Regularization
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Multi-Objective Agent-Based Model Predictive Controller for Plug-and-Play Vehicle Control
2026-09-10 18:35:08Jiaming Zhong, Ladan Khoshnevisan, Shucheng Huang, Mohammad Pirani, Yash Vardhan Pant, Amir KhajepourAbstract
Functional integration is a growing trend in vehicle control, often involving the coordination of multiple controllers to achieve various objectives simultaneously. The need for flexibility and reliability has led to a "plug-and-play" approach in control system design, which presents challenges for traditional integrated model predictive control (MPC). Agent-based model predictive control (AMPC) has recently emerged as a distributed solution that treats controllers as agents, creating a collaborative framework among them to reach a common goal. However, this approach struggles to manage distributed conflicting objectives when agents are coupled or interdependent. To address this, we propose a novel, practical distributed control scheme called multi-objective AMPC, which adapts the alternating direction method of multipliers (ADMM) into a general control strategy that approximates global optimization while decoupling objectives. We systematically develop three formulations that maintain convergence while addressing control regularization and inequality constraints, applying them to complex vehicle control systems for the first time. The proposed method has been tested on two vehicle control scenarios with a multi-objective topology. Different formulations are compared through simulations, and the most computationally efficient one was implemented on an electric vehicle for real-world evaluations. The results demonstrate that the proposed multi-objective AMPC can converge approximately to the same global optimum as integrated MPC with greater flexibility and the potential to reduce computational costs.
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URL
https://arxiv.org/abs/2609.12108
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Data Scarcity and Model Sparsity: Mixtures-of-Experts Overfit More to Repeated Data
2026-09-10 17:57:33Atindra Jha, Margaret Li, Jure Leskovec, Percy Liang, Luke ZettlemoyerAbstract
As the supply of human-written text is exhausted, it has become standard practice to repeat language model training data. Prior work has studied data repetition for densely activated Transformers, but the effects of data repetition remains largely unexplored for recently dominant sparse architectures such as Mixture-of-Experts (MoE), despite their increased compute efficiency. We vary data repetition rates across single- and multi-domain data mixes, and across MoE settings, including expert count and granularity. We consistently find, for models ranging from 80M to 1B active (8.5B total) parameters, that MoEs degrade more rapidly under data repetition. This effect increases with sparsity, dictated by total rather than active parameters. While 80M dense models can repeat data over 8x with minimal degradation, MoEs instead begin to suffer at 4x, and deteriorate rapidly, ceding their performance benefits in all-unique data settings to underperform dense models after 32x. We experiment with existing regularization methods as a potential remedy. We find that some methods, such as dropout, can mitigate overfitting. In particular, with strong masking-based regularization, MoEs are able to outperform dense models even when data is repeated more than 64 times. However, no method fully matches the performance of all-unique training data. Finally, we analyze internal mechanisms correlated with MoE overfitting in high repetition regimes, and find that MoE routing universally stabilizes early in training, and that expert specialization correlates with overfitting to repeated data. In sum, our work addresses the adverse interactions between sparsity and data repetition: we present evidence for the core mechanisms of overfitting and its potential remediation, and suggest promising avenues for future methods to reduce over-specialization in model parameters by disrupting memorization patterns.
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https://arxiv.org/abs/2609.11917
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On the Regularization Landscape for the Linear Recommendation Models
2026-09-10 17:45:06Dong Li, Zhenming Liu, Ruoming Jin, Hao Zhou, Zhi Liu, Jing Gao, Bin RenAbstract
Recently, a wide range of recommendation algorithms inspired by deep learning techniques have emerged as the performance leaders on several standard recommendation benchmarks. While these algorithms were built on different DL techniques (e.g., dropouts, autoencoder), they have similar performance and even similar cost functions. This paper studies whether the models' comparable performance are sheer coincidence, or they can be unified under a single framework. We find that all linear performance leaders effectively add only a nuclear-norm based regularizer, or a Frobenius-norm based regularizer. The former ones possess a (surprising) rigid structure that limits the models' predictive power but their solutions are low rank and have closed form. The latter ones are more expressive and more efficient for recommendation but their solutions are either full-rank or require executing hard-to-tune numeric procedures such as ADMM. Along this line of finding, we further propose two low-rank, closed-form solutions, derived from carefully generalizing Frobenius-norm based regularizers. The new solutions get the best of both nuclear-norm and Frobenius-norm world.
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URL
https://arxiv.org/abs/2609.11876
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Investigating catastrophic forgetting in sound event classification
2026-09-10 12:16:56Riccardo Casciotti, Annamaria MesarosAbstract
This work investigates a number of approaches to prevent catastrophic forgetting in class incremental learning scenarios for sound event classification tasks. We analyze the problem using architectural and regularization approaches, using FSD50K and AudioSet datasets. We design incremental stages and solutions that selectively protect the kernels of the network from weight updates to prevent catastrophic forgetting, and a dynamic head solution that expands itself each time a new task is learned. The findings show that catastrophic forgetting mainly happens in deeper layers, in particular in the classifier head. For the studied in-domain sound classification problem, the solution that seems to alleviate catastrophic forgetting and is the most efficient is a full freezing of the feature extractor with a fine-tuning of the dynamic head classifier, showing little to no forgetting and great training stability, and a good balance between memory-stability and learning plasticity.
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https://arxiv.org/abs/2609.11447
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Empirical Evaluation of Membership Inference Attacks on NLP Text Classifiers: A Baseline Study on SST-2
2026-09-10 00:53:20William Novak (Minot State University), Muhammad Abusaqer (Minot State University)Abstract
Membership inference attacks (MIAs) try to determine whether a specific record was used to train a model, a privacy risk that matters in natural language processing (NLP), where training data can contain sensitive user text. This paper presents a controlled benchmark of membership inference vulnerability for text classification on the GLUE SST-2 sentiment dataset. A TF-IDF + Logistic Regression pipeline and a fine-tuned DistilBERT classifier are compared under a loss-threshold MIA, with utility measured by development accuracy and macro F1. DistilBERT reached 0.9466 accuracy and 0.9460 macro F1 against 0.8756 and 0.8727 for Logistic Regression, yet both models leaked membership signal (Attack AUC 0.5615 and 0.5800, respectively). Two mitigations were tested. Stronger regularization reduced leakage for Logistic Regression at a visible utility cost, whereas fine-tuning DistilBERT for 2 epochs instead of 3 reduced leakage with negligible accuracy loss. Lightweight training adjustments can improve the privacy-utility trade-off without complex defenses.
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URL
https://arxiv.org/abs/2609.10935
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When Synthetic Data Hurts: On Catastrophic Forgetting in Skill Retrieval for LLM Agents
2026-09-09 18:48:36Syed Shariyar Murtaza, Yifan Nie, Utkarsh Soni, Eugene Wen, Arvid FrydenlundAbstract
LLM agents increasingly rely on external skills retrieved at runtime, making skill selection from large repositories a critical challenge. We present a production skill router over 34,396 skills and a large-scale study of skill retrieval using limited real supervision and synthetic data. We found that the synthetic-data fine-tuning improves in-distribution retrieval but it causes catastrophic forgetting on real and out-of-distribution (OOD) data. We evaluate several forgetting mitigation fine-tuning approaches inspired by continual learning, including embedding-anchor regularization, Learning without Forgetting (LwF), Elastic Weight Consolidation (EWC), and L2-initialization. The results show that these approaches not only retain the performance on OOD skills retrieval but also improve the retrieval on synthetic in-distribution skills by 13.98\% for 0.6B Qwen retriever and reranker. Our results provide a practical benchmark and a robust fine-tuning recipe for scarce, multi-positive supervision.
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https://arxiv.org/abs/2609.10750
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Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking
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Neural networks trained past memorization frequently undergo a delayed transition to generalization, a phenomenon known as grokking. Despite theoretical progress on \emph{why} this transition occurs, the quantitative structure of \emph{when} it occurs in hyperparameter space remains uncharacterized. We map the memorization-to-generalization boundary across 384 configurations of two-hidden-layer MLPs on modular arithmetic, fitting a power-law scaling relation for generalization onset time: $T_{\mathrm{grok}} \propto H^{-0.27}\, D^{-2.04}\, \eta^{-0.50}\, \lambda^{-0.64}$ ($R^2 = 0.732$; $0.821$ with interactions). The exponent hierarchy reveals that data complexity ($D^{-2.04}$) is the dominant driver of regime transition, not model capacity ($H^{-0.27}$): doubling data accelerates generalization by ${\sim}4\times$, while doubling width yields only ${\sim}1.2\times$. A sharp phase boundary at weight decay $\lambda \gtrsim 1.0$ separates grokking from non-grokking configurations, and weight norm trajectories show monotonic compression during the transition, consistent with implicit regularization selecting low-complexity solutions. These results provide a quantitative foundation for predicting and controlling regime transitions in overparameterized networks.
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URL
https://arxiv.org/abs/2609.10657
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Shape-guided Gaussian Splatting for Sparse-View X-ray 3D Reconstruction
2026-09-09 16:05:09Pranav Poudel, Florence Dell'Aniello Picard, Nairouz Shehata, Fr\'ed\'eric Lavoie, Herve LombaertAbstract
Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: this https URL
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URL
https://arxiv.org/abs/2609.10376
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Isotropic Embedding Perturbations for Robust Vision Language Encoders
2026-09-09 15:08:05Hyesong Choi, Daeun Kim, Song Park, Taekyung Kim, Byeongho Heo, Sangdoo Yun, Dongbo Min, Dongyoon HanAbstract
Data augmentation is fundamental to training modern deep vision and multimodal models. While individual methods, such as RandAug, CutMix, Mixup, RandErase, and DropPath, offer strong regularization effects, their combined use has saturated in performance due to overlapping functionalities, and aggressive pixel-level manipulations may disrupt delicate cross-modal alignment. This saturation motivates the search for a new augmentation axis within the embedding space rather than the input space. We introduce Aether, a simple plug-in method that applies diffusion-style random perturbations in the embedding space via controlled alpha-mixing, specifically designed to provide isotropic regularization that remains semantically consistent. Inspired by feature-space perturbations in language models and image degradation in generative pretraining, Aether induces mild yet effective perturbations that smooth the representations without compromising the fine-grained structural information required for strong vision-language encoders. Across diverse architectures and across multiple recognition tasks, Aether delivers consistent gains over the advanced recipe combining CutMix, Mixup, DropPath, and RandAug---a level of improvement rarely observed with modern augmentation alternatives. Notably, Aether demonstrates superior effectiveness in multi-modal alignment, succeeding where traditional pixel-space augmentations fail by providing a stable, isotropic regularization signal that respects the integrity of the high-dimensional feature space.
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URL
https://arxiv.org/abs/2609.10292
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Adaptive Distributed Physical-Layer Authentication and Attack Detection in 6G Non-Terrestrial Networks via Causal Meta-Learning
2026-09-08 22:53:32Parsa Rajabi, Mohammad Reza Abedi, Nader Mokari, Paeiz Azmi, Halim YanikomerogluAbstract
Physical-layer authentication (PLA) in non-terrestrial networks (NTNs) is challenged by severe Doppler shifts, long delays, and fast channel variations, which cause distribution shifts and degrade conventional learning methods. Existing PLA schemes often rely on single features or generalize poorly to unseen environments. This paper proposes a secure adaptive framework for authentication in multi-zone networks (SAFA-MZ), a causal meta-learning framework for distributed PLA (DPLA) in NTNs. First, we design a multi-feature fingerprint that combines spatial, angular, combiner, subspace, and Doppler-delay features. The fingerprint is adaptive and distributed, as it fuses heterogeneous physical-layer features and measurements from multiple aerial nodes. Second, we formulate a structural causal model (SCM) to capture the relations among design choices, environmental factors, extracted features, and authentication outcomes. Third, we develop a model-agnostic meta-learning (MAML) strategy with invariant risk minimization (IRM) and causal consistency regularization for fast adaptation to unseen NTN environments with few labeled samples. Fourth, we propose a two-stage authentication scheme that performs local recognition and activates time-difference-of-arrival (TDOA) localization with a graph attention (GAT) network only when needed, which reduces backhaul overhead. Simulations show that SAFA-MZ achieves 92% accuracy and 96% AUC, outperforming centralized deep learning and single-feature baselines across diverse environments.
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URL
https://arxiv.org/abs/2609.09511
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Critical initialization destabilizes higher input derivatives in wide scalar-input networks
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The edge-of-chaos condition preserves first-order input perturbations in wide randomly initialized networks, but physics-informed losses, score matching and derivative regularization depend on higher input derivatives. For smooth scalar-input fully connected networks, using a joint Gaussianity of the finite derivative jet that holds in the infinite-width limit at each fixed depth, we derive mean-field recursions through third order that are exact at the variance fixed point, with finite-depth corrections that decay geometrically. At criticality, the first-derivative variance is depth-invariant, whereas the second-derivative variance grows linearly whenever the activation has nonzero curvature. The resulting third-order system closes on mean-field susceptibilities. For residual networks with branch scale L^{-1/2}, we prove that every fixed finite derivative order has uniformly bounded variance under explicit regularity assumptions. Simulations verify the critical growth laws, the residual bound, and the closed recursion. The results concern initialization, not trained-network performance.
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URL
https://arxiv.org/abs/2609.09244
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Inference-Time Nash Alignment
2026-09-08 00:50:12Hadi Hosseini, Debmalya Mandal, Duohan ZhangAbstract
Preference-based fine-tuning methods such as RLHF and DPO require substantial compute and large preference datasets. They also need direct access to the model parameters which are not provided by many state-of-the art models. Inference-time alignment offers a cost-effective alternative without updating model parameters. However, existing inference-time methods rely on a scalar reward model derived under a Bradley-Terry assumption, which cannot represent general preferences. Following recent work on fine-tuning with generalized preferences, in this work, we initiate the study of inference-time alignment under general preferences. We formulate the problem as obtaining a Nash equilibrium of a two-player zero-sum game between policies. We propose two algorithms: Best-of-Nash (BoN) and Nash Mirror Descent (NMD). We prove that both algorithms achieve a duality gap that matches the problem lower bound. Empirically, we implement the two methods on three datasets, which shows that our methods substantially outperform the base policy, converging to the performance of the fine-tuned models. Moreover, our results show that NMD remains robust across the regularization parameter.
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URL
https://arxiv.org/abs/2609.08082
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MSSP: Multi-Scale Spatially-Constrained Partition for Unsupervised Semantic Segmentation of 3D Point Clouds
2026-09-07 02:56:37Zhenghao Zhang, Xinjie Wang, Wei Wang, Jun Zhang, Hanyun WangAbstract
3D point cloud semantic segmentation is essential for real-world spatial understanding, yet the prohibitive cost of human annotations motivates unsupervised approaches that require no labels. Existing superpoint-based methods typically rely on spectral analysis at a fixed granularity, failing to capture the hierarchical semantic structures inherent in complex indoor scenes. To bridge this gap, we present a Multi-Scale Spatially-Constrained Partition (MSSP) framework that combines multi-scale spectral analysis with spatially-constrained clustering. Multi-scale spectral analysis constructs enriched superpoint descriptors across multiple clustering granularities; however, the resulting high-dimensional feature space calls for a structural prior to translate into cleaner segmentation. Spatially-constrained clustering supplies this prior by restricting superpoint merging to physically adjacent regions, imposing the spatial coherence needed for multi-scale features to be effective. Extensive experiments on S3DIS and ScanNet show that MSSP achieves the best mIoU among unsupervised methods on the main benchmarks, with particularly significant gains on S3DIS. Notably, our ablation reveals a regularize-then-enrich interaction: multi-scale features alone do not improve final segmentation, yet become highly effective when coupled with spatial regularization, underscoring that spatial coherence is aprerequisite for multi-scale representations in superpoint clustering.
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URL
https://arxiv.org/abs/2609.06959
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Second-Order Smooth Planning with Optimal-Transport Bellman Smoothing
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Planning with a generative model aims to estimate the value of a state using as few simulator calls as possible. SmoothCruiser achieves problem-independent complexity $\widetilde O(\varepsilon^{-4})$ by exploiting the smoothness of the entropy-regularized Bellman backup, but its estimator is only first-order. We show that the sample-complexity exponent of SmoothCruiser-type planners is governed by the order $\beta$ of the local Taylor remainder, giving oracle complexity $\widetilde O(\varepsilon^{-(2+2/(\beta-1))})$: the first-order case $\beta=2$ recovers SmoothCruiser, while a second-order/cubic remainder $\beta=3$ yields $\widetilde O(\varepsilon^{-3})$. We reach this regime with an optimal-transport-smoothed Bellman backup over action distributions, which has a closed form, a policy gradient, and a Lipschitz Hessian, and whose quadratic correction admits an unbiased cross-product estimator. The resulting SecondOrderSmoothCruiser achieves $\widetilde O(\varepsilon^{-3})$ oracle complexity for fixed OT parameters, and we relate the OT, entropy-regularized, and unregularized objectives through explicit regularization-bias bounds.
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URL
https://arxiv.org/abs/2609.06484
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What Matters, When? Diagnosing and Improving Conditional Visual Grounding in Visuomotor Imitation Policies
2026-09-04 17:27:35Vivek Chavan, Pengtao Xie, Yahuan Shi, Oliver Heimann, Kevin Haninger, J\"org Kr\"ugerAbstract
Visuomotor imitation policies can achieve high performance under in-distribution visual conditions yet fail when visually similar objects or receptacles are introduced. We study this behavior as a problem of conditional visual grounding: the visual target required for successful control changes with the manipulation phase and, in more complex tasks, with the observed task state. Using Action Chunking with Transformers (ACT), we systematically introduce distractor objects and receptacles with controlled color and shape similarity and localize failures to picking and placement. We find that distractor sensitivity is specific to both the type of visual similarity and the manipulation stage. Guided by this diagnosis, we evaluate distractor augmentation, phase-dependent attention regularization, and appearance-based visual prompting as complementary interventions for improving target selection while preserving spatial information required for control. These interventions substantially improve robustness in simulation and on a physical UR3e. We further examine the same failure pattern in a pretrained vision-language-action policy on a state-conditioned instrument-handling task, where the observed state of a medical instrument determines the correct destination. Together, the results show that visual distractors can cause incorrect object or destination selection even when the underlying manipulation skill remains intact, and that explicitly improving target selection can substantially recover performance across distinct visuomotor policy-learning regimes.
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URL
https://arxiv.org/abs/2609.05376
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BLASt3R: Bundle Adjustment of Any Image Set with Multi-View Matching and Monocular Priors
2026-09-04 14:41:52Vincent Leroy, Philippe Weinzaepfel, Lojze Zust, Yohann Cabon, J\'erome RevaudAbstract
Recent hybrid Structure-from-Motion (SfM) systems combine the robustness of feed-forward 3D reconstruction with the accuracy of traditional bundle adjustment (BA) with pixel matching. They are usually the best performing methods however their scalability and usability remains limited since estimating dense correspondences between views is prohibitively costly, especially considering time constraints inherent to online applications like Visual SLAM (VSLAM). In this paper, we introduce a regularized BA framework that leverages a fast multi-view matcher and monocular priors for initialization and regularization. In contrast to existing systems, our unified approach seamlessly supports both online VSLAM and offline reconstruction from unordered image collections within the same optimization framework and sharing common hyperparameters for all tasks. Extensive experiments across both domains demonstrate improved performance and speed tradeoffs over traditional, feed-forward, and hybrid baselines. Notably for VSLAM, our uncalibrated method outperforms all previous calibrated approaches.
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https://arxiv.org/abs/2609.05210
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VoxelFix: Post-Hoc Semantic Correction of Completed 3D Voxel Maps
2026-09-04 13:08:07Sunesh Praveen Raja Sundarasami, Taehyoung Kim, Johannes Scherer, Toma\v{z} Coti\v{c}, Sivasubiramaniam Subbiah, Andreas Greiner, Paul Spannaus, Sebastian HoubenAbstract
Semantic 3D maps are increasingly constructed automatically for aerial robotics by integrating learned semantic predictions into 3D representations. While this avoids costly manual 3D annotation, errors in the perception and mapping pipeline can persist in the resulting map, reducing its reliability for downstream autonomous tasks. Existing 3D semantic map refinement methods either rely on the original observations, treat occupancy as part of the prediction problem, or apply non-learned local regularization to completed maps. Instead, we study post-hoc semantic correction, asking whether semantic accuracy can be recovered directly from the completed map while keeping its geometry and occupancy fixed. We introduce \method, a graph-based model that corrects voxel labels based on local geometry and neighboring semantic information. To obtain training pairs, we corrupt contiguous regions of annotated OccuFly maps according to class confusions observed in upstream maps. We evaluate \method on completed OccuFly maps generated from predictions of four independently trained 2D segmentation models. \method consistently improves mIoU by 4.23--5.00 percentage points, with gains broadly distributed across the evaluated semantic classes and particularly strong improvements for tree, roof, and wall. Results on an independently reconstructed out-of-distribution aerial scene further suggest that the learned correction can transfer beyond the environments seen during training.
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URL
https://arxiv.org/abs/2609.05114
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Learning 3D Editing without Paired Supervision via Generative Prior Distillation
2026-09-04 09:51:11Hao Wen, Weibin Yun, Hongxing Fan, Haotian Lu, Rui Chen, Zehuan Huang, Lu ShengAbstract
Instruction-guided 3D editing is essential for interactive content creation, yet it faces a significant bottleneck: the severe scarcity of high-quality paired training data. Existing approaches attempt to bypass this by either relying on slow test-time optimization or training on pseudo-pairs constructed via complex pipelines, which often introduce structural drift and geometric artifacts. In this paper, we propose a novel framework that learns feed-forward 3D editing without paired 3D supervision via Generative Prior Distillation. Instead of relying on ground-truth 3D pairs, our core idea is to distill visual, semantic, and geometric knowledge from powerful foundation models directly into a 3D editing model. Specifically, through a differentiable rendering pipeline, we supervise the 3D representation using two complementary signals: a 2D visual prior from an image editing model at the main editing view, and a semantic prior from a Vision-Language Model at novel views to ensure strict instruction following and source identity preservation. Crucially, to address the geometric collapse and multi-view inconsistencies inherent in 2D projection supervision, we introduce a 3D-aware Distribution Matching regularization. Acting as a geometric prior, this term operates in the 3D latent space, constraining the edited output to remain within the manifold of realistic 3D assets defined by a pretrained image to 3D teacher model. Extensive experiments demonstrate that our method achieves superior instruction fidelity and cross-view consistency, significantly outperforming state-of-the-art baselines. Our project is available at: this https URL.
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URL
https://arxiv.org/abs/2609.04942
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PAPT++: Risk-Aware Adversarial Tuning and Generation for Single Domain Generalization
2026-09-04 07:54:30Zhipeng Xu, De Cheng, Xinyang Jiang, Lingfeng He, Huaijie Wang, Dongsheng Li, Nannan Wang, Xinbo GaoAbstract
Single domain generalization (SDG) aims to learn a model from one labeled source domain that generalizes to unseen target domains. A common strategy is to enrich the source distribution with augmented or generated samples, and recent text-to-image (T2I) diffusion models provide a strong generative prior for this purpose. However, diversity alone is insufficient for robust generalization, because useful generated samples should also capture variations that the current classifier finds difficult. Motivated by distributionally robust optimization (DRO), we define a semantic ambiguity set in the class-conditional generative space of a pretrained T2I model and search it for samples with high classification loss under the current classifier. To this end, we introduce PAPT++, a risk-aware adversarial generation-training framework for SDG. PAPT++ first learns diverse semantic reference images for each class through image-text alignment and intra-class diversity regularization. These references then serve as denoising targets during classifier-guided diffusion synthesis, reducing semantic drift while guiding generation toward challenging variations. The generated samples are combined with the source data to update the classifier, and the updated classifier guides the next synthesis round in return. In this way, PAPT++ progressively exposes the classifier to challenging yet semantically consistent variations. Extensive experiments on standard SDG benchmarks demonstrate the superiority of the proposed PAPT++ method and the effectiveness of its main components.
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URL
https://arxiv.org/abs/2609.04837
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Stable and Scalable Bundle Adjustment of Holistic 3D Structures
2026-09-03 16:08:03Shaohui Liu, R\'emi Pautrat, Daniel Barath, Richard Hartley, Viktor Larsson, Marc PollefeysAbstract
Bundle Adjustment (BA) is a cornerstone of 3D computer vision and has benefited from decades of advances in sparse optimization and numerical methods. It was originally developed for jointly optimizing camera intrinsics, poses and sparse 3D points. While extensions incorporate lines and other primitives, integrating richer geometric structures such as parallelism, coplanarity, or wireframes often introduces significantly increased computational cost and reduced numerical stability. In this paper, we propose a unified framework that extends bundle adjustment to jointly optimize geometric features and higher-order relations. We first introduce a taxonomy that distinguishes scalable geometric features with direct 2D measurements (e.g., points and lines), from groups encoding higher-order relations (e.g., coplanarity, parallelism, etc.), where we show that groups can be modeled as camera-like entities within the bundle adjustment framework. Building on this formulation, we propose that both group constraints and cross-feature relations (i.e., point-line associations) can be expressed through 2D reprojection measurements. By formulating group-induced and cross-feature reprojection errors, we preserve the sparsity structure of classical point-based BA under Schur elimination, while avoiding direct 3D regularization that degrades the conditioning and stability. Experiments on both real-world and synthetic datasets demonstrate runtime performance comparable to classical point-only bundle adjustment, while producing significantly richer 3D structures and improved geometric accuracy.
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https://arxiv.org/abs/2609.04026
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