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.

TenExp: Mixture-of-Experts-Based Tensor Decomposition Structure Search Framework

Recently, tensor decompositions continue to emerge and receive increasing attention. Selecting a suitable tensor decomposition to exactly capture the low-rank structures behind the data is at the heart of the tensor decomposition field, which remains a challenging and relatively under-explored problem. Current tensor decomposition structure search methods are still confined by a fixed factor-interaction family (e.g., tensor contraction) and cannot deliver the mixture of decompositions. To address this problem, we elaborately design a mixture-of-experts-based tensor decomposition structure search framework (termed as TenExp), which allows us to dynamically select and activate suitable tensor decompositions in an unsupervised fashion. This framework enjoys two unique advantages over the state-of-the-art tensor decomposition structure search methods. Firstly, TenExp can provide a suitable single decomposition beyond a fixed factor-interaction family. Secondly, TenExp can deliver a suitable mixture of decompositions beyond a single decomposition. Theoretically, we also provide the approximation error bound of TenExp, which reveals the approximation capability of TenExp. Extensive experiments on both synthetic and realistic datasets demonstrate the superiority of the proposed TenExp compared to the state-of-the-art tensor decomposition-based methods.

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.

Enhancing Underwater Light Field Images via Global Geometry-aware Diffusion Process

This work studies the challenging problem of acquiring high-quality underwater images via 4-D light field (LF) imaging. To this end, we propose GeoDiff-LF, a novel diffusion-based framework built upon SD-Turbo to enhance underwater 4-D LF imaging by leveraging its spatial-angular structure. GeoDiff-LF consists of three key adaptations: (1) a modified U-Net architecture with convolutional and attention adapters to model geometric cues, (2) a geometry-guided loss function using tensor decomposition and progressive weighting to regularize global structure, and (3) an optimized sampling strategy with noise prediction to improve efficiency. By integrating diffusion priors and LF geometry, GeoDiff-LF effectively mitigates color distortion in underwater scenes. Extensive experiments demonstrate that our framework outperforms existing methods across both visual fidelity and quantitative performance, advancing the state-of-the-art in enhancing underwater imaging. The code will be publicly available at https://github.com/linlos1234/GeoDiff-LF.

SegEarth-R2: Towards Comprehensive Language-guided Segmentation for Remote Sensing Images

Effectively grounding complex language to pixels in remote sensing (RS) images is a critical challenge for applications like disaster response and environmental monitoring. Current models can parse simple, single-target commands but fail when presented with complex geospatial scenarios, e.g., segmenting objects at various granularities, executing multi-target instructions, and interpreting implicit user intent. To drive progress against these failures, we present LaSeRS, the first large-scale dataset built for comprehensive training and evaluation across four critical dimensions of language-guided segmentation: hierarchical granularity, target multiplicity, reasoning requirements, and linguistic variability. By capturing these dimensions, LaSeRS moves beyond simple commands, providing a benchmark for complex geospatial reasoning. This addresses a critical gap: existing datasets oversimplify, leading to sensitivity-prone real-world models. We also propose SegEarth-R2, an MLLM architecture designed for comprehensive language-guided segmentation in RS, which directly confronts these challenges. The model's effectiveness stems from two key improvements: (1) a spatial attention supervision mechanism specifically handles the localization of small objects and their components, and (2) a flexible and efficient segmentation query mechanism that handles both single-target and multi-target scenarios. Experimental results demonstrate that our SegEarth-R2 achieves outstanding performance on LaSeRS and other benchmarks, establishing a powerful baseline for the next generation of geospatial segmentation. All data and code will be released at https://github.com/earth-insights/SegEarth-R2.

Phase-space entropy at acquisition reflects downstream learnability

Modern learning systems work with data that vary widely across domains, but they all ultimately depend on how much structure is already present in the measurements before any model is trained. This raises a basic question: is there a general, modality-agnostic way to quantify how acquisition itself preserves or destroys the information that downstream learners could use? Here we propose an acquisition-level scalar $ΔS_{\mathcal B}$ based on instrument-resolved phase space. Unlike pixelwise distortion or purely spectral errors that often saturate under aggressive undersampling, $ΔS_{\mathcal B}$ directly quantifies how acquisition mixes or removes joint space--frequency structure at the instrument scale. We show theoretically that \(ΔS_{\mathcal B}\) correctly identifies the phase-space coherence of periodic sampling as the physical source of aliasing, recovering classical sampling-theorem consequences. Empirically, across masked image classification, accelerated MRI, and massive MIMO (including over-the-air measurements), $|ΔS_{\mathcal B}|$ consistently ranks sampling geometries and predicts downstream reconstruction/recognition difficulty \emph{without training}. In particular, minimizing $|ΔS_{\mathcal B}|$ enables zero-training selection of variable-density MRI mask parameters that matches designs tuned by conventional pre-reconstruction criteria. These results suggest that phase-space entropy at acquisition reflects downstream learnability, enabling pre-training selection of candidate sampling policies and as a shared notion of information preservation across modalities.