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Deyu Meng

Publications and source records attributed to Deyu Meng.

At least 37 records · Page 2Linked to original sources
arXiv2026

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.

cs.LG↗
arXiv2026

Consistency of Variational Inference for Nonlinear Inverse Problems of Partial Differential Equations

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference transforms the inference problem into an optimization problem by introducing variational sets. Based on a modified ``prior mass and testing'' framework, we propose general conditions for three categories of inverse problems: mildly ill-posed, severely ill-posed, and those with unknown model parameters. Concentrating on the variational sets comprising the restricted Gaussian or widely utilized Gaussian mean-field families, we demonstrate that for all three categories, the convergence rate can be decomposed into a true distribution term and a variational approximation term. Moreover, we illustrate that the true distribution term dominates the convergence rates, thereby substantiating the effectiveness of the variational inference method for inverse problems of PDEs. As specific examples, we examine a collection of non-linear inverse problems, including the Darcy flow problem, the inverse potential problem for a subdiffusion equation, and the inverse medium scattering problem. Besides, we show that our convergence rates are minimax optimal for these inverse problems.

math.ST↗
arXiv2026

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.

cs.CV↗
arXiv2026

A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle

Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-$K$ activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model.

cs.CV↗
arXiv2026

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.

physics.geo-ph↗
arXiv2026

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.

cs.CV↗
arXiv2026

Practical exposure correction via compensation

In computer vision, correcting the exposure level is a fundamental task for enhancing the visual quality of observations with inappropriate lightness. However, existing methodologies tend to be impractical because they lack adaptability to unknown scenes due to restricted modeling patterns and struggle to achieve satisfactory efficiency due to complex computational flows. To tackle these challenges, we establish a new practical exposure corrector (PEC) that excels in both quality and efficiency. Specifically, to overcome the limited expressive power of existing modeling patterns, we build a general model with exposure-sensitive compensation to provide an intuitive modeling perspective. We also design a simple but effective exposure adversarial function to catalyze scene-adaptive compensation. Building on the aforementioned key concepts, we develop a stable and robust iterative shrinkage scheme, avoiding the complex inferences encountered in existing studies. Extensive experimental evaluations across eight challenging datasets showcase the strong adaptability of the developed model to unknown environments. The model offers impressive processing speed, requiring only 0.0009 s to handle a 2K image on a device equipped with a GeForce RTX 2080Ti GPU. Experimental analysis of different downstream vision tasks further verifies the flexibility of the model. The code is available at https://rsliu.tech/PEC.

cs.CV↗
arXiv2026

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.

cs.CV↗
arXiv2026

SegEarth-OV3: Exploring SAM 3 for Open-Vocabulary Semantic Segmentation in Remote Sensing Images

Most existing methods for training-free open-vocabulary semantic segmentation are based on CLIP. While these approaches have made progress, they often face challenges in precise localization or require complex pipelines to combine separate modules, especially in remote sensing scenarios where numerous dense and small targets are present. Recently, Segment Anything Model 3 (SAM 3) was proposed, unifying segmentation and recognition in a promptable framework. In this paper, we present a comprehensive exploration of applying SAM 3 to the remote sensing open-vocabulary tasks (i.e., 2D semantic segmentation, change detection, and 3D semantic segmentation) without any training. First, we implement a mask fusion strategy that combines the outputs from SAM 3's semantic segmentation head and the Transformer decoder (instance head). This allows us to leverage the strengths of both heads for better land coverage. Second, we utilize the presence score from the presence head to filter out categories that do not exist in the scene, reducing false positives caused by the vast vocabulary sizes and patch-level processing in geospatial scenes. Furthermore, we extend our method to open-vocabulary change detection by a joint instance- and pixel-level verification strategy built directly upon our fused logits. We evaluate our method on extensive remote sensing datasets and tasks, including 20 segmentation datasets, 3 change detection datasets, and a 3D segmentation dataset. Experiments show that our method achieves promising performance, demonstrating the potential of SAM 3 for remote sensing open-vocabulary tasks. Our code is released at https://github.com/earth-insights/SegEarth-OV-3.

cs.CV↗
arXiv2026

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

cs.CV↗
arXiv2026

A Data-driven Loss Weighting Scheme across Heterogeneous Tasks for Image Denoising

In a variational denoising model, weight in the data fidelity term plays the role of enhancing the noise-removal capability. It is profoundly correlated with noise information, while also balancing the data fidelity and regularization terms. However, the difficulty of assigning weight is expected to be substantial when the noise pattern is beyond independent identical Gaussian distribution, e.g., impulse noise, stripe noise, or a mixture of several patterns, etc. Furthermore, how to leverage weight to balance the data fidelity and regularization terms is even less evident. In this work, we propose a data-driven loss weighting (DLW) scheme to address these issues. Specifically, DLW trains a parameterized weight function (i.e., a neural network) that maps the noisy image to the weight. The training is achieved by a bilevel optimization framework, where the lower level problem is solving several denoising models with the same weight predicted by the weight function and the upper level problem minimizes the distance between the restored image and the clean image. In this way, information from both the noise and the regularization can be efficiently extracted to determine the weight function. DLW also facilitates the easy implementation of a trained weight function on denoising models. Numerical results verify the remarkable performance of DLW on improving the ability of various variational denoising models to handle different complex noise. This implies that DLW has the ability to transfer the noise knowledge at the model level to heterogeneous tasks beyond the training ones and the generalization theory underlying DLW is studied, validating its intrinsic transferability.

eess.IV↗
arXiv2026

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 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, mid-level semantic segmentation, and low-level image super-resolution -- demonstrate that EQ-VMamba consistently improves rotation robustness and 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.

cs.CV↗
arXiv2026

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.

cs.LG↗
arXiv2026

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.

cs.LG↗
arXiv2026

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.

cs.CV↗
arXiv2026

Neural Approximation and Its Applications

Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation ability and data adaptation ability, resulting in unsatisfactory performance. To address these challenges, we introduce the neural basis function by leveraging an untrained neural network as the basis function. Equipped with the proposed neural basis function, we suggest the neural approximation (NeuApprox) paradigm for multivariate function approximation. Specifically, the underlying multivariate function behind the multi-dimensional data is decomposed into a sum of block terms. The clear physically-interpreted block term is the product of expressive neural basis functions and their corresponding learnable coefficients, which allows us to faithfully capture distinct components of the underlying data and also flexibly adapt to new data by readily fine-tuning the neural basis functions. Attributed to the elaborately designed block terms, the suggested NeuApprox enjoys strong approximation ability and flexible data adaptation ability over the hand-crafted basis function-based methods. We also theoretically prove that NeuApprox can approximate any multivariate continuous function to arbitrary accuracy. Extensive experiments on diverse multi-dimensional datasets (including multispectral images, light field data, videos, traffic data, and point cloud data) demonstrate the promising performance of NeuApprox in terms of both approximation capability and adaptability.

cs.LG↗
arXiv2026

IV-tuning: Parameter-Efficient Transfer Learning for Infrared-Visible Tasks

Existing infrared and visible (IR-VIS) methods inherit the general representations of Pre-trained Visual Models (PVMs) to facilitate complementary learning. However, our analysis indicates that under the full fine-tuning paradigm, the feature space becomes highly constrained and low-ranked, which has been proven to seriously impair generalization. One remedy is to freeze the parameters, which preserves pretrained knowledge and helps maintain feature diversity. To this end, we propose IV-tuning, to parameter-efficiently harness PVMs for various IR-VIS downstream tasks, including salient object detection, semantic segmentation, and object detection. Extensive experiments across various settings demonstrate that IV-tuning outperforms previous state-of-the-art methods, and exhibits superior generalization and scalability. Remarkably, with only a single backbone, IV-tuning effectively facilitates the complementary learning of infrared and visible modalities with merely 3% trainable backbone parameters, and achieves superior computational efficiency compared to conventional IR-VIS paradigms.

cs.CV↗
arXiv2026

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.

cs.LG↗