challenge design, dataset, evaluation protocol, main results, and the representative methods of each team. The challenge serves as a benchmark to advance research in infrared image super-resolution and promote the development of effective solutions for real-world remote sensing applications.

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

Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Framework

Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

Neural Uncertainty Principle: A Unified View of Adversarial Fragility and LLM Hallucination

Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems, each addressed with modality-specific patches. This study first reveals that they share a common geometric origin: the input and its loss gradient are conjugate observables subject to an irreducible uncertainty bound. Formalizing a Neural Uncertainty Principle (NUP) under a loss-induced state, we find that in near-bound regimes, further compression must be accompanied by increased sensitivity dispersion (adversarial fragility), while weak prompt-gradient coupling leaves generation under-constrained (hallucination). Crucially, this bound is modulated by an input-gradient correlation channel, captured by a specifically designed single-backward probe. In vision, masking highly coupled components improves robustness without costly adversarial training; in language, the same prefill-stage probe detects hallucination risk before generating any answer tokens. NUP thus turns two seemingly separate failure taxonomies into a shared uncertainty-budget view and provides a principled lens for reliability analysis. Guided by this NUP theory, we propose ConjMask (masking high-contribution input components) and LogitReg (logit-side regularization) to improve robustness without adversarial training, and use the probe as a decoding-free risk signal for LLMs, enabling hallucination detection and prompt selection. NUP thus provides a unified, practical framework for diagnosing and mitigating boundary anomalies across perception and generation tasks.

Layout-Guided Controllable Pathology Image Generation with In-Context Diffusion Transformers

Controllable pathology image synthesis requires reliable regulation of spatial layout, tissue morphology, and semantic detail. However, existing text-guided diffusion models offer only coarse global control and lack the ability to enforce fine-grained structural constraints. Progress is further limited by the absence of large datasets that pair patch-level spatial layouts with detailed diagnostic descriptions, since generating such annotations for gigapixel whole-slide images is prohibitively time-consuming for human experts. To overcome these challenges, we first develop a scalable multi-agent LVLM annotation framework that integrates image description, diagnostic step extraction, and automatic quality judgment into a coordinated pipeline, and we evaluate the reliability of the system through a human verification process. This framework enables efficient construction of fine-grained and clinically aligned supervision at scale. Building on the curated data, we propose In-Context Diffusion Transformer (IC-DiT), a layout-aware generative model that incorporates spatial layouts, textual descriptions, and visual embeddings into a unified diffusion transformer. Through hierarchical multimodal attention, IC-DiT maintains global semantic coherence while accurately preserving structural and morphological details. Extensive experiments on five histopathology datasets show that IC-DiT achieves higher fidelity, stronger spatial controllability, and better diagnostic consistency than existing methods. In addition, the generated images serve as effective data augmentation resources for downstream tasks such as cancer classification and survival analysis.

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.