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Boya Shi, Thomas N Guan, Yi Xiaodong

Existing dynamic scene rendering methods often struggle to preserve sharp edges and maintain temporal consistency. To address these challenges, we introduce Edge 4D Gaussian Splatting (Edge4DGS), a real-time rendering framework that renders fine-grained geometry from sparse monocular inputs in dynamic scenes. Edge4DGS proposes a hybrid geometric representation that augments Gaussian primitives with convex hulls, enabling accurate modeling of hard surfaces and complex boundaries. To enhance spatial precision, we introduce edge consistency regularization leveraging optical flow, guiding Gaussian distributions to align with true object contours. To enforce temporal coherence, we extend the regularization from discrete time steps to continuous unit intervals, enabling accurate motion modeling and reducing flickering artifacts. A two-stage coarse-to-fine optimization further improves geometric fidelity while preserving computational efficiency. Extensive experiments on monocular and multi-view motion datasets demonstrate that Edge4DGS achieves real-time, high-resolution rendering and consistently surpasses state-of-the-art methods, reducing LPIPS by 56.25%.

Duy-Tho Le, Trung Pham, Jianfei Cai, Hamid Rezatofighi

Optimizing the similarity between parametric shapes is crucial for numerous computer vision tasks, where Intersection over Union (IoU) stands as the canonical measure. However, existing optimization methods exhibit significant shortcomings: regression-based losses like L1/L2 lack correlation with IoU, IoU-based losses are unstable and limited to simple shapes, and task-specific methods are computationally intensive and not generalizable across domains. As a result, the current landscape of parametric shape objective functions has become scattered, with each domain proposing distinct IoU approximations. To address this, we unify the parametric shape optimization objective functions by introducing Marginalized Generalized IoU (MGIoU), a novel loss function that overcomes these challenges by projecting structured convex shapes onto their unique shape Normals to compute one-dimensional normalized GIoU. MGIoU offers a simple, efficient, fully differentiable approximation strongly correlated with IoU. We extend MGIoU to MGIoU+ that supports optimizing unstructured convex shapes. Together, MGIoU and MGIoU+ unify parametric shape optimization across diverse applications. Experiments on standard benchmarks demonstrate that MGIoU and MGIoU+ demonstrate higher performance while reducing loss computation latency up to 10-40x. Also, MGIoU and MGIoU+ satisfy metric properties and scale-invariance, ensuring robustness as an objective function. We further propose MGIoU- for minimizing overlaps in tasks like collision-free trajectory prediction.

Shuxin Zhuang, Linjian Meng, Shuxin Li, Minming Li, Youzhi Zhang

Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors that limit the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

Zhuwei Wen, Zimin Xia, He Chen, Linwei Yue, Xianwei Zheng

In remote sensing pansharpening, spectrally mixed regions, where the spectral interactions among adjacent land covers lead to highly inconsistent reconstruction patterns, remain the most challenging areas. Due to the complex spatial distribution and heterogeneous spectral characteristics of ground objects, existing methods relying on rigid architectures and physical constraints struggle to learn generalized reconstruction patterns from limited spectral mixing samples, resulting in unstable generalization. To address this limitation, we propose an architecture-agnostic regularization-guided mechanism that adaptively directs the model to focus on learning reliable reconstruction priors for challenging regions. Specifically, we introduce a simple data-level transformation, MixShuffle, which performs random convex combinations across spatial positions and spectral channels to generate training data with richer spatial structures and stronger spectral mixing. In parallel, we propose a hierarchical attention weighting mechanism, a loss-level gradient reallocation strategy at the sample, channel, and pixel levels, enabling the model to emphasize structurally complex regions. Extensive experiments on multiple benchmark datasets (WV3, GF2, QB) and across various network architectures demonstrate the strong generality and effectiveness of the proposed strategies, achieving state-of-the-art performance when integrated into DANet. Our code is available at https://github.com/Geo-Tell/DANet.

Zhan Wang, Leiquan Wang, Chunlei Wu, Yu Meng

Image denoising is a fundamental task in computer vision aimed at recovering clean images from noise-corrupted observations. While supervised deep learning methods achieve remarkable performance when trained on paired data with known noise levels, their real-world applicability is limited as noise characteristics are often unknown. Existing unsupervised techniques, such as blind-spot networks or methods based on statistical estimation, either compromise performance due to information loss or suffer from inaccuracies in noise level estimation. To address these challenges, we propose a novel two-stage self-supervised denoising framework that first accurately estimates the noise level directly from noisy images, without requiring clean references or prior noise knowledge. Building upon theoretical insights from Noisier2Noise, we rigorously derive a relationship between the noise level and the variance of the denoised image, enabling robust estimation via a deep learning model and a ternary search strategy. The estimated noise level is then used to synthesize training pairs for supervised denoising. Experiments demonstrate that our method outperforms existing unsupervised approaches and traditional noise estimation techniques, achieving performance competitive with--and in some cases surpassing--supervised methods trained with known noise levels. The proposed framework effectively overcomes the training data pair limitations of supervised approaches for unknown additive white Gaussian noise. Our code is available at https://github.com/zhanzhanblue/CANC.

Shengzhe Chen, Hao Yan

Convexity is a fundamental geometric prior that underlies many natural and man-made structures, yet remains challenging to impose effectively in end-to-end trainable segmentation networks. We revisit convexity from a functional perspective and propose a unified, threshold-free convexity prior based on the quasi-concavity of the network's output mask function u. Instead of constraining a single binary segmentation, we require all super-level sets of u to be convex, transforming global shape constraints into local, differentiable inequalities on u and its derivatives. From this principle, we derive zero, first, and second-order characterizations, yielding respectively a local midpoint convexification algorithm, a gradient-based condition linked to supporting hyperplanes, and a sufficient second-order inequality expressed as a quadratic form on the tangent plane. The first and second-order formulations produce a compact convolutional loss that can be densely applied across the image without thresholding. Our quasi-concavity losses integrate seamlessly with modern segmentation networks via the proposed convex gradient projection module (CGPM). They consistently enforce convexity and improve shape regularity across multiple datasets, outperforming networks tailored for retinal segmentation and surpassing previous shape-aware methods. Remarkably, our analysis unifies a wide spectrum of previous convex shape models, from discrete 1-0-1 line constraints and graph-cuts convexity formulations to curvature or signed distance Laplacian based level-set priors, within a single continuous and differentiable framework.

Jiale Wu, Xiaoyang Bai, Zongqi He, Weiwei Xu, Yifan Peng

Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated great success in modeling reflective 3D objects and their interaction with the environment via deferred rendering (DR). However, existing methods often struggle with correctly reconstructing physical attributes such as albedo and reflectance, and therefore they do not support high-fidelity relighting. Observing that this limitation stems from the lack of shape and material information in RGB images, we present PhyGaP, a physically-grounded 3DGS method that leverages polarization cues to facilitate precise reflection decomposition and visually consistent relighting of reconstructed objects. Specifically, we design a polarimetric deferred rendering (PolarDR) process to model polarization by reflection, and a self-occlusion-aware environment map building technique (GridMap) to resolve indirect lighting of non-convex objects. We validate on multiple synthetic and real-world scenes, including those featuring only partial polarization cues, that PhyGaP not only excels in reconstructing the appearance and surface normal of reflective 3D objects ( 2 dB in PSNR and 45.7% in Cosine Distance better than existing RGB-based methods on average), but also achieves state-of-the-art inverse rendering and relighting capability.

Yan-Ting Chen, Hao-Wei Chen, Tsu-Ching Hsiao, Chun-Yi Lee

Accurate camera viewpoint estimation under sparse-view conditions remains challenging, particularly in two-view scenarios. Recent approaches leverage diffusion models such as Zero123 to synthesize novel views conditioned on relative viewpoint, showing promising results when repurposed for viewpoint estimation via optimization with MSE loss. However, existing methods often suffer from non-convex loss landscape with numerous local minima, making them sensitive to initialization and reliant on naive multi-start strategies. We analyze these optimization challenges and visualize failure cases, showing that geometric ambiguities, such as symmetry and self-similarity, can mislead gradient-based updates toward incorrect viewpoints. To address these limitations, we propose a score-based method that reshapes the optimization landscape to guide updates toward the ground-truth viewpoint, followed by a refinement stage using a viewpoint-conditioned diffusion model. Experiments show that our method improves convergence, reduces reliance on brute-force sampling, and achieves competitive accuracy with higher sample-efficiency.

Jakob Paul Zimmermann, Georg Loho

It has been demonstrated in various contexts that monotonicity leads to better explainability in neural networks. However, not every function can be well approximated by a monotone neural network.We demonstrate that monotonicity can still be used in two ways to boost explainability. First, we use an adaptation of the decomposition of a trained ReLU network into two monotone and convex parts, thereby overcoming numerical obstacles from an inherent blowup of the weights in this procedure. Our proposed saliency methods -- SplitCAM and SplitLRP --improve onstate of the art results on both VGG16 and Resnet18 networks on ImageNet-S across all Quantus saliency metric categories.Second, we exhibit that training a model as the difference between two monotone neural networks results in a system with strong self-explainability properties.

Wenjie Hou, Tianxiang Chen, Feng Wang, Tiantong Wu, Zhiming Zheng, Shaoting Tang, Wei Yang Bryan Lim

Federated learning (FL) has emerged as a widely adopted training paradigm for privacy-preserving machine learning. Despite the past success of SGD-based methods, they still suffer from severe data heterogeneity and the lack of adaptivity in practical applications. While several adaptive federated optimization methods (such as FedAdam) have been proposed and demonstrated to achieve faster convergence, they fail to show significant improvements in generalization performance under highly heterogeneous data distributions, and their optimization and generalization mechanisms remain insufficiently understood. To fill this gap, we introduce diffusion theory into the adaptive federated optimization framework and analyze the distinct effects of adaptive learning rate and global momentum from the perspectives of saddle-point escaping and flat-minima selection. Theoretical results show that although FedAdam outperforms FedAvg/FedAvgM in escaping saddle points, the latter escapes sharp minima more efficiently. The root cause lies in that adaptive learning rates, while enhancing saddle-point escape, weaken the preference for flat minima. Motivated by these insights, we propose FedAdamom, a new adaptive federated optimization algorithm that adapts the momentum hyperparameter rather than the learning rate. FedAdamom maintains strong saddle-point escaping capability while enhancing flat-minima selection. We further establish its convergence guarantees under non-convex objectives. Extensive experiments demonstrate that FedAdamom significantly outperforms existing adaptive federated optimization methods in terms of convergence speed, generalization performance, and preference for flat minima.

Jiaying Ying, Heming Du, Kaihao Zhang, Sean M. Tweedy, Xin Yu

Single-image human mesh recovery provides a compact 3D, person-centric representation that supports analysis, animation, AR and VR, rehabilitation, and human-computer interaction. However, prevailing systems impose an intact-limb prior and degrade on people with limb loss, because fixed-topology models cannot represent residual limbs. In this work, we present ResiHMR, a residual-limb aware framework for single-image 3D human modeling. ResiHMR adopts residual-limb keypoints and introduces two components: (i) a topology-adaptive Residual Anchor-Factor Optimization module that constrains estimation to the observed kinematic subgraph of anatomically valid structures, and (ii) a geometry-based Residual-Limb Reconstruction module that estimates residual-limb boundaries and convex limb-termination geometry. Together, these modules introduce topology-aware optimization and explicit termination geometry as tools for human mesh recovery under non-standard limb anatomy. Unlike joint-removal methods in a fixed topology, ResiHMR explicitly reconstructs residual-limb surfaces and aligns optimization with limb-loss topology, which better matches prosthetic biomechanics and real-world use. To the best of our knowledge, this is the first single-image HMR system that explicitly reconstructs residual-limb surfaces and performs topology-adaptive optimization for individuals with limb loss. On a curated dataset of real-world images with limb loss, ResiHMR improves reconstruction quality under both SMPLify-X and HSMR backbones, reducing intact-joint 2D MPJPE from 41.32 to 37.40 with SMPLify-X and residual-limb 2D MPJPE from 73.61 to 23.19 with HSMR.

Yuezhi Yang, Qixing Huang, Mikaela Angelina Uy, Nicholas Sharp

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world learning of convex decomposition. Our method produces high-quality decompositions of 3D shapes into a union of convex bodies, which are essential to accelerate collision detection in physical simulation, amongst many other applications.The key insight is to adopt a feature learning approach and learn a continuous feature field that can later be clustered to yield a good convex decomposition via our self-supervised, purely-geometric objective derived from the classical definition of convexity.Our formulation can be used for single shape optimization, but more importantly, feature prediction unlocks scalable, self-supervised learning on large datasets resulting in the first learned open-world for convex decomposition.Experiments show that our decompositions are higher-quality than alternatives and generalize across open-world objects as well as across representations to meshes, CAD models, and even Gaussian splats.

Shihao Zou, Wei Wei

Dynamic multimodal fusion methods lack robust theoretical guidance for handling modal conflicts and inconsistent data quality. While recent theoretical work has associated modal weights with scalar quantities such as loss or confidence, this paradigm struggles to comprehensively address the risks caused by inconsistent predictive distributions across modalities. In this paper, we propose a **Co**nflict-driven **Ri**sk **M**inimization (**CoRiM**) dynamic fusion paradigm. Specifically, we redefine dynamic fusion as a principled, per-sample, direct risk minimization task. To this end, we first design a novel, differentiable Modality Conflict Risk (MCR) function, \mathcal R (w), which quantifies risk by directly modeling fused uncertainty and inter-modal consistency. Second, we identify that minimizing \mathcal R (w) is fundamentally a non-convex constrained optimization problem over the probabilistic simplex. To efficiently solve this specific challenge, we innovatively introduce the projection free Frank-Wolfe (FW) algorithm, as it is perfectly suited for optimization on the simplex.We prove that our designed \mathcal R (w) possesses L-smoothness, which provides theoretical guarantees for the convergence of the FW algorithm on our non-convex objective. Extensive experiments on multiple benchmark datasets demonstrate that CoRiM outperforms current state-of-the-art methods in high-conflict and noisy environments, validating the robustness of our method.

Hithem Lamri, Michail Maniatakos

Machine unlearning (MU) seeks to remove the influence of specified data from a trained model in response to privacy requests or data poisoning. While certified unlearning has been analyzed in centralized and server-orchestrated federated settings (via guarantees analogous to differential privacy, DP), the decentralized setting--where peers communicate without a coordinator--remains underexplored. We study certified unlearning in decentralized networks with fixed topologies and propose \methodname, a random-walk procedure that performs one projected gradient ascent step on the forget set at the unlearning client and a geometrically distributed number of projected descent steps on the retained data elsewhere, combined with subsampled Gaussian noise and projection onto a trust region around the original model. We provide (i) convergence guarantees in the convex case and stationarity guarantees in the nonconvex case, (ii) (\varepsilon,\delta) network-unlearning certificates on client views via subsampled Gaussian Renyi DP (RDP) with segment-level subsampling, and (iii) deletion-capacity bounds that scale with the forget-to-local data ratio and quantify the effect of decentralization (network mixing and randomized subsampling) on the privacy-utility trade-off. Empirically, on image benchmarks, \methodname matches a given (\varepsilon,\delta) while achieving higher test accuracy than decentralized DP baselines and reducing backdoor accuracy (ASR) to the random-guessing baseline ((~ 10%)).

Jungwook Seo, Minjeong Kim, Younkwan Lee, Seungho Shin, Sungyong Baik

Detecting subtle visual anomalies in images remains challenging, particularly when only normal samples are available a priori. Such unsupervised anomaly detection is typically solved by measuring feature similarity of a query patch to a memory of normal patches. However, similarity alone does not reveal how strongly a query patch violates the structure of the normal feature manifold. We propose a training-free Laplacian graph energy optimization formulation, named ANoCo that scores Anomaly by the cost of Non-Conformity of a query patch to align with a fixed normal manifold. For each query patch, we construct a bipartite query to normal graph weighted by cosine affinity, explicitly removing query-query and normal-normal edges to prevent evidence dilution. We formulate anomaly scoring as a convex Laplacian energy with anchored normal nodes, and solve in closed form. In particular, we do not use the optimized features themselves--the anomaly score is the magnitude of the update required to satisfy normality constraints, reframing the graph Laplacian as a non-conformity operator rather than a smoothing prior. The proposed method introduces no learnable parameters, message passing, or sampling, and has complexity comparable to a single linear solve. Across standard benchmarks, it delivers strong image-level AUROC, stable localization maps, and improved robustness over prior methods, demonstrating the effectiveness of using optimization-induced feature drift as anomaly measure.

Haoru Tan, Wang Wang, Sitong Wu, Xiuzhe Wu, Yang-Tian Sun, Chirui Chang, Shaofeng Zhang, Xiaojuan Qi

We revisit dataset distillation from an outcome-centric perspective. Rather than aligning process surrogates (per-step gradients or training trajectories), Influence Matching (Inf-Match) aligns the final outcome of training: it learns a compact synthetic set whose effect on the converged parameters matches that of the full dataset. Concretely, we introduce a fully differentiable, sample-level influence estimator that quantifies parameter shifts from adding or removing data, without time-consuming inverse-Hessian products or convexity assumptions. The estimator runs in linear time by unrolling the optimization dynamics and applying a first-order Taylor approximation. We then learn the synthetic set by minimizing the mismatch between its influence and that of the real dataset, yielding outcome alignment rather than heuristic process imitation. Inf-Match delivers the best accuracy across standard classification benchmarks. For instance, on Tiny-ImageNet (IPC=10), Inf-Match attains 31.5%, a +4.7% improvement over NCFM. Beyond classification, Inf-Match scales to vision-language distillation on Flickr30K, outperforming strong process-matching baselines. For instance, with 200 to 1000 synthetic samples, our method achieved a leading impressive average on image/text retrieval tasks, higher than NCFM by 2.5%. The code will be released via https://github.com/hrtan/infmatch.

Agniva Sengupta, Dilara Kus, Jianning Li, Stefan Zachow

We solve the problem of determining the pose of known shapes in \mathbb R ^3 from their unoccluded silhouettes. The pose is determined up to global optimality using a simple yet under-explored property of the area-of-silhouette: its continuity w.r.t trajectories in the rotation space. The proposed method utilises pre-computed silhouette-signatures, modelled as a response surface of the area-of-silhouettes. Querying this silhouette-signature response surface for pose estimation leads to a strong branching of the rotation search space, making resolution-guided candidate search feasible. Additionally, we utilise the aspect ratio of 2D ellipses fitted to projected silhouettes as an auxiliary global shape signature to accelerate the pose search. This combined strategy forms the first method to efficiently estimate globally optimal pose from just the silhouettes, without being guided by correspondences, for any shape, irrespective of its convexity and genus. We validate our method on synthetic and real examples, demonstrating significantly improved accuracy against comparable approaches.

Jun Li, Lizhi Xiong, Ziqiang Li, Weiwei Jiang, Zhangjie Fu, Yong Li, Guo-Sen Xie

Text-to-image generative models have achieved impressive fidelity and diversity, but can inadvertently produce unsafe or undesirable content due to implicit biases embedded in large-scale training datasets.Existing concept erasure methods, whether text-only or image-assisted, face trade-offs: textual approaches often fail to fully suppress concepts, while naive image-guided methods risk over-erasing unrelated content. We propose TICoE, a Text-Image Collaborative Erasing framework that achieves precise and faithful concept removal through a continuous convex concept manifold and hierarchical visual representation learning. TICoE precisely removes target concepts while preserving unrelated semantic and visual content. To objectively assess the quality of erasure, we further introduce a fidelity-oriented evaluation strategy that measures post-erasure usability. Experiments on multiple benchmarks show that TICoE surpasses prior methods in concept removal precision and content fidelity, enabling safer, more controllable text-to-image generation.

Lu Xu, Guosheng Yin

Fully decentralized deep learning removes global servers and ensures local data privacy. However, Euclidean consensus, averaging weights, gradients or momentum, may degrade under the situations with non-i.i.d. (non-independent and identically distributed) data and client size imbalance. We propose a geometry-aware approach based on natural gradient variational inference. Clients communicate in the expectation parameter space of an exponential family, where simple linear mixing yields a forward Kullback--Leibler (KL) barycenter consensus. The aggregate is the model closest to all client distributions, aligning updates across heterogeneous sites and mitigating distribution shift. We further provide a lightweight decentralized Adam implementation where each client maintains a diagonal Gaussian posterior and operates entirely in the expectation space for both optimization and consensus. We prove convergence for convex losses on connected graphs. On CIFAR-100 and a medical image segmentation benchmark, our method substantially outperforms Euclidean-space consensus baselines under severe non-i.i.d. and client-imbalance cases, achieving around 20% accuracy gain on CIFAR-100, while matching the communication budget and improving training stability. The code is available at https://github.com/x-lu/Beyond-euclidean-gossip.

Tianyu Pang, Yujie Fang, Zihang Liu, Shenyang Deng, Lei Hsiung, Shuhua Yu, Yaoqing Yang

Muon has recently shown promising results in LLM training. In this work, we study how to further improve Muon. We argue that Muon’s orthogonalized update rule suppresses the emergence of heavy-tailed weight spectra and over-emphasizes the training along noise-dominated directions. Motivated by the Heavy-Tailed Self-Regularization (HT-SR) theory, we propose HTMuon. HTMuon preserves Muon’s ability to capture parameter interdependencies while producing heavier-tailed updates and inducing heavier-tailed weight spectra. Experiments on LLM pretraining and image classification show that HTMuon consistently improves performance over state-of-the-art baselines and can also serve as a plug-in on top of existing Muon variants. For example, on LLaMA pretraining on the C4 dataset, HTMuon reduces perplexity by up to 0.98 compared to Muon. We further theoretically show that HTMuon corresponds to steepest descent under the Schatten-q norm constraint and provide convergence analysis in smooth non-convex settings. The implementation of HTMuon is available at https://github.com/TDCSZ327/HTmuon.