Geometric Regularization

Most research on the manipulation of deformable objects focuses on lightweight systems with negligible mechanical response, effectively restricting attention to quasi-static regimes. This assumption excludes a broad class of practically relevant objects, such as hoses, pipes, and wiring harnesses, whose dynamics cannot be ignored during manipulation. In this work, we address this limitation by introducing a closed-loop control architecture that explicitly accounts for object dynamics and recasts manipulation as a shape-regulation problem. Control is achieved by modulating forces and torques applied at multiple fixed points along the object. This approach builds on three methodological contributions: a fully dynamic model of linear deformable objects based on discrete strain parameterizations; an extension of the notion of actuation coordinates to SE(3), yielding a structured and inherently underactuated control architecture; and nonlinear feedback strategies providing explicit conditions for steady-state convergence to desired configurations. Extensive simulations on representative manipulation tasks demonstrate the performance gains enabled by the proposed modelbased formulation. We finally validate the approach experimentally through a real-time closed-loop implementation with online shape estimation, confirming its practical feasibility and effectiveness

Angular-margin speaker encoders are widely used in voice conversion, yet the geometry of their classifier prototypes remains poorly understood. We analyze ECAPA-TDNN classifier prototypes as points on the unit hypersphere and characterize their organization using rotation-invariant angular statistics together with global and local effective dimensionality measures. Our analysis shows that standard training can induce angular concentration and a substantial reduction in effective dimensionality. To address this, we investigate two geometric regularization strategies (hinged Riesz log-energy and effective-dimension maximization) applied to classifier prototypes to encourage more uniform hyperspherical coverage. The resulting prototype sets exhibit higher effective dimensionality and improved isotropy, with configuration-dependent effects on speaker-recognition performance. When the corresponding ECAPA-TDNN models are used as speaker encoders for Fast-VGAN, the regularized systems also exhibit improved robustness in zero-shot voice conversion, particularly for previously unseen speakers.

Sparse-view 3D scene reconstruction with 3D Gaussian Splatting (3DGS) is inherently underconstrained. Plausible renderings can also coexist with erroneous Gaussian geometry, as errors in positions or depths may be concealed by opacity, scale, and appearance; we term this failure mode Geometry Cheating. Existing regularization methods constrain geometry but remain limited to observed views, while video-diffusion-based methods complete unseen views yet mainly use them as RGB pseudo-supervision, underusing motion and temporal priors and lacking explicit geometry supervision. We present Bi-FlowGS, which uses optical flow to bridge generative view completion and Gaussian geometry regularization. Our plug-and-play Video-to-Geometry Flow Distillation (V2G) distills temporal correspondence priors from restored videos into Gaussian geometry to alleviate Geometry Cheating. Conversely, Geometry-to-Video Flow-Guided Restoration (G2V) uses the current 3DGS geometry to guide temporally consistent video restoration, providing more reliable generative supervision. Together, V2G and G2V form an implicit bidirectional co-refinement process, enabling restored videos and the optimized 3DGS scene to iteratively improve each other. Experiments demonstrate improved rendering quality and geometric consistency across wide-baseline and unbounded 360° benchmarks.

Accurate diagnostic and risk-prediction models are important for supporting clinical decision-making during infectious disease outbreaks. However, privacy and governance requirements may restrict patient-level data sharing across healthcare institutions, and data distributions often vary. Moreover, AUC is widely used to evaluate discriminative performance, motivating its direct optimization in model development. We propose geographically regularized AUC-maximizing personalized federated learning (GrAUC-PFL), which directly optimizes a smooth pairwise AUC surrogate to learn personalized models while keeping patient-level data local and accounting for institutional heterogeneity. Graph-based regularization encourages geographically neighboring institutions to have similar coefficient vectors while retaining a personalized models. Simulations and a real-data application suggest improved discriminative performance, particularly when geographically neighboring institutions have similar data-generating characteristics.

Sparse voxel reconstruction offers an efficient representation for high-fidelity 3D modeling, yet its geometry is commonly optimized from local photometric evidence and discrete visibility statistics. This often leads to fragmented surfaces, excessive subdivision, and floating artifacts, particularly in weakly textured or sparsely observed regions. We introduce SurfSVR, a novel sparse voxel reconstruction paradigm that treats 2D surface priors as explicit 3D geometric regularizers. Instead of directly lifting noisy pixel-wise depth predictions, SurfSVR first organizes each image into coherent surface regions by jointly reasoning over appearance, monocular depth, normals and cross-view geometry. Each region is then represented by an adaptively selected planar or quadratic surface model based on fitting reliability and geometric complexity, while cross-model agreement distinguishes reliable geometry from ambiguous predictions. These structured 2D priors are lifted into 3D and integrated throughout the reconstruction pipeline. They guide surface-adaptive voxel subdivision, provide region-level depth and normal supervision during optimization, enhance geometrically reliable sparse-observed surfaces in voxel pruning, and suppress off-surface floaters during post-refinement training. This unified design converts semantic and geometric coherence in image space into persistent structural constraints in 3D. Extensive experiments on 3 public benchmarks demonstrate that SurfSVR consistently improves sparse voxel reconstruction across scenes with substantially different visibility and geometry characteristics, achieving state-of-the-art reconstruction quality. Codes and models will be released soon.

World models are usually evaluated as components of model-based reinforcement learning (MBRL) systems, while the world models themselves are rarely studied in isolation. We examine five representative visual world-model agents in Atari Pong: DreamerV3, DIAMOND, TWISTER, Simulus, and STORM. After reproducing their training pipelines and matching the reported agent performance, we freeze the learned world models and evaluate them with a closed-loop rollout diagnostic: a policy trained separately from the corresponding MBRL agent interacts with each frozen model, and the generated video trajectories are inspected for visual and dynamical errors. Across all five models, the rollouts contain clear failures, including ball disappearance, incorrect ball motion, and invalid ball-paddle interactions. Beyond visual trajectories, we further evaluate them with pixel-space zero-shot MBRL, where a new policy is trained entirely inside a frozen world model and then evaluated in the real environment. Across all five models, the resulting policies substantially underperform those produced by the corresponding original MBRL training pipelines. The gap is particularly large for DreamerV3, whose mean return drops from -5.5 to -20.9, near the minimum Pong return of -21. We hypothesize that insufficient modeling of task-critical concepts, such as the ball in Pong, may contribute to these failures. We therefore propose Concept-Guided Spatial Regularization (CGSReg), an auxiliary pixel reconstruction loss applied to segmented concept regions. Experiments show that CGSReg improves both closed-loop rollouts and pixel-space zero-shot MBRL in DreamerV3, DIAMOND, and TWISTER. Its effects vary across the remaining models and evaluation metrics, indicating that CGSReg alone does not address all world-model bottlenecks.

In this paper, we propose a training strategy for confidence estimation in omnidirectional stereo, targeting the ambiguous matches that frequently occur in wide-baseline setups. Reinterpreting the matching responses produced by the 3D encoder decoder block, we show that their expectation values provide intrinsic confidence signals. Building on this, our method directly penalizes ambiguous responses without auxiliary heads, multi-pass inference, or additional modules, resulting in more efficient and generalized predictions. Beyond confidence, we introduce swept feature volume resampling, where response features produced by 3D CNNs are resampled using regressed positive matching indices and then processed by 2D CNNs to predict meta-information such as surface normals. This joint learning introduces auxiliary geometric regularization and improves depth coherence by leveraging additional contextual cues during response aggregation stage. Experimental results demonstrate that our approach enhances both confidence estimation and surface normal prediction while maintaining deployment practicality for autonomous mobility applications.

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the Wiener KL (KL_W), which is empirically more effective under certain conditions on the noise model, and the drift-variance regularizer (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems -- including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor -- along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5x noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain.

Printed circuit board (PCB) defect detection is an essential part of automated optical inspection (AOI); yet it remains challenging in practice because many defects are tiny, low-contrast, and embedded in dense circuit backgrounds. To address these issues, this paper presents a two-phase PCB defect detection framework that combines structure-guided mixed masked pretraining with spatial continuity regularization. In the pretraining stage, we design a sparse convolutional masked pretraining scheme to exploit unlabeled PCB images, where structure-guided mixed masking is used to construct informative masked inputs. The sparse convolutional reconstruction pipeline suppresses invalid responses from masked regions and enables the detector backbone to infer missing PCB structures from visible conductive patterns, thereby learning PCB structural priors. In the fine-tuning stage, the pretrained backbone is transferred to the downstream defect detection task. For the task, a spatial continuity regularization term is introduced during fine-tuning. This term constrains dispersed positive predictions assigned to the same defect instance and promotes more compact localization on elongated defect regions. Experiments on the DsPCBSD+ dataset show that the proposed method achieves 85.5% mAP0.5 and 52.3% mAP0.5:0.95, outperforming several strong baseline detectors. Ablation studies and qualitative results further confirm the effectiveness of the proposed framework for robust PCB defect detection in industrial AOI scenarios.

We present a single-image head mesh reconstruction framework that addresses the longstanding challenge of simultaneously preserving facial identity and producing industry-grade topology. Our framework adopts a coarse-to-fine optimization pipeline that refines a rigged template across three stages -- rig, joint, and vertex -- achieving stable convergence and consistent topology. To mitigate the ill-posed nature of single-image 3D face reconstruction and ensure identity preservation, we employ a normal consistency objective jointly with landmark alignment. To further preserve local surface structure and enforce topological regularity, we introduce geometry-aware constraints based on Gaussian curvature and conformal consistency, along with auxiliary regularizations that correct fine artifacts such as lip seams and eyelid discontinuities. Our hierarchical optimization with geometry-aware regularization yields meshes with semantically meaningful edge flow and industry-grade topology. After geometry reconstruction, we extract UV-space texture and normal maps to preserve appearance details for visualization and downstream use. In a user study with 22 professional technical artists, our results were assessed as approaching industry-grade usability, and 95% of participants ranked our method as the top-performing approach, underscoring its effectiveness for real-world digital human production.

Quantile-based distributional reinforcement learning methods learn return distributions through sampled quantile regression, but their bootstrapped target quantiles may induce distorted or degenerate distribution estimates. We propose Robust Quantile-based Implicit Quantile Networks (RQIQN), a lightweight Wasserstein distributionally robust enhancement boosted from a quantile estimation perspective. We first reinterpret a snapshot of IQN loss as a collection of local empirical quantile estimation problems over sampled current fractions. We then robustify each local slot with a Wasserstein distributionally robust quantile estimation formulation, yielding a closed-form, fraction-dependent correction to the Bellman target. This correction directly addresses distributional degeneration: its median antisymmetry preserves the risk-neutral quantile average, while its monotonicity enlarges upper-lower quantile gaps and counteracts collapsed distributional spread. RQIQN thus regularizes quantile geometry without changing the underlying value objective or requiring additional sample set reconstruction. Finally, we empirically show that the proposed RQIQN outperforms other existing quantile-based distributional reinforcement learning algorithms in risk-sensitive navigation and Atari games.

We study homogeneous refinement operators $(Vγ)(t)=\sum_{j\in\mathbb Z}A_jγ(Mt-j)$, acting on compactly supported continuous piecewise linear curves $γ:\mathbb R\to\mathbb R^p$, where $M\ge2$ and only finitely many matrices $A_j\in\mathbb R^{p\times p}$ are nonzero. We prove that the iterates $V^nγ$ admit exact ReLU realizations of fixed width and depth $O(n)$. The main new ingredient is an exact loop controller for the residual dynamics. Instead of propagating scalar residual surrogates, the construction transports the residual orbit by a forward-exact state on a polygonal loop. Scalar factors and digit selectors are then recovered from this loop state by complementary CPwL readouts. The loop seam is not removed, but its remaining ambiguity is confined to the final readout/selector stage, where it is harmless because the scalar atom is supported away from the seam. This gives a homogeneous $M$-ary vector-valued extension of the scalar binary refinable-function construction with a more geometric controller architecture. We also record crude exponential bounds on the network weights and biases. Affine forcing terms are handled by expanding affine iterates into finite sums of homogeneous iterates, giving exact fixed-width realizations with depth $O(n^2)$, and anchored open curves reduce to compactly supported defects with affine anchor mismatch. We also describe homogeneous polygonal generators, including dragon-type examples and a self-intersecting Hilbert-type prototype in arbitrary dimension. The extended version includes stage-dependent forcing, finite-state stacking reductions, and further geometric constructions such as Koch-, Gosper-, Morton-, and connector-based Hilbert-type variants.

Spatial transcriptomics (ST) enables spatially resolved gene profiling but remains expensive and low-throughput, limiting large-cohort studies and routine clinical use. Predicting spatial gene expression from routine hematoxylin and eosin (H&E) slides is a promising alternative, yet under realistic leave-one-slide-out evaluation, existing models often suffer from slide-level appearance shifts and regression-driven over-smoothing that suppress biologically meaningful variation. CHRep is a two-phase framework for robust histology-to-expression prediction. In the training phase, CHRep learns a structure-aware representation by jointly optimizing correlation-aware regression, symmetric image-expression alignment, and coordinate-induced spatial topology regularization. In the inference phase, cross-slide robustness is improved without backbone fine-tuning through a lightweight calibration module trained on the training slides, which combines a non-parametric estimate from a training gallery with a magnitude-regularized correction module. Unlike prior embedding-alignment or retrieval-based transfer methods that rely on a single prediction route, CHRep couples topology-preserving representation learning with post-hoc calibration, enabling stable neighborhood retrieval and controlled bias correction under slide-level shifts. Across the three cohorts, CHRep consistently improves gene-wise correlation under leave-one-slide-out evaluation, with the largest gains observed on Alex+10x. Relative to HAGE, the Pearson correlation coefficient on all considered genes [PCC(ACG)] increases by 4.0% on cSCC and 9.8% on HER2+. Relative to mclSTExp, PCC(ACG) further improves by 39.5% on Alex+10x, together with 9.7% and 9.0% reductions in mean squared error (MSE) and mean absolute error (MAE), respectively.

Semantic Tube Prediction (STP) leverages representation geometric to regularize LLM hidden-state trajectories toward locally linear geodesics during fine-tuning, thereby greatly improving data efficiency. The original STP recipe samples random token sub-spans, which is compatible with the base large language model (LLM) training architecture. Inspired by STP, we are interested to investigate whether the sampling position can further enhance the semantic structure of multi-step reasoning, and hence affect its geometric impact. We applied STP at consecutive semantic reasoning step boundaries and achieved 168x more accurate multi-step latent prediction than frozen baselines on ProcessBench (3,400 samples), compared to only 4x for the random-token STP. Probing the latent manifold with a learned non-linear predictor reveals that STP-shaped trajectories are smooth curves, not straight lines: a 3-layer MLP reduces prediction error by a further 3-12x over linear extrapolation on step-boundary models. Removing the language modeling loss yields trajectories that are 2x more MLP-predictable than the combined loss, revealing a tradeoff between generation quality and geometric purity. Our results identify sampling position as the critical variable in geometric regularization and establish multi-step latent prediction MSE as a new evaluation metric for this class of methods.

Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a long-standing problem: local-chart methods like ATLAS suffer from exponential landmark scaling and per-step reprojection, while autoencoder alternatives leave tangent-bundle geometry poorly constrained, and the errors propagate into the learned drift and diffusion. We observe that the ambient covariance~$Λ$ already encodes coordinate-invariant tangent-space information, its range spanning the tangent bundle. Using this, we construct a tangent-bundle penalty and an inverse-consistency penalty for a three-stage pipeline (chart learning, latent drift, latent diffusion) that learns a single nonlinear chart and the latent SDE. The penalties induce a function-space metric, the $ρ$-metric, strictly weaker than the Sobolev $H^1$ norm yet achieving the same chart-quality generalization rate up to logarithmic factors. For the drift, we derive an encoder-pullback target via Itô's formula on the learned encoder and prove a bias decomposition showing the standard decoder-side formula carries systematic error for any imperfect chart. Under a $W^{2,\infty}$ chart-convergence assumption, chart-level error propagates controllably to weak convergence of the ambient dynamics and to convergence of radial mean first-passage times. Experiments on four surfaces embedded in up to $201$ ambient dimensions reduce radial MFPT error by $50$--$70\%$ under rotation dynamics and achieve the lowest inter-well MFPT error on most surface--transition pairs under metastable Müller--Brown Langevin dynamics, while reducing end-to-end ambient coefficient errors by up to an order of magnitude relative to an unregularized autoencoder.