Daily Papers

The scaling of Large Language Models (LLMs) is increasingly limited by data quality. Most methods handle data mixing and sample selection separately, which can break the structure in code corpora. We introduce UniGeM, a framework that unifies mixing and selection by treating data curation as a manifold approximation problem without training proxy models or relying on external reference datasets. UniGeM operates hierarchically: Macro-Exploration learns mixing weights with stability-based clustering; Micro-Mining filters high-quality instances by their geometric distribution to ensure logical consistency. Validated by training 8B and 16B MoE models on 100B tokens, UniGeM achieves 2.0times data efficiency over a random baseline and further improves overall performance compared to SOTA methods in reasoning-heavy evaluations and multilingual generalization.

3D Gaussian Splatting (3DGS) has exhibited remarkable efficacy in novel view synthesis (NVS). However, it suffers from a significant drawback: achieving high-fidelity rendering typically necessitates a large number of 3D Gaussians, resulting in substantial memory consumption and storage requirements. To address this challenge, we propose the first knowledge distillation framework for 3DGS, featuring various teacher models, including vanilla 3DGS, noise-augmented variants, and dropout-regularized versions. The outputs of these teachers are aggregated to guide the optimization of a lightweight student model. To distill the hidden geometric structure, we propose a structural similarity loss to boost the consistency of spatial geometric distributions between the student and teacher model. Through comprehensive quantitative and qualitative evaluations across diverse datasets, the proposed Distilled-3DGS, a simple yet effective framework without bells and whistles, achieves promising rendering results in both rendering quality and storage efficiency compared to state-of-the-art methods. Project page: https://distilled3dgs.github.io . Code: https://github.com/lt-xiang/Distilled-3DGS .

Object pose estimation, which plays a vital role in robotics, augmented reality, and autonomous driving, has been of great interest in computer vision. Existing studies either require multi-stage pose regression or rely on 2D-3D feature matching. Though these approaches have shown promising results, they rely heavily on appearance information, requiring complex input (i.e., multi-view reference input, depth, or CAD models) and intricate pipeline (i.e., feature extraction-SfM-2D to 3D matching-PnP). We propose AxisPose, a model-free, matching-free, single-shot solution for robust 6D pose estimation, which fundamentally diverges from the existing paradigm. Unlike existing methods that rely on 2D-3D or 2D-2D matching using 3D techniques, such as SfM and PnP, AxisPose directly infers a robust 6D pose from a single view by leveraging a diffusion model to learn the latent axis distribution of objects without reference views. Specifically, AxisPose constructs an Axis Generation Module (AGM) to capture the latent geometric distribution of object axes through a diffusion model. The diffusion process is guided by injecting the gradient of geometric consistency loss into the noise estimation to maintain the geometric consistency of the generated tri-axis. With the generated tri-axis projection, AxisPose further adopts a Triaxial Back-projection Module (TBM) to recover the 6D pose from the object tri-axis. The proposed AxisPose achieves robust performance at the cross-instance level (i.e., one model for N instances) using only a single view as input without reference images, with great potential for generalization to unseen-object level.

Large Language Models (LLMs) have demonstrated impressive capabilities in a wide range of code generation tasks. However, generating code for certain domains remains challenging. One such domain is Computer-Aided Design (CAD) program, where the goal is to produce scripted parametric models that define object geometry for precise design and manufacturing applications. A key challenge in LLM-based CAD program generation is the limited geometric complexity of generated shapes compared to those found in real-world industrial designs. This shortfall is in part due to the lack of diversity in the available CAD program training data. To address this, we propose a novel data augmentation paradigm that prompts an LLM to generate CAD programs conditioned on a reference surface program and a modeling procedure - an idea inspired by practices in industrial design. By varying the reference surface using a collection of organic shapes, our method enriches the geometric distribution of generated CAD models. In particular, it introduces edges and faces defined by spline-based curvature, which are typically missing or underrepresented in existing open-source CAD program datasets. Experiments show that our method produces CAD samples with significantly greater geometric diversity and a higher resemblance to industry-grade CAD designs in terms of the proportion of organic shape primitives. This enhancement makes our CAD data augmentation approach a useful tool for training LLMs and other deep learning models in CAD generation.

We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

The wide-angle lens shows appealing applications in VR technologies, but it introduces severe radial distortion into its captured image. To recover the realistic scene, previous works devote to rectifying the content of the wide-angle image. However, such a rectification solution inevitably distorts the image boundary, which potentially changes related geometric distributions and misleads the current vision perception models. In this work, we explore constructing a win-win representation on both content and boundary by contributing a new learning model, i.e., Rectangling Rectification Network (RecRecNet). In particular, we propose a thin-plate spline (TPS) module to formulate the non-linear and non-rigid transformation for rectangling images. By learning the control points on the rectified image, our model can flexibly warp the source structure to the target domain and achieves an end-to-end unsupervised deformation. To relieve the complexity of structure approximation, we then inspire our RecRecNet to learn the gradual deformation rules with a DoF (Degree of Freedom)-based curriculum learning. By increasing the DoF in each curriculum stage, namely, from similarity transformation (4-DoF) to homography transformation (8-DoF), the network is capable of investigating more detailed deformations, offering fast convergence on the final rectangling task. Experiments show the superiority of our solution over the compared methods on both quantitative and qualitative evaluations. The code and dataset will be made available.

Recent 3D content generation pipelines often leverage Variational Autoencoders (VAEs) to encode shapes into compact latent representations, facilitating diffusion-based generation. Efficiently compressing 3D shapes while preserving intricate geometric details remains a key challenge. Existing 3D shape VAEs often employ uniform point sampling and 1D/2D latent representations, such as vector sets or triplanes, leading to significant geometric detail loss due to inadequate surface coverage and the absence of explicit 3D representations in the latent space. Although recent work explores 3D latent representations, their large scale hinders high-resolution encoding and efficient training. Given these challenges, we introduce Hyper3D, which enhances VAE reconstruction through efficient 3D representation that integrates hybrid triplane and octree features. First, we adopt an octree-based feature representation to embed mesh information into the network, mitigating the limitations of uniform point sampling in capturing geometric distributions along the mesh surface. Furthermore, we propose a hybrid latent space representation that integrates a high-resolution triplane with a low-resolution 3D grid. This design not only compensates for the lack of explicit 3D representations but also leverages a triplane to preserve high-resolution details. Experimental results demonstrate that Hyper3D outperforms traditional representations by reconstructing 3D shapes with higher fidelity and finer details, making it well-suited for 3D generation pipelines.

Document image rectification aims to eliminate geometric deformation in photographed documents to facilitate text recognition. However, existing methods often neglect the significance of foreground elements, which provide essential geometric references and layout information for document image correction. In this paper, we introduce Foreground-Centric Network (ForCenNet) to eliminate geometric distortions in document images. Specifically, we initially propose a foreground-centric label generation method, which extracts detailed foreground elements from an undistorted image. Then we introduce a foreground-centric mask mechanism to enhance the distinction between readable and background regions. Furthermore, we design a curvature consistency loss to leverage the detailed foreground labels to help the model understand the distorted geometric distribution. Extensive experiments demonstrate that ForCenNet achieves new state-of-the-art on four real-world benchmarks, such as DocUNet, DIR300, WarpDoc, and DocReal. Quantitative analysis shows that the proposed method effectively undistorts layout elements, such as text lines and table borders. The resources for further comparison are provided at https://github.com/caipeng328/ForCenNet.

The past a few years have witnessed the great success of large language models, demonstrating powerful capabilities in comprehending textual data and generating human-like languages. Large language models achieve success by being trained on vast amounts of textual data, including online sources with copyrighted content and user-generated knowledge. However, this comes at a cost: the potential risk of exposing users' privacy and violating copyright protections. Thus, to safeguard individuals' "right to be forgotten", there has been increasing interests in machine unlearning -- the process of removing information carried by particular training samples from a model while not deteriorating its predictive quality. This is a challenging task due to the black-box nature of language models. Most existing studies focus on mitigating the impact of those forgot samples upon a model's outputs, and do not explicitly consider the geometric distributions of samples in the latent space of a model. To address this issue, we propose a machine unlearning framework, named Deep Contrastive Unlearning for fine-Tuning (DeepCUT) language models. Our proposed model achieves machine unlearning by directly optimizing the latent space of a model. Comprehensive experiments on real-world datasets demonstrate the effectiveness and efficiency of DeepCUT with consistent and significant improvement over baseline methods.

This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and belong to a certain distributional uncertainty set. In our paper, we study three uncertainty sets for the unknown distributions. The neurodynamic duplex is designed based on three projection equations. The main contribution of our work is to propose a neural network-based method to solve distributionally robust joint chance-constrained optimization problems that converges in probability to the global optimum without the use of standard state-of-the-art solving methods. We show that neural networks can be used to solve multiple instances of a problem. In the numerical experiments, we apply the proposed approach to solve a problem of shape optimisation and a telecommunication problem.

We tackle the task of reconstructing hand-object interactions from short video clips. Given an input video, our approach casts 3D inference as a per-video optimization and recovers a neural 3D representation of the object shape, as well as the time-varying motion and hand articulation. While the input video naturally provides some multi-view cues to guide 3D inference, these are insufficient on their own due to occlusions and limited viewpoint variations. To obtain accurate 3D, we augment the multi-view signals with generic data-driven priors to guide reconstruction. Specifically, we learn a diffusion network to model the conditional distribution of (geometric) renderings of objects conditioned on hand configuration and category label, and leverage it as a prior to guide the novel-view renderings of the reconstructed scene. We empirically evaluate our approach on egocentric videos across 6 object categories, and observe significant improvements over prior single-view and multi-view methods. Finally, we demonstrate our system's ability to reconstruct arbitrary clips from YouTube, showing both 1st and 3rd person interactions.

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via composition. However, notwithstanding the potential performance benefit, the syntactically-aware DSMs proposed to date have huge numbers of parameters (compared to conventional DSMs) and suffer from data sparsity. Furthermore, the encoding of the SyG links (i.e., the syntactic relations) has been largely limited to linear maps. The knowledge graphs' literature, on the other hand, has proposed light-weight models employing different geometric transformations (GTs) to encode edges in a knowledge graph (KG). Our work explores the possibility of adopting this family of models to encode SyGs. Furthermore, we investigate which GT better encodes syntactic relations, so that these representations can be used to enhance phrase-level composition via syntactic contextualisation.

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing a complementary process of Reinforcement Learning with Verifiable Rewards (RLVR) into the data generation pipeline. By adopting RLVR to refine captions for geometric images synthesized from 50 basic geometric relations and using reward signals derived from mathematical problem-solving tasks, our pipeline successfully captures the key features of geometry problem-solving. This enables better task generalization and yields non-trivial improvements. Furthermore, even in out-of-distribution scenarios, the generated dataset enhances the general reasoning capabilities of multimodal large language models, yielding accuracy improvements of 2.8%-4.8% in statistics, arithmetic, algebraic, and numerical tasks with non-geometric input images of MathVista and MathVerse, along with 2.4%-3.9% improvements in Art, Design, Tech, and Engineering tasks in MMMU.

Deep Neural Networks are highly susceptible to shortcut learning, frequently memorizing low-dimensional spurious correlations instead of underlying causal mechanisms. This phenomenon not only degrades out-of-distribution robustness but also induces severe demographic biases in sensitive applications. In this paper, we propose a geometric a priori methodology to mitigate shortcut learning. By deploying a zero-hidden-layer (N=1) Topological Auditor, we mathematically isolate features that monopolize the gradient without human intervention. We empirically demonstrate a Capacity Phase Transition: once linear shortcuts are pruned, networks are forced to utilize higher geometric capacity (N geq 16) to curve the decision boundary and learn ethical representations. Our approach outperforms L1 Regularization -- which collapses into demographic bias -- and operates at a fraction of the computational cost of post-hoc methods like Just Train Twice (JTT), successfully reducing counterfactual gender vulnerability from 21.18\% to 7.66\%.

Modern video diffusion models require tens of denoising evaluations over long spatiotemporal token sequences. Distribution Matching Distillation (DMD) reduces the number of function evaluations (NFE) to just a few. However, DMD samples can degrade during training, exhibiting progressive oversaturation and artifacts. We trace this instability to critic errors, which enter successive student updates and accumulate over time. We introduce Projected Distribution Matching Distillation (PDMD) to filter critic errors. PDMD projects out the component of the DMD update parallel to the student-critic endpoint residual. At a fixed noisy query, we prove that this residual is an unbiased estimate of the critic's endpoint error. Under high-dimensional assumptions, this projection removes a constant fraction of critic error while discarding only a vanishing fraction of ideal DMD signal. Empirically, the projection stabilizes training and improves sample quality where DMD degrades and develops unnatural textures. PDMD requires only a one-line code change to DMD, with no extra loss, network, data, model pass, or multi-stage training. With Wan2.1, PDMD achieves a VBench total score of 83.73 at 4 NFE, surpassing matched DMD by 1.03 points. On MiniMax-H3 joint video-audio generation, PDMD achieves a VideoGen-Eval visual total score of 83.17, 0.41 points above the strongest distilled baseline. PDMD also achieves the best performance on all six audio metrics among the compared 4-NFE models. Qualitative comparisons and user studies favor PDMD over the distilled baselines in visual quality, motion, and audio quality. Code and models are available at https://pdmd2026.github.io/.

Local geometric information, i.e. normal and distribution of points, is crucial for LiDAR-based simultaneous localization and mapping (SLAM) because it provides constraints for data association, which further determines the direction of optimization and ultimately affects the accuracy of localization. However, estimating normal and distribution of points are time-consuming tasks even with the assistance of kdtree or volumetric maps. To achieve fast normal estimation, we look into the structure of LiDAR scan and propose a ring-based fast approximate least squares (Ring FALS) method. With the Ring structural information, estimating the normal requires only the range information of the points when a new scan arrives. To efficiently estimate the distribution of points, we extend the ikd-tree to manage the map in voxels and update the distribution of points in each voxel incrementally while maintaining its consistency with the normal estimation. We further fix the distribution after its convergence to balance the time consumption and the correctness of representation. Based on the extracted and maintained local geometric information, we devise a robust and accurate hierarchical data association scheme where point-to-surfel association is prioritized over point-to-plane. Extensive experiments on diverse public datasets demonstrate the advantages of our system compared to other state-of-the-art methods. Our open source implementation is available at https://github.com/tiev-tongji/LOG-LIO.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Object pose estimation is crucial to robotic perception and typically provides a single-pose estimate. However, a single estimate cannot capture pose uncertainty deriving from visual ambiguity, which can lead to unreliable behavior. Existing pose distribution methods rely heavily on color information, often unavailable in industrial settings. We propose a novel neural network-based method for estimating object pose uncertainty using only 3D colorless data. To the best of our knowledge, this is the first approach that leverages deep learning for pose distribution estimation without relying on RGB input. We validate our method in a real-world bin picking scenario with objects of varying geometric ambiguity. Our current implementation focuses on symmetries in reflection and revolution, but the framework is extendable to full SE(3) pose distribution estimation. Source code available at opde3d.github.io

We introduce VEGA, an approach for training navigation VisionLanguage-Action (VLA) models from unlabeled egocentric navigation videos. Internet-scale egocentric videos provide a scalable source of navigation-relevant visual observations, capturing cluttered scenes, close-range obstacles, and natural human motion through real-world spaces. However, these videos are not directly usable for policy learning because they do not provide obstacle-aware trajectories conditioned on explicit navigation goals in the robot's coordinate frame. VEGA addresses this gap by reconstructing local scene geometry from monocular video, sampling navigation goals (represented as text, image, or spatial waypoints) and generating obstacle-aware trajectories using the constructed geometry. The resulting trajectory distribution is then used to train a flow-matching VLA navigation policy. By using geometry exclusively during training, VEGA distills obstacle-aware planning directly into a vision-based policy. Furthermore, we introduce VEGA-Bench, a benchmark containing 250k scenes and approximately 5 million navigation goals paired with scene geometry, designed to evaluate goal progress, collision avoidance, and obstacle clearance of VLAs. Our evaluation shows that VEGA achieves competitive goal progress while reducing collisions by 33.0% and improving obstacle clearance by 17.9% over the strongest baseline on VEGABench, while improving success by at least 150.0%, reducing collisions by at least 66.7%, and improving obstacle clearance by at least 60.0% in real-world trials. Ultimately, we demonstrate that video-derived geometric supervision provides a scalable and effective signal for training obstacle-aware navigation VLAs. The code and benchmark will be released at the time of publication.

Joint-Embedding Predictive Architectures (JEPA) offer an appealing approach to self-supervised learning, but are typically prone to representation collapse. LeJEPA resolves this by introducing a theoretically grounded distribution-matching objective that drives the embedding towards an isotropic Gaussian. However, this approach is fundamentally tied to Euclidean assumptions, and its global target does not reflect domain-specific geometric priors, such as the use of non-Euclidean embedding geometries, e.g., equivariant CNNs or hyperbolic ViTs. We thus introduce LocaLeJEPA, a framework motivated by a manifold-theoretic reformulation of LeJEPA's entropy-maximization property. The accompanying LocaLeReg, a novel locally Euclidean distribution-matching regularizer, enables a stable and scalable implementation of the LocaLeJEPA framework. We then perform extensive experiments in the vision setting on models trained on ImageNet-1K. LocaLeJEPA significantly outperforms LeJEPA when paired with hyperbolic ViT-S/8 and equivariant ResNet-50 backbones, and also with ordinary Euclidean ViT-S/8 and ViT-L/14 backbones. This holds both in terms of linear and k-NN classification performance on ImageNet and on a series of downstream tasks tested. We view the LocaLeJEPA formalism as a principled approach to the JEPA paradigm that better respects intrinsic data geometry while also accommodating generalizations to exotic embedding geometries. Code available at https://github.com/alessioborgi/LocaLeJEPA.

Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width d_S can encode at most d_S cdot g(α) features, where g(α) = 1/((1-α)ln1{1-α}) is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure F approx 28{,}700 features at αapprox 0.992 (critical width d_S^* approx 1{,}065). Distillation into five student widths confirms the predicted monotonic floor ordering. The observed floor decomposes into a geometric component and a width-independent architectural baseline (R^2 = 0.993). Linear probing shows coarse concepts survive even 88% feature loss, revealing the floor arises from aggregate loss of fine-grained features in the importance distribution's long tail. Our results connect representation geometry to distillation limits and provide a practical tool for predicting distillation performance from SAE measurements alone.

Unbounded 3D world generation is emerging as a foundational task for scene modeling in computer vision, graphics, and robotics. In this work, we present WorldFlow3D, a novel method capable of generating unbounded 3D worlds. Building upon a foundational property of flow matching - namely, defining a path of transport between two data distributions - we model 3D generation more generally as a problem of flowing through 3D data distributions, not limited to conditional denoising. We find that our latent-free flow approach generates causal and accurate 3D structure, and can use this as an intermediate distribution to guide the generation of more complex structure and high-quality texture - all while converging more rapidly than existing methods. We enable controllability over generated scenes with vectorized scene layout conditions for geometric structure control and visual texture control through scene attributes. We confirm the effectiveness of WorldFlow3D on both real outdoor driving scenes and synthetic indoor scenes, validating cross-domain generalizability and high-quality generation on real data distributions. We confirm favorable scene generation fidelity over approaches in all tested settings for unbounded scene generation. For more, see https://light.princeton.edu/worldflow3d.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

3D point clouds play a pivotal role in outdoor scene perception, especially in the context of autonomous driving. Recent advancements in 3D LiDAR segmentation often focus intensely on the spatial positioning and distribution of points for accurate segmentation. However, these methods, while robust in variable conditions, encounter challenges due to sole reliance on coordinates and point intensity, leading to poor isometric invariance and suboptimal segmentation. To tackle this challenge, our work introduces Range-Aware Pointwise Distance Distribution (RAPiD) features and the associated RAPiD-Seg architecture. Our RAPiD features exhibit rigid transformation invariance and effectively adapt to variations in point density, with a design focus on capturing the localized geometry of neighboring structures. They utilize inherent LiDAR isotropic radiation and semantic categorization for enhanced local representation and computational efficiency, while incorporating a 4D distance metric that integrates geometric and surface material reflectivity for improved semantic segmentation. To effectively embed high-dimensional RAPiD features, we propose a double-nested autoencoder structure with a novel class-aware embedding objective to encode high-dimensional features into manageable voxel-wise embeddings. Additionally, we propose RAPiD-Seg which incorporates a channel-wise attention fusion and two effective RAPiD-Seg variants, further optimizing the embedding for enhanced performance and generalization. Our method outperforms contemporary LiDAR segmentation work in terms of mIoU on SemanticKITTI (76.1) and nuScenes (83.6) datasets.

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.

Standard LLM evaluation practices compress diverse abilities into single scores, obscuring their inherently multidimensional nature. We present JE-IRT, a geometric item-response framework that embeds both LLMs and questions in a shared space. For question embeddings, the direction encodes semantics and the norm encodes difficulty, while correctness on each question is determined by the geometric interaction between the model and question embeddings. This geometry replaces a global ranking of LLMs with topical specialization and enables smooth variation across related questions. Building on this framework, our experimental results reveal that out-of-distribution behavior can be explained through directional alignment, and that larger norms consistently indicate harder questions. Moreover, JE-IRT naturally supports generalization: once the space is learned, new LLMs are added by fitting a single embedding. The learned space further reveals an LLM-internal taxonomy that only partially aligns with human-defined subject categories. JE-IRT thus establishes a unified and interpretable geometric lens that connects LLM abilities with the structure of questions, offering a distinctive perspective on model evaluation and generalization.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

We introduce DrugFlow, a generative model for structure-based drug design that integrates continuous flow matching with discrete Markov bridges, demonstrating state-of-the-art performance in learning chemical, geometric, and physical aspects of three-dimensional protein-ligand data. We endow DrugFlow with an uncertainty estimate that is able to detect out-of-distribution samples. To further enhance the sampling process towards distribution regions with desirable metric values, we propose a joint preference alignment scheme applicable to both flow matching and Markov bridge frameworks. Furthermore, we extend our model to also explore the conformational landscape of the protein by jointly sampling side chain angles and molecules.

Persistent memory is a central capability for AI agents, yet the mathematical foundations of memory retrieval, lifecycle management, and consistency remain unexplored. Current systems employ cosine similarity for retrieval, heuristic decay for salience, and provide no formal contradiction detection. We establish information-geometric foundations through three contributions. First, a retrieval metric derived from the Fisher information structure of diagonal Gaussian families, satisfying Riemannian metric axioms, invariant under sufficient statistics, and computable in O(d) time. Second, memory lifecycle formulated as Riemannian Langevin dynamics with proven existence and uniqueness of the stationary distribution via the Fokker-Planck equation, replacing hand-tuned decay with principled convergence guarantees. Third, a cellular sheaf model where non-trivial first cohomology classes correspond precisely to irreconcilable contradictions across memory contexts. On the LoCoMo benchmark, the mathematical layers yield +12.7 percentage points over engineering baselines across six conversations, reaching +19.9 pp on the most challenging dialogues. A four-channel retrieval architecture achieves 75% accuracy without cloud dependency. Cloud-augmented results reach 87.7%. A zero-LLM configuration satisfies EU AI Act data sovereignty requirements by architectural design. To our knowledge, this is the first work establishing information-geometric, sheaf-theoretic, and stochastic-dynamical foundations for AI agent memory systems.

LiDAR-based 3D object detection is a critical technology for the development of autonomous driving and robotics. However, the high cost of data annotation limits its advancement. We propose a novel and effective active learning (AL) method called Distribution Discrepancy and Feature Heterogeneity (DDFH), which simultaneously considers geometric features and model embeddings, assessing information from both the instance-level and frame-level perspectives. Distribution Discrepancy evaluates the difference and novelty of instances within the unlabeled and labeled distributions, enabling the model to learn efficiently with limited data. Feature Heterogeneity ensures the heterogeneity of intra-frame instance features, maintaining feature diversity while avoiding redundant or similar instances, thus minimizing annotation costs. Finally, multiple indicators are efficiently aggregated using Quantile Transform, providing a unified measure of informativeness. Extensive experiments demonstrate that DDFH outperforms the current state-of-the-art (SOTA) methods on the KITTI and Waymo datasets, effectively reducing the bounding box annotation cost by 56.3% and showing robustness when working with both one-stage and two-stage models.

Flow matching (FM) has become a popular action head paradigm for modern embodied models. However, as a conditional generative model, it does not explicitly expose its inherent uncertainty, producing faulty action chunks even when it misinterprets the scene or encounters out-of-distribution (OOD) inputs. Therefore, determining when an FM-generated action can be trusted is essential for safe deployment, yet existing uncertainty estimation methods on real-time control suffer from several issues: extra training budget, high computational overhead, and low generalization ability. In this work, we provide a geometric interpretation of FM uncertainty in the velocity field, showing that uncertainty manifests as deviation from an ideal affine-isotropic contraction field. Building on this observation, we introduce denoising acceleration (accel), a highly-generalizable and cost-free uncertainty proxy that measures the bending of the denoising trajectory from a single forward pass, without additional model evaluations, training, or resampling. We theoretically and empirically demonstrate that accel is a faithful proxy for FM uncertainty and further test its utility in online failure detection. Results show that accel identifies failing rollouts well before termination, matching or even outperforming costly resampling- and training-based baselines across settings under realistic deployment budget. Code and demos available at: https://github.com/rrrrrrzy/fm-geometry.

Object detectors often produce over-confident predictions for objects outside their training categories, leading to so-called out-of-distribution (OoD) hallucinations. Existing approaches for detecting or mitigating such hallucinations typically either construct scoring functions directly over learned object detector representations or modify the object detector itself to suppress hallucination emergence. However, the latent priors implicitly encoded in these representations remain largely unexplored and have not been explicitly decoded for OoD detection. To uncover and exploit these latent priors, we propose Structured Prior Knowledge (SPK), a hallucination-oriented framework that explicitly elicits OoD-relevant priors from pretrained object detectors. Specifically, SPK leverages in-distribution data and hallucination-inducing samples as diagnostic supervision to elicit part-level semantic concepts underlying object detector decision-making, rather than using them merely for rejection or object detector adaptation. The elicited semantic priors are further integrated with geometric and contextual priors to form a compact five-dimensional SPK representation for OoD detection. Extensive experiments across diverse object detector architectures and multiple OoD benchmarks demonstrate that SPK achieves state-of-the-art OoD detection. Our findings reveal that pretrained object detectors already encode substantially richer latent knowledge than is typically exploited for OoD detection. More importantly, this knowledge can be explicitly elicited and organized into a compact, structured, and interpretable knowledge space for prediction reliability analysis. This suggests a promising proactive route for improving object detector reliability by explicitly uncovering and leveraging latent priors. Code and data are available at: https://gricad-gitlab.univ-grenoble-alpes.fr/dnn-safety/spk

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Visual Place Recognition (VPR) aims to match query images against a database using visual cues. State-of-the-art methods aggregate features from deep backbones to form global descriptors. Optimal transport-based aggregation methods reformulate feature-to-cluster assignment as a transport problem, but the standard Sinkhorn algorithm symmetrically treats source and target marginals, limiting effectiveness when image features and cluster centers exhibit substantially different distributions. We propose an asymmetric aggregation VPR method with geometric constraints for locally aggregated descriptors, called A^2GC-VPR. Our method employs row-column normalization averaging with separate marginal calibration, enabling asymmetric matching that adapts to distributional discrepancies in visual place recognition. Geometric constraints are incorporated through learnable coordinate embeddings, computing compatibility scores fused with feature similarities, thereby promoting spatially proximal features to the same cluster and enhancing spatial awareness. Experimental results on MSLS, NordLand, and Pittsburgh datasets demonstrate superior performance, validating the effectiveness of our approach in improving matching accuracy and robustness.

We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space P_2(M) is characterized by the geodesic convexity of entropy and is formulated as the response of probability distributions to optimal transport. We introduce effective Ricci curvatures K_{eff}^{(infty)} and K_{eff}^{(N)} associated with Kullback--Leibler-type and Rényi-type entropies, corresponding respectively to the curvature-dimension conditions CD(K,infty) and CD(K,N). By localizing these curvatures to finite scales using local and reference measures, we construct curvature indicators applicable to observational data. Under a local quadratic approximation, the effective curvature reduces to the Hessian of the log-density, showing that conventional Hessian-based structure classifications arise as a limiting case of the present framework. We further show that effective curvature depends on observational scale and formulate this dependence as a scale flow, distinct from Ricci flow because it describes a change of resolution rather than a time evolution of geometry. Treating curvature as a random field then extends the statistical description of density fields: curvature statistics are given by higher-order weighted integrals of the power spectrum and by spatial derivatives of the correlation function, emphasizing geometric rather than amplitude information. This framework provides a unified connection between optimal transport geometry and cosmological structure analysis, and offers a new perspective on multiscale structure and nonlinear statistics.

Adversarial training is effective on balanced datasets, but its robustness degrades under longtailed class distributions, where tail classes suffer high robust error and unstable decision boundaries. We propose Manifold-Constrained Adversarial Training (MCAT), a unified framework that enforces the semantic validity of adversarial examples by penalizing deviations from class-conditional manifolds in feature space, while promoting balanced geometric separation across classes via an ETF-inspired regularization. We provide theoretical results that link geometric separation to lower bounds on adversarially robust margins, and show that manifold-constrained adversarial risk upperbounds robust risk on high-density semantic regions. Extensive experiments on standard longtailed benchmarks demonstrate consistent improvements in overall, balanced, and tail-class adversarial robustness.

Supervised proxy-based deep cross-modal hashing has become the dominant paradigm for large-scale retrieval. However, prevalent methods model class proxies as deterministic points in the embedding space. This rigid assumption causes severe gradient conflicts in multi-label scenarios, where gradient conflicts arising from label co-occurrence lead to severe gradient contention and optimization collapse. To resolve this, we propose Kent-based Distributional Proxy Hashing (KDPH), a novel framework that shifts proxy representation from static points to flexible anisotropic Kent distributions on the hypersphere. Unlike point proxies that must shift their positions to accommodate conflicting gradients, KDPH absorbs these conflicts by dynamically adjusting its directional variance. This allows the proxy to maintain a stable semantic mean direction while stretching to cover diverse label correlations. Furthermore, to ensure stable training of these geometric parameters, we derive a tailored loss function incorporating the Cayley transform to enforce strict orthogonality. To the best of our knowledge, KDPH is the first framework to successfully introduce the Kent distributions into cross-modal hashing. Experiments on three benchmark datasets demonstrate that KDPH mitigates proxy collapse and chaotic oscillation, significantly outperforms state-of-the-art methods. Code is available at https://github.com/Senmo996/KDPH-official-code.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Recent advances in vision-language models (VLMs) have demonstrated remarkable zero-shot capabilities, yet adapting these models to specialized domains remains a significant challenge. Building on recent theoretical insights suggesting that independently trained VLMs are related by a canonical transformation, we extend this understanding to the concept of domains. We hypothesize that image features across disparate domains are related by a canonicalized geometric transformation that can be recovered using a small set of anchors. Few-shot classification provides a natural setting for this alignment, as the limited labeled samples serve as the anchors required to estimate this transformation. Motivated by this hypothesis, we introduce BiCLIP, a framework that applies a targeted transformation to multimodal features to enhance cross-modal alignment. Our approach is characterized by its extreme simplicity and low parameter footprint. Extensive evaluations across 11 standard benchmarks, including EuroSAT, DTD, and FGVCAircraft, demonstrate that BiCLIP consistently achieves state-of-the-art results. Furthermore, we provide empirical verification of existing geometric findings by analyzing the orthogonality and angular distribution of the learned transformations, confirming that structured alignment is the key to robust domain adaptation. Code is available at https://github.com/QuantitativeImagingLaboratory/BilinearCLIP

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via the 1-Wasserstein distance, using only paired data. This two-step approach minimizes an upper bound on the 1-Wasserstein distance between joint distributions, reducing reliance on scarce paired samples while enabling fast one-step generation. Theoretically, we establish non-asymptotic error bounds and demonstrate a key benefit of unpaired data: enhanced geometric fidelity in generated outputs. Furthermore, by extending the scope of its two core steps, LSDM provides a coherent statistical perspective that connects to a broad class of latent-space approaches. Notably, Latent Diffusion Models (LDMs) can be viewed as a variant of LSDM, in which joint distribution matching is achieved indirectly via score matching. Consequently, our results also provide theoretical insights into the consistency of LDMs. Empirical evaluations on real-world image tasks, including class-conditional generation and image super-resolution, demonstrate the effectiveness of LSDM in leveraging unpaired data to enhance generation quality.

Text-driven inversion of generative models is a core paradigm for manipulating 2D or 3D content, unlocking numerous applications such as text-based editing, style transfer, or inverse problems. However, it relies on the assumption that generative models remain sensitive to natural language prompts. We demonstrate that for state-of-the-art native text-to-3D generative models, this assumption often collapses. We identify a critical failure mode where generation trajectories are drawn into latent ``sink traps'': regions where the model becomes insensitive to prompt modifications. In these regimes, changes to the input text fail to alter internal representations in a way that alters the output geometry. Crucially, we observe that this is not a limitation of the model's geometric expressivity; the same generative models possess the ability to produce a vast diversity of shapes but, as we demonstrate, become insensitive to out-of-distribution text guidance. We investigate this behavior by analyzing the sampling trajectories of the generative model, and find that complex geometries can still be represented and produced by leveraging the model's unconditional generative prior. This leads to a more robust framework for text-based 3D shape editing that bypasses latent sinks by decoupling a model's geometric representation power from its linguistic sensitivity. Our approach addresses the limitations of current 3D pipelines and enables high-fidelity semantic manipulation of out-of-distribution 3D shapes. Project webpage: https://daidedou.sorpi.fr/publication/beyondprompts

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

Routine inspection of power distribution infrastructure remains challenging for utilities operating geographically dispersed networks, where conventional manual inspection can be difficult to perform consistently and at scale. This work presents a smartphone-based AI inspection system for assessing targeted distribution-infrastructure conditions from images captured by field personnel. The proposed workflow integrates image-quality and viewing-perspective validation with AI-assisted assessment of pole lean, crossarm and top-cleat tilt, voltage level, vegetation-clearance risk, and distribution-transformer (DTR)-ground clearance. The system integrates deep-learning models with monocular depth estimation, geometric analysis, and rule-based processing within a common multi-stage inspection workflow designed for practical field operation. The system was pilot deployed across five selected distribution feeders within the Eastern Power Distribution Company of Andhra Pradesh Ltd. (APEPDCL), where 1,222 defect instances were identified across the assessed categories and subsequently tracked through a rectification and verification workflow, with 84 defect instances recorded as rectified during the study period. Feeder-level interruption records were also examined over the study period; however, the available observations do not provide sufficient evidence to establish a reliability improvement attributable to the proposed system. A curated multi-module field-captured dataset, PD-Defect, is also publicly released to support reproducible research in distribution-infrastructure inspection. The field deployment demonstrates the practical integration of smartphone-based AI-assisted inspection into field inspection and maintenance activities, providing a mechanism for systematic identification, documentation, rectification tracking, and verification of targeted distribution-infrastructure defects.

Reconstructing 3D scenes from sparse views without per-scene optimization remains highly challenging, especially for recovering accurate geometry and fine textures. While recent feedforward approaches leverage generalizable 3D Gaussian Splatting (3DGS) for scene generation, they typically assign one or multiple Gaussians to each pixel. Such uniform allocation not only produces highly redundant representations by wasting primitives in homogeneous areas, but also fails to exploit the inherent geometric priors of planar surfaces, often resulting in sub-optimal structural modeling. To address these limitations, we present CompactSplat, a novel feedforward framework that enables a content-aware allocation of 3D Gaussians. By integrating texture-guided spatial partitioning with hierarchical sampling, CompactSplat adaptively distributes primitives - concentrating dense Gaussians in complex regions while tiling flat areas with expanded, scale-modulated primitives. Moreover, our framework inherently supports dynamic sparsity control at inference time, enabling seamless trade-offs between rendering fidelity and memory footprint without requiring network retraining. Extensive experiments on RealEstate10K, DL3DV, and ScanNet demonstrate that CompactSplat consistently outperforms prior methods on both standard metrics and high-resolution rendering consistency, achieving high-fidelity reconstructions with significantly fewer primitives.

Autonomous vehicles operating in open-world scenarios are inevitably confronted with previously unknown objects, such as exotic animals or loose cargo. The reliable detection and segmentation of these out-of-distribution (OOD) objects is therefore crucial for a safe understanding of the environment and decision-making. Most existing approaches require access to OOD training samples, retraining of the segmentation backbone, or dedicated auxiliary architectures, limiting their practical applicability. We propose a training-free method that derives dense OOD scores directly from the confidence predictions of a foundation segmentation model, without any task-specific fine-tuning or access to anomalous data. To improve the robustness of our OOD segmentation, geometric information from monocular depth estimation is incorporated into the decision process, providing complementary cues to uncertainty-based predictions. We evaluate the proposed method on the SegmentMeIfYouCan benchmark and additionally assess its performance on OOD tracking in video sequences, reflecting the temporal nature of real-world perception systems. The method performs strongly on road-centered benchmarks.

Diffusion-based virtual try-on methods achieve photorealistic synthesis through cross-attention mechanisms that transfer garment features to target body regions. However, these approaches rely on implicit learning of spatial correspondences, struggling to preserve fine details such as text and illustrations. We propose a novel approach, which we call SIFT-VTON, that utilizes SIFT keypoint matching to provide explicit geometric guidance for diffusion-based virtual try-on. Our method applies domain-specific filtering to SIFT keypoint matches between garment and person images, then converts these correspondences into spatial probability distributions that supervise cross-attention layers during training. This explicit supervision guides the model to learn precise spatial alignment, concentrating attention on geometrically consistent garment regions. Experiments on the VITON-HD dataset demonstrate significant improvements on unpaired metrics while maintaining competitive paired reconstruction metrics. Qualitative comparisons show superior preservation of text clarity and pattern alignment. Attention visualizations confirm that our method produces sharply focused attention on relevant garment details. This work demonstrates that classical geometric correspondence methods can effectively enhance modern diffusion models for conditional synthesis tasks. The source code will be available at https://github.com/takesukeDS/SIFT-VTON.

Consolidating specialized foundation models into a unified generalist is a central goal of post-training. Two approaches are in common use: model merging, which is fast but treated as a heuristic, and multi-teacher on-policy distillation, which matches distributions but demands heavy rollout compute and suffers from cross-task gradient conflict. We show that the two are one objective seen at different orders. Within a shared basin of homologous specialists, the multi-teacher on-policy distillation objective is, to second order, exactly the Fisher-merging objective. Its minimizer is therefore the Fisher merge, a classic model-merging method given by a closed-form combination of the specialists, so merging is optimal, to second order, as a closed-form stage of distillation. Building on this identification, we propose Residual-Governed Branch-and-Merge(RGBM), a two-phase consolidation procedure. Concretely, a full-parameter Fisher merge is intractable on foundation models, so Phase~1 restricts the merge to the task-vector subspace. Extending tangent-space analyses of merging, we show that the same coefficients that mix task vectors also mix implicit rewards, which lets a residual program on unlabelled prompts solve for them. The program minimizes the worst per-domain residual and reports its energy-normalized values as the domain residual spectrum. Phase~2 lets this spectrum govern what may be added: RGBM passivates domains with low normalized residuals, trains isolated branches only for domains above the spectral gap, and writes back the admitted updates with calibrated shrinkage. On two open-source consolidation suites, the Phase~1 merge alone matches or outperforms fully trained multi-teacher distillation, and RGBM improves on it further with zero extra joint-training steps, whereas every un-gated write-back, including continued joint distillation from the merge, falls below it.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

LiDAR place recognition approaches based on deep learning suffer a significant degradation in performance when there is a shift between the distribution of the training and testing datasets, with re-training often required to achieve top performance. However, obtaining accurate ground truth on new environments can be prohibitively expensive, especially in complex or GPS-deprived environments. To address this issue we propose GeoAdapt, which introduces a novel auxiliary classification head to generate pseudo-labels for re-training on unseen environments in a self-supervised manner. GeoAdapt uses geometric consistency as a prior to improve the robustness of our generated pseudo-labels against domain shift, improving the performance and reliability of our Test-Time Adaptation approach. Comprehensive experiments show that GeoAdapt significantly boosts place recognition performance across moderate to severe domain shifts, and is competitive with fully supervised test-time adaptation approaches. Our code will be available at https://github.com/csiro-robotics/GeoAdapt.

Detecting out-of-distribution (OOD) data is a critical challenge in machine learning due to model overconfidence, often without awareness of their epistemological limits. We hypothesize that ``neural collapse'', a phenomenon affecting in-distribution data for models trained beyond loss convergence, also influences OOD data. To benefit from this interplay, we introduce NECO, a novel post-hoc method for OOD detection, which leverages the geometric properties of ``neural collapse'' and of principal component spaces to identify OOD data. Our extensive experiments demonstrate that NECO achieves state-of-the-art results on both small and large-scale OOD detection tasks while exhibiting strong generalization capabilities across different network architectures. Furthermore, we provide a theoretical explanation for the effectiveness of our method in OOD detection. Code is available at https://gitlab.com/drti/neco

3D Morphable Models (3DMMs) provide promising 3D face reconstructions in various applications. However, existing methods struggle to reconstruct faces with extreme expressions due to deficiencies in supervisory signals, such as sparse or inaccurate landmarks. Segmentation information contains effective geometric contexts for face reconstruction. Certain attempts intuitively depend on differentiable renderers to compare the rendered silhouettes of reconstruction with segmentation, which is prone to issues like local optima and gradient instability. In this paper, we fully utilize the facial part segmentation geometry by introducing Part Re-projection Distance Loss (PRDL). Specifically, PRDL transforms facial part segmentation into 2D points and re-projects the reconstruction onto the image plane. Subsequently, by introducing grid anchors and computing different statistical distances from these anchors to the point sets, PRDL establishes geometry descriptors to optimize the distribution of the point sets for face reconstruction. PRDL exhibits a clear gradient compared to the renderer-based methods and presents state-of-the-art reconstruction performance in extensive quantitative and qualitative experiments. Our project is available at https://github.com/wang-zidu/3DDFA-V3 .

The reconstruction of indoor scenes remains challenging due to the inherent complexity of spatial structures and the prevalence of textureless regions. Recent advancements in 3D Gaussian Splatting have improved novel view synthesis with accelerated processing but have yet to deliver comparable performance in surface reconstruction. In this paper, we introduce 2DGS-Room, a novel method leveraging 2D Gaussian Splatting for high-fidelity indoor scene reconstruction. Specifically, we employ a seed-guided mechanism to control the distribution of 2D Gaussians, with the density of seed points dynamically optimized through adaptive growth and pruning mechanisms. To further improve geometric accuracy, we incorporate monocular depth and normal priors to provide constraints for details and textureless regions respectively. Additionally, multi-view consistency constraints are employed to mitigate artifacts and further enhance reconstruction quality. Extensive experiments on ScanNet and ScanNet++ datasets demonstrate that our method achieves state-of-the-art performance in indoor scene reconstruction.

Mechanistic interpretability aims to explain a model's behavior by identifying causally responsible internal structures. Dictionary-based explainers such as sparse autoencoders and transcoders are a primary tool, but their faithfulness under out-of-distribution (OOD) shift has received little systematic attention. We show that distribution shift rotates the subspace that the model actively uses, misaligning the explainer's dictionary trained on in-distribution (ID) activations. We formalize this misalignment as the faithfulness gap, a geometric distance between the ID dictionary and the OOD-active subspace, and show that it controls OOD faithfulness degradation. To reduce this gap, we propose the Geometry-Adaptive Explainer (GAE), which realigns the explainer's dictionary with the OOD-active subspace while preserving the original feature structure. This requires only unlabeled OOD activations and no gradient updates. We prove that GAE improves over the unadapted ID explainer, with excess loss bounded quadratically by the second-moment shift. Empirically, GAE even matches or surpasses all training-based baselines in causal faithfulness across multiple models and OOD settings.

Vision-Language-Action (VLA) models drive next-generation autonomous systems, but training them requires scalable, high-quality annotations from complex environments. Current cloud pipelines rely on generic vision-language models (VLMs) that lack geometric reasoning and domain semantics due to their 2D image-text pretraining. To address this mismatch, we propose XEmbodied, a cloud-side foundation model that endows VLMs with intrinsic 3D geometric awareness and interaction with physical cues (e.g., occupancy grids, 3D boxes). Instead of treating geometry as auxiliary input, XEmbodied integrates geometric representations via a structured 3D Adapter and distills physical signals into context tokens using an Efficient Image-Embodied Adapter. Through progressive domain curriculum and reinforcement learning post-training, XEmbodied preserves general capabilities while demonstrating robust performance across 18 public benchmarks. It significantly improves spatial reasoning, traffic semantics, embodied affordance, and out-of-distribution generalization for large-scale scenario mining and embodied VQA.

Chain-of-Thought (CoT) improves the reasoning ability of Large Language Models (LLMs) but incurs substantial computation and context costs. Existing methods either lose intermediate information through hard pruning or lack a principled criterion for continuous compression. We present A*-Thought-V2, a geometric dynamics of LLM guided framework that models CoT as a hidden-state trajectory and replaces hard deletion with an explicit-implicit interleaved latent architecture. After projecting question, step, and solution representations into a 3D PCA space, it measures alignment between each local transition and global question-to-solution direction. Aligned steps remain explicit text, whereas deviating steps are compressed into continuous latent tokens. Directional angles capture both local semantics and reasoning dynamics: small angles indicate direct execution and answer formation, while large angles more frequently involve checking, correction, and branch exploration; their temporal variation reveals exploration, convergence, and refinement stages. To train this architecture, we introduce stepwise embedding forcing, which pools each redundant step into a single latent embedding, and label forcing, which supervises that latent token with a soft multi-modal vocabulary distribution instead of a hard one-hot label. Experiments on Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks show that A*-Thought-V2 improves average accuracy by up to 2.6% while reducing response length by up to half, increasing Accuracy per Computation Unit by 2.29times, and reducing preprocessing and training time by 94.6% and up to 80.3%, respectively. Representation analyses suggest that latent states form a compact region distinct from textual states, while higher entropy at latent-token positions reflects broader soft targets that encourage richer step-level feature learning.

Biometric authentication systems increasingly use privacy-preserving mechanisms to protect sensitive templates. However, the authentication interface itself may still leak information that enables reconstruction attacks. Prior attacks exploit released similarity scores, whereas more advanced systems reveal only the binary accept/reject decision. This binary feedback provides substantially less information, making template reconstruction far more challenging. In this work, we introduce query-efficient reconstruction attacks under extremely limited feedback, addressing two key limitations of prior attacks. First, we introduce the first attack that reconstructs protected biometric templates using only authentication success/failure feedback by exploiting the geometric constraints of biometric authentication. Second, we introduce distribution-aware query-efficient reconstruction methods for score-releasing systems, achieving a more realistic threat model by reducing the number of required queries by a factor of 5times compared to recent prior score-based attacks. Finally, we combine these two insights by incorporating a pretrained facial diffusion prior into our geometric binary attack, reducing the number of required queries by a factor of 5times. Our findings reveal a fundamental security limitation of biometric authentication: independently of the template protection mechanism, the authentication process itself exposes geometric information that can enable perfect template reconstruction up to numerical precision. Moreover, the distribution of biometric templates can be leveraged to make significantly more effective reconstruction attacks.

Depth images captured by Time-of-Flight (ToF) sensors are prone to noise, requiring denoising for reliable downstream applications. Previous works either focus on single-frame processing, or perform multi-frame processing without considering depth variations at corresponding pixels across frames, leading to undesirable temporal inconsistency and spatial ambiguity. In this paper, we propose a novel ToF depth denoising network leveraging motion-invariant graph fusion to simultaneously enhance temporal stability and spatial sharpness. Specifically, despite depth shifts across frames, graph structures exhibit temporal self-similarity, enabling cross-frame geometric attention for graph fusion. Then, by incorporating an image smoothness prior on the fused graph and data fidelity term derived from ToF noise distribution, we formulate a maximum a posterior problem for ToF denoising. Finally, the solution is unrolled into iterative filters whose weights are adaptively learned from the graph-informed geometric attention, producing a high-performance yet interpretable network. Experimental results demonstrate that the proposed scheme achieves state-of-the-art performance in terms of accuracy and consistency on synthetic DVToF dataset and exhibits robust generalization on the real Kinectv2 dataset. Source code will be released at https://github.com/davidweidawang/GIGA-ToF{https://github.com/davidweidawang/GIGA-ToF}.

Recent advances in foundational Video Diffusion Models (VDMs) have yielded significant progress. Yet, despite the remarkable visual quality of generated videos, reconstructing consistent 3D scenes from these outputs remains challenging, due to limited camera controllability and inconsistent generated content when viewed from distinct camera trajectories. In this paper, we propose WorldStereo, a novel framework that bridges camera-guided video generation and 3D reconstruction via two dedicated geometric memory modules. Formally, the global-geometric memory enables precise camera control while injecting coarse structural priors through incrementally updated point clouds. Moreover, the spatial-stereo memory constrains the model's attention receptive fields with 3D correspondence to focus on fine-grained details from the memory bank. These components enable WorldStereo to generate multi-view-consistent videos under precise camera control, facilitating high-quality 3D reconstruction. Furthermore, the flexible control branch-based WorldStereo shows impressive efficiency, benefiting from the distribution matching distilled VDM backbone without joint training. Extensive experiments across both camera-guided video generation and 3D reconstruction benchmarks demonstrate the effectiveness of our approach. Notably, we show that WorldStereo acts as a powerful world model, tackling diverse scene generation tasks (whether starting from perspective or panoramic images) with high-fidelity 3D results. Models will be released.

Geometric analysis fundamentally distinguishes between extrinsic and intrinsic perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely PRISM, for Pre-training, which learns isometric embeddings by Recovering the Intrinsic Surface geodesic Metric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.

Recent progress in 3D/4D scene generation emphasizes the importance of physical alignment throughout video generation and scene reconstruction. However, existing methods improve the alignment separately at each stage, making it difficult to manage subtle misalignments arising from another stage. Here, we present SteerX, a zero-shot inference-time steering method that unifies scene reconstruction into the generation process, tilting data distributions toward better geometric alignment. To this end, we introduce two geometric reward functions for 3D/4D scene generation by using pose-free feed-forward scene reconstruction models. Through extensive experiments, we demonstrate the effectiveness of SteerX in improving 3D/4D scene generation.

Category-level object pose estimation aims to predict the 6D pose and size of previously unseen instances from predefined categories, requiring strong generalization across diverse object instances. Although many previous methods attempt to mitigate intra-class variations, they often struggle with instances exhibiting complex geometries or significant deviations from canonical shapes. To address this issue, we propose INKL-Pose, a novel category-level object pose estimation framework that enables INstance-adaptive Keypoint Learning with local-to-global geometric aggregation. Specifically, our method first predicts semantically consistent and geometrically informative keypoints using an Instance-Adaptive Keypoint Detector, then refines them: (1) a Local Keypoint Feature Aggregator capturing fine-grained geometries, and (2) a Global Keypoint Feature Aggregator using bidirectional Mamba for structural consistency. To enable bidirectional modeling in Mamba, we introduce a simple yet effective Feature Sequence Flipping strategy that preserves spatial coherence while constructing backward feature sequence. Additionally, we design a surface loss and a separation loss to encourage uniform coverage and spatial diversity in keypoint distribution. The resulting keypoints are mapped to a canonical space for 6D pose and size regression. Extensive experiments on CAMERA25, REAL275, and HouseCat6D show that INKL-Pose achieves state-of-the-art performance with 16.7M parameters and runs at 36 FPS on an NVIDIA RTX 4090D GPU.

Latent action world models let agents plan new behaviors at test time by predicting how actions change the environment, and joint-embedding predictive architectures (JEPAs) do so by forecasting future latent states rather than pixels. Yet nearly all such models see the world through a camera, even though robotic manipulation is fundamentally geometric: in robotics goals for manipulation are traditionally specified by target object poses, not by images of the object once placed. We ask whether latent planning survives a shift from appearance to geometry, on the observation side as well as on the goal specifications side. To answer this, we extend the stable-worldmodel evaluation platform with simulated LiDAR-style raycast point clouds as a new sensor modality, and adapt three JEPA designs to point clouds: a frozen-encoder model built on Utonia features, a distribution-prior model based on LeWM, and an action-sensitive model based on Delta-JEPA. We further introduce a goal-encoding mechanism that constructs the goal latent from the current latent and a 3D target pose, removing the need for goal images or goal point clouds. A comparative evaluation of the different anti-collapse mechanisms shows that point-cloud world models can match their image-based counterparts, demonstrating that the modality shift from appearance to geometry is achievable. All models are released as open weights with open-source training and inference code, to make world-model planning accessible for LiDAR-driven and pose-directed robotic tasks.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

Software vulnerability detection is critical for ensuring software security and reliability. Despite recent advances in deep learning, real-world vulnerability datasets suffer from two severe challenges: frequency imbalance and difficulty imbalance. We reinterpret these challenges from an embedding geometry perspective, observing that such imbalances induce geometric distortions in hyperspherical representation space. To address this issue, we propose MARGIN, a metric-based framework that learns discriminative vulnerability representations through adaptive margin metric learning and hyperspherical prototype modeling. MARGIN dynamically adjusts geometric regularization according to the distribution structure estimated by the von Mises-Fisher concentration, aligning the probability mass of embedding distributions with their corresponding Voronoi cells, thereby reducing geometric distortion and yielding more stable decision boundaries. Extensive experiments on public vulnerability datasets show that MARGIN consistently outperforms strong baselines, achieving notable improvements in classification and detection, especially on challenging, imbalanced datasets. Further analysis demonstrates that MARGIN produces more structured embedding geometries, improving robustness, interpretability, and generalization.

How can a robot efficiently extract a desired object from a shelf when it is fully occluded by other objects? Prior works propose geometric approaches for this problem but do not consider object semantics. Shelves in pharmacies, restaurant kitchens, and grocery stores are often organized such that semantically similar objects are placed close to one another. Can large language models (LLMs) serve as semantic knowledge sources to accelerate robotic mechanical search in semantically arranged environments? With Semantic Spatial Search on Shelves (S^4), we use LLMs to generate affinity matrices, where entries correspond to semantic likelihood of physical proximity between objects. We derive semantic spatial distributions by synthesizing semantics with learned geometric constraints. S^4 incorporates Optical Character Recognition (OCR) and semantic refinement with predictions from ViLD, an open-vocabulary object detection model. Simulation experiments suggest that semantic spatial search reduces the search time relative to pure spatial search by an average of 24% across three domains: pharmacy, kitchen, and office shelves. A manually collected dataset of 100 semantic scenes suggests that OCR and semantic refinement improve object detection accuracy by 35%. Lastly, physical experiments in a pharmacy shelf suggest 47.1% improvement over pure spatial search. Supplementary material can be found at https://sites.google.com/view/s4-rss/home.

Background: Accurate glottal segmentation in high-speed videoendoscopy (HSV) is essential for extracting kinematic biomarkers of laryngeal function. However, existing deep learning models often produce spurious artifacts in non-glottal frames and fail to generalize across different clinical settings. Methods: We propose a detection-gated pipeline that integrates a localizer with a segmenter. A temporal consistency wrapper ensures robustness by suppressing false positives during glottal closure and occlusion. The segmenter was trained on a limited subset of the GIRAFE dataset (600 frames), while the localizer was trained on the BAGLS training set. The in-distribution localizer provides a tight region of interest (ROI), removing geometric anatomical variations and enabling cross-dataset generalization without fine-tuning. Results: The pipeline achieved state-of-the-art performance on the GIRAFE (DSC=0.81) and BAGLS (DSC=0.85) benchmarks and demonstrated superior generalizability. Notably, the framework maintained robust cross-dataset generalization (DSC=0.77). Downstream validation on a 65-subject clinical cohort confirmed that automated kinematic features - specifically the Open Quotient and Glottal Area Waveform (GAW) - remained consistent with clinical benchmarks. The coefficient of variation (CV) of the glottal area was a significant marker for distinguishing healthy from pathological vocal function (p=0.006). Conclusions: This architecture provides a computationally efficient solution (~35 frames/s) suitable for real-time clinical use. By overcoming cross-dataset variability, this framework facilitates the standardized, large-scale extraction of clinical biomarkers across diverse endoscopy platforms. Code, trained weights, and evaluation scripts are released at https://github.com/hari-krishnan/openglottal.

Classic 3D scene graph generation approaches fail to work in real-time due to the heavy computational cost of environment mapping and the need to generate intermediate point-cloud representations. To alleviate this issue, a recent work eschews point clouds in favor of a lightweight Gaussian distribution for each object. This approximation drastically speeds up inference and enables real-time 3D scene graph generation. However, the representation has two key weaknesses. 1) Each object is approximated by a single 3D Gaussian, which causes a severe loss of 3D geometric detail. 2) The discrepancy between this approximation and the true object geometry exacerbates the inaccurate merging of object candidates during online inference. To address these issues, we propose NoPA, which represents each object as a separate non-parametric distribution. This formulation retains 3D geometric information while preserving real-time inference of the parametric Gaussian formulation. To build upon our novel object representation, we propose a tailored merging strategy to recover coherent object instances. Specifically, we leverage maximum mean discrepancy on kernel density estimates to enable robust merging of object candidates during online exploration while minimizing added computational complexity. The key is to maintain a fixed particle set per object. Furthermore, to rectify the relation loss caused by misclassified objects, NoPA propagates relationships between objects with high affinity. Experiments show that NoPA substantially outperforms current methods without sacrificing real-time inference speed.

Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens -- a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that interprets LLM hidden states as points on a latent semantic manifold: a Riemannian submanifold equipped with the Fisher information metric, where tokens correspond to Voronoi regions partitioning the manifold. We define the expressibility gap, a geometric measure of the semantic distortion from vocabulary discretization, and prove two theorems: a rate-distortion lower bound on distortion for any finite vocabulary, and a linear volume scaling law for the expressibility gap via the coarea formula. We validate these predictions across six transformer architectures (124M-1.5B parameters), confirming universal hourglass intrinsic dimension profiles, smooth curvature structure, and linear gap scaling with slopes 0.87-1.12 (R^2 > 0.985). The margin distribution across models reveals a persistent hard core of boundary-proximal representations invariant to scale, providing a geometric decomposition of perplexity. We discuss implications for architecture design, model compression, decoding strategies, and scaling laws

Auxiliary signal pathways in VLMs are routinely fitted with learnable gates so the optimiser can decide how much of the signal to admit. We find that the optimiser almost always decides on zero: across five injection designs, every gated pathway becomes behaviourally closed, with accuracy invariant to ablating the pathway at inference even when the gate parameter would nominally pass 30-45% of the signal. We attribute this suppression phenomenon to two regimes, a dead-gradient regime formalised through the caption-invariance of image-derived signals, and a negative-utility regime in which the auxiliary signal actively hurts the loss. Rather than fight suppression, we exploit it: we regularise LoRA fine-tuning with geometric auxiliary losses from hyperbolic visual relational graphs (IoA-driven entailment cones and angular repulsion on the Lorentz manifold), coupled only through the forward pass at training time and dropped at inference. Disaggregating GQA by question type exposes a clean dissociation. Three configurations without geometric losses at inference lose 2.85-3.39pp on relational questions while gaining ~1pp on attribute questions; a fourth that trains with the losses but infers through a soft prompt loses 5.14pp on rel for only +0.23pp on attr, so training-time regularisation alone does not protect relational accuracy without a geometric inference pathway. Configurations that keep the geometric pathway at inference preserve vanilla-level relational accuracy and match the attribute gain. Out of distribution on VSR, the RMS-prefix recipe preserves the spatial signal; stripping the geometric losses (G2) collapses VSR by 4.6pp, isolating them as the OOD source. A secondary result: embedding-norm alignment is necessary for generation-safe prefix injection, and learnable gates should be replaced with fixed, non-optional injection at matched scales.

While static word embedding models are known to represent linguistic analogies as parallel lines in high-dimensional space, the underlying mechanism as to why they result in such geometric structures remains obscure. We find that an elementary contrastive-style method employed over distributional information performs competitively with popular word embedding models on analogy recovery tasks, while achieving dramatic speedups in training time. Further, we demonstrate that a contrastive loss is sufficient to create these parallel structures in word embeddings, and establish a precise relationship between the co-occurrence statistics and the geometric structure of the resulting word embeddings.

Autonomous manipulation of articulated objects remains a fundamental challenge for robots in human environments. Vision-based methods can infer hidden kinematics but can yield imprecise estimates on unfamiliar objects. Tactile approaches achieve robust control through contact feedback but require accurate initialization. This suggests a natural synergy: vision for global guidance, touch for local precision. Yet no framework systematically exploits this complementarity for generalized articulated manipulation. Here we present Vi-TacMan, which uses vision to propose grasps and coarse directions that seed a tactile controller for precise execution. By incorporating surface normals as geometric priors and modeling directions via von Mises-Fisher distributions, our approach achieves significant gains over baselines (all p<0.0001). Critically, manipulation succeeds without explicit kinematic models -- the tactile controller refines coarse visual estimates through real-time contact regulation. Tests on more than 50,000 simulated and diverse real-world objects confirm robust cross-category generalization. This work establishes that coarse visual cues suffice for reliable manipulation when coupled with tactile feedback, offering a scalable paradigm for autonomous systems in unstructured environments.

Implicit Neural Representations (INRs) have become an essential tool for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Popular architectures such as SIREN, WIRE, and FINER demonstrate the potential of INR for capturing fine-grained image details. However, traditional INRs often lack explicit geometric structure and have limited capabilities for local editing or integration with physical simulation, restricting their applicability in dynamic or interactive settings. To address these limitations, we propose GaINeR: Geometry-Aware Implicit Network Representation, a novel framework for 2D images that combines trainable Gaussian distributions with a neural network-based INR. For a given image coordinate, the model retrieves the K nearest Gaussians, aggregates distance-weighted embeddings, and predicts the RGB value via a neural network. This design enables continuous image representation, interpretable geometric structure, and flexible local editing, providing a foundation for physically aware and interactive image manipulation. The official implementation of our method is publicly available at https://github.com/WJakubowska/GaINeR.

Low-light image enhancement is challenging due to complex degradations, including amplified noise, artifacts, and color distortion. While Retinex-based deep learning methods have achieved promising results, they primarily rely on single-modality RGB information. We propose M2Retinexformer (Multi-Modal Retinexformer), a novel framework that extends Retinexformer by incorporating depth cues, luminance priors, and semantic features within a progressive refinement pipeline. Depth provides geometric context that is invariant to lighting variations, while luminance and semantic features offer explicit guidance on brightness distribution and scene understanding. Modalities are extracted at multiple scales and fused through cross-attention, with adaptive gating dynamically balancing illumination-guided self-attention and cross-attention based on the reliability of auxiliary cues. Evaluations on the LOL, SID, SMID, and SDSD benchmarks demonstrate overall improvements over Retinexformer and recent state-of-the-art methods. Code and pretrained weights are available at https://github.com/YoussefAboelwafa/M2Retinexformer

Vision-Language models like CLIP have been widely adopted for various tasks due to their impressive zero-shot capabilities. However, CLIP is not suitable for extracting 3D geometric features as it was trained on only images and text by natural language supervision. We work on addressing this limitation and propose a new framework termed CG3D (CLIP Goes 3D) where a 3D encoder is learned to exhibit zero-shot capabilities. CG3D is trained using triplets of pointclouds, corresponding rendered 2D images, and texts using natural language supervision. To align the features in a multimodal embedding space, we utilize contrastive loss on 3D features obtained from the 3D encoder, as well as visual and text features extracted from CLIP. We note that the natural images used to train CLIP and the rendered 2D images in CG3D have a distribution shift. Attempting to train the visual and text encoder to account for this shift results in catastrophic forgetting and a notable decrease in performance. To solve this, we employ prompt tuning and introduce trainable parameters in the input space to shift CLIP towards the 3D pre-training dataset utilized in CG3D. We extensively test our pre-trained CG3D framework and demonstrate its impressive capabilities in zero-shot, open scene understanding, and retrieval tasks. Further, it also serves as strong starting weights for fine-tuning in downstream 3D recognition tasks.

Recent work has promoted task-aware layer pruning as a way to improve model performance on particular tasks, as shown by TALE. In this paper, we investigate when such improvements occur and why. We show first that, across controlled polynomial regression tasks and large language models, such pruning yields no benefit on in-distribution (ID) data but consistently improves out-of-distribution (OOD) accuracy. We further show empirically that OOD inputs induce layerwise norm and pairwise-distance profiles that deviate from the corresponding ID profiles. This leads to a geometric explanation of task-aware pruning: each task induces a task-adapted geometry, characterized empirically by the representation profiles observed on ID inputs. OOD inputs can introduce a distorted version of the task-adapted geometry. Task-aware pruning identifies layers that create or amplify this distortion; by removing them, it shifts OOD representational norms and pairwise distances toward those observed on the adapted distribution. This realigns OOD inputs with the model's task-adapted geometry and improves performance. We provide causal evidence through controlled distribution shifts and residual-scaling interventions, and demonstrate consistent behavior across model scales.

Modern deep networks remain fragile under distribution shift and adversarial perturbations, often due to excessive or poorly structured input sensitivity. We introduce TASER (Task-Aware Stein Regularisation), a training-time regularisation framework derived from Langevin Stein operators. By penalising pointwise Stein residuals under the training distribution, TASER encourages geometric compatibility between predictors and data density, inducing anisotropic, data-aware smoothness. We provide theoretical links between Stein regularisation and reduced first-order shift sensitivity, develop scalable implementation variants compatible with modern architectures, and demonstrate improved robustness and stability across regression and vision benchmarks. Across CIFAR-10 experiments, TASER consistently improves the adversarial robustness of established training methods without incurring statistically significant clean-accuracy degradation.

Vision-language models (VLMs) pretrained on large-scale image-text pairs demonstrate strong image-level understanding, but are primarily optimized for global alignment and do not explicitly encode fine-grained anatomical structure, limiting their suitability for spatially precise tasks such as segmentation. We introduce CheXanatomy, a framework that integrates explicit anatomical knowledge into a pretrained VLM through autoregressive token-space supervision. Instead of adding task-specific decoder heads, the model is trained to generate anatomical segmentation masks via next-token prediction. To enable scalable supervision, we synthesize realistic chest radiographs from CT volumes and forward-project CT segmentation labels to obtain anatomically consistent 2D masks. We evaluate the approach on synthetic and real chest radiographs against a U-Net baseline, including ablations on model scale, input resolution, and vision encoder fine-tuning. Autoregressive anatomical supervision achieves performance comparable to specialized convolutional models in-distribution and demonstrates improved geometric robustness under domain shift to real CXR data. In addition, anatomy-pretrained models exhibit improved sample efficiency when adapting to novel localization tasks under limited supervision. Larger models and higher input image resolution improve performance, while vision encoder fine-tuning has limited effect. These results show that embedding anatomical structure directly into the generative objective promotes spatially grounded representations and supports anatomy-aware medical vision-language modeling.

Kinematic rigs provide a structured interface for articulating 3D meshes but lack any associated pose space, i.e., an explicit representation of the plausible manifold of joint configurations for a given mesh. Without such a pose space, stochastic sampling or manual manipulation of raw rig parameters easily results in semantic and/or geometric violations, such as anatomical hyperextension and non-physical self-intersections. We propose Video-informed Pose Spaces (ViPS), a feedforward framework that discovers the latent distribution of valid articulations for auto-rigged meshes by distilling motion priors from a pretrained video diffusion model. Unlike existing methods that rely on scarce, artist-authored 4D datasets, or focus on reconstructing instances of individual motions, ViPS transfers generative video model priors into a universal distribution over the given rig parameterization. Differentiable geometric validators applied to the skinned mesh enforce shape-specific integrity without requiring manual regularizers. Our feedforward model reveals a smooth, compact, and controllable pose space. This, in turn, supports sampling for diverse shape variations, manifold projection for inverse kinematics, and temporally coherent trajectories for animation and keyframing. Further, the distilled 3D pose samples serve as semantic proxies to guide video diffusion, effectively closing the loop between generative 2D priors and structured 3D kinematic control. Our evaluations show that ViPS, trained solely using video priors, matches the performance of state-of-the-art models trained on synthetic artist-created 4D data in both plausibility and diversity. Additionally, as a universal model, ViPS exhibits robust zero-shot generalization to out-of-distribution species and unseen skeletal topologies.

Panoramic video depth estimation is pivotal for applications such as Virtual Reality and World Models. However, advancements in this field are impeded by two primary obstacles: the scarcity of large-scale training data and the unique spatiotemporal challenges of Equirectangular Projection (ERP), which hinder the direct transfer of perspective models. In this paper, we first present PanoCARLA, a large-scale synthetic RGB-D panoramic video dataset, featuring natural motion trajectories and drone-like roaming perspectives. Building on this foundation, we propose PVDepth, an end-to-end framework adapted from perspective video depth models. To tackle ERP-specific geometric distortions and consequent non-linear temporal dynamics, we introduce two core mechanisms: (1) A Progressive Sphere-aware Noise Initialization strategy that anneals the noise distribution from planar to spherical, guiding the model to adapt to non-uniform information density; and (2) A Cube-rectified Temporal Modeling module that incorporates an auxiliary cubemap temporal branch to rectify non-linear temporal dynamics in the ERP domain. Extensive experiments demonstrate that PVDepth achieves superior performance, generating geometrically accurate and temporally consistent depth sequences. Code and data will be released at https:// github.com/ChuanxinSong/PVDepth.

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the multi-modality and noise-sensitive nature of molecule geometry. This work introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits molecule geometry by modeling diverse modalities in the differentiable parameter space of distributions. GeoBFN maintains the SE-(3) invariant density modeling property by incorporating equivariant inter-dependency modeling on parameters of distributions and unifying the probabilistic modeling of different modalities. Through optimized training and sampling techniques, we demonstrate that GeoBFN achieves state-of-the-art performance on multiple 3D molecule generation benchmarks in terms of generation quality (90.87% molecule stability in QM9 and 85.6% atom stability in GEOM-DRUG. GeoBFN can also conduct sampling with any number of steps to reach an optimal trade-off between efficiency and quality (e.g., 20-times speedup without sacrificing performance).

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

Vision-Language-Action (VLA) models trained with flow matching have demonstrated impressive capabilities on robotic manipulation tasks. However, their performance often degrades under distribution shift and on complex multi-step tasks, suggesting that the learned representations may not robustly capture task-relevant semantics. We introduce DiG-Flow, a principled framework that enhances VLA robustness through geometric regularization. Our key insight is that the distributional discrepancy between observation and action embeddings provides a meaningful geometric signal: lower transport cost indicates compatible representations, while higher cost suggests potential misalignment. DiG-Flow computes a discrepancy measure between empirical distributions of observation and action embeddings, maps it to a modulation weight via a monotone function, and applies residual updates to the observation embeddings before flow matching. Crucially, this intervention operates at the representation level without modifying the flow matching path or target vector field. We provide theoretical guarantees showing that discrepancy-guided training provably decreases the training objective, and that guided inference refinement converges with contraction. Empirically, DiG-Flow integrates into existing VLA architectures with negligible overhead and consistently improves performance, with particularly pronounced gains on complex multi-step tasks and under limited training data.

Industrial quality inspection plays a critical role in modern manufacturing by identifying defective products during production. While single-modality approaches using either 3D point clouds or 2D RGB images suffer from information incompleteness, multimodal anomaly detection offers promise through the complementary fusion of crossmodal data. However, existing methods face challenges in effectively integrating unimodal results and improving discriminative power. To address these limitations, we first reinterpret memory bank-based anomaly scores in single modalities as isotropic Euclidean distances in local feature spaces. Dynamically evolving from Euclidean metrics, we propose a novel Geometry-Guided Score Fusion (G^{2}SF) framework that progressively learns an anisotropic local distance metric as a unified score for the fusion task. Through a geometric encoding operator, a novel Local Scale Prediction Network (LSPN) is proposed to predict direction-aware scaling factors that characterize first-order local feature distributions, thereby enhancing discrimination between normal and anomalous patterns. Additionally, we develop specialized loss functions and score aggregation strategy from geometric priors to ensure both metric generalization and efficacy. Comprehensive evaluations on the MVTec-3D AD and Eyecandies datasets demonstrate the state-of-the-art detection performance of our method, and detailed ablation analysis validates each component's contribution. Our code is available at https://github.com/ctaoaa/G2SF.

Safety-aligned language models refuse harmful requests through learned refusal behaviors encoded in their internal representations. Recent activation-based jailbreaking methods circumvent these safety mechanisms by applying orthogonal projections to remove refusal directions, but these approaches treat refusal as a one-dimensional phenomenon and ignore the rich distributional structure of model activations. We introduce a principled framework based on optimal transport theory that transforms the entire distribution of harmful activations to match harmless ones. By combining PCA with closed-form Gaussian optimal transport, we achieve efficient computation in high-dimensional representation spaces while preserving essential geometric structure. Across six models (Llama-2, Llama-3.1, Qwen-2.5; 7B-32B parameters), our method achieves up to 11% higher attack success rates than state-of-the-art baselines while maintaining comparable perplexity, demonstrating superior preservation of model capabilities. Critically, we discover that layer-selective intervention (applying optimal transport to 1-2 carefully chosen layers at approximately 40-60% network depth) substantially outperforms full-network interventions, revealing that refusal mechanisms may be localized rather than distributed. Our analysis provides new insights into the geometric structure of safety representations and suggests that current alignment methods may be vulnerable to distributional attacks beyond simple direction removal.

We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing state-of-the-art 1-bit methods. We attribute this degradation to Latent Geometry Misalignment: standard singular vectors exhibit high coherence (spiky distribution), the worst-case geometry for binary quantization. To realize this gain, we propose LittleBit-2, a framework employing Internal Latent Rotation and Joint Iterative Quantization (Joint-ITQ). This approach acts as a geometric preconditioner, aligning coherent latent distributions with the binary hypercube with zero inference overhead. Empirically, LittleBit-2 establishes a new state-of-the-art in the sub-1-bit regime (1sim0.1 bpp) on Llama-2 and Llama-3, matching the fidelity of leading 1-bit baselines.

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance.

For human-centric large-scale scenes, fine-grained modeling for 3D human global pose and shape is significant for scene understanding and can benefit many real-world applications. In this paper, we present LiveHPS, a novel single-LiDAR-based approach for scene-level human pose and shape estimation without any limitation of light conditions and wearable devices. In particular, we design a distillation mechanism to mitigate the distribution-varying effect of LiDAR point clouds and exploit the temporal-spatial geometric and dynamic information existing in consecutive frames to solve the occlusion and noise disturbance. LiveHPS, with its efficient configuration and high-quality output, is well-suited for real-world applications. Moreover, we propose a huge human motion dataset, named FreeMotion, which is collected in various scenarios with diverse human poses, shapes and translations. It consists of multi-modal and multi-view acquisition data from calibrated and synchronized LiDARs, cameras, and IMUs. Extensive experiments on our new dataset and other public datasets demonstrate the SOTA performance and robustness of our approach. We will release our code and dataset soon.

3D Gaussian Splatting (3DGS) has recently attracted wide attentions in various areas such as 3D navigation, Virtual Reality (VR) and 3D simulation, due to its photorealistic and efficient rendering performance. High-quality reconstrution of 3DGS relies on sufficient splats and a reasonable distribution of these splats to fit real geometric surface and texture details, which turns out to be a challenging problem. We present GeoTexDensifier, a novel geometry-texture-aware densification strategy to reconstruct high-quality Gaussian splats which better comply with the geometric structure and texture richness of the scene. Specifically, our GeoTexDensifier framework carries out an auxiliary texture-aware densification method to produce a denser distribution of splats in fully textured areas, while keeping sparsity in low-texture regions to maintain the quality of Gaussian point cloud. Meanwhile, a geometry-aware splitting strategy takes depth and normal priors to guide the splitting sampling and filter out the noisy splats whose initial positions are far from the actual geometric surfaces they aim to fit, under a Validation of Depth Ratio Change checking. With the help of relative monocular depth prior, such geometry-aware validation can effectively reduce the influence of scattered Gaussians to the final rendering quality, especially in regions with weak textures or without sufficient training views. The texture-aware densification and geometry-aware splitting strategies are fully combined to obtain a set of high-quality Gaussian splats. We experiment our GeoTexDensifier framework on various datasets and compare our Novel View Synthesis results to other state-of-the-art 3DGS approaches, with detailed quantitative and qualitative evaluations to demonstrate the effectiveness of our method in producing more photorealistic 3DGS models.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

Cross-modal ship re-identification (ReID) between optical and synthetic aperture radar (SAR) imagery is fundamentally challenged by the severe radiometric discrepancy between passive optical imaging and coherent active radar sensing. While existing approaches primarily rely on statistical distribution alignment or semantic matching, they often overlook a critical physical prior: ships are rigid objects whose geometric structures remain stable across sensing modalities, whereas texture appearance is highly modality-dependent. In this work, we propose SDF-Net, a Structure-Aware Disentangled Feature Learning Network that systematically incorporates geometric consistency into optical--SAR ship ReID. Built upon a ViT backbone, SDF-Net introduces a structure consistency constraint that extracts scale-invariant gradient energy statistics from intermediate layers to robustly anchor representations against radiometric variations. At the terminal stage, SDF-Net disentangles the learned representations into modality-invariant identity features and modality-specific characteristics. These decoupled cues are then integrated through a parameter-free additive residual fusion, effectively enhancing discriminative power. Extensive experiments on the HOSS-ReID dataset demonstrate that SDF-Net consistently outperforms existing state-of-the-art methods. The code and trained models are publicly available at https://github.com/cfrfree/SDF-Net.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Text-driven 3D scene editing has recently attracted increasing attention. Most existing methods follow a render-edit-optimize pipeline, where multi-view images are rendered from a 3D scene, edited with 2D image editors, and then used to optimize the underlying 3D representation. However, cross-view inconsistency remains a major bottleneck. Although recent methods introduce geometric cues, cross-view interactions, or video priors to mitigate this issue, they still largely rely on inference-time synchronization and thus remain limited in robustness and generalization.In this work, we recast multi-view consistent 3D editing from a distributional perspective: 3D scene editing essentially requires a joint distribution modeling across viewpoints.Based on this insight, we propose a view-consistent 3D editing framework that explicitly introduces cross-view dependencies into the editing process. Furthermore, motivated by the observation that structural correspondence and semantic continuity rely on different cross-view cues, we introduce a dual-path consistency mechanism consisting of projection-guided structural guidance and patch-level semantic propagation for effective cross-view editing. Further, we construct a paired multi-view editing dataset that provides reliable supervision for learning cross-view consistency in edited scenes. Extensive experiments demonstrate that our method achieves superior editing performance with precise and consistent views for complex scenes.

Contrastive audio-language pretraining yields powerful joint representations, yet a persistent audio-text modality gap limits the benefits of coupling multimodal encoders with large language models (LLMs). We present Diffusion-Link, a diffusion-based modality-bridging module that generatively maps audio embeddings into the text-embedding distribution. The module is trained at the output embedding from the frozen multimodal encoder and implemented as a lightweight network with three residual MLP blocks. To assess the effect of Diffusion-Link on multimodal encoder-LLM coupling, we evaluate on Automatic Audio Captioning (AAC); to our knowledge, this is the first application of diffusion-based modality bridging to AAC. We report two results. (1) Modality-gap analysis: on similarity and geometric criteria, Diffusion-Link reduces the modality gap the most among prior diffusion-based methods and shows a collective migration of audio embeddings toward the text distribution. (2) Downstream AAC: attaching Diffusion-Link to the same multimodal LLM baseline achieves state-of-the-art on AudioCaps in both zero-shot and fully supervised captioning without external knowledge, with relative gains up to 52.5% and 7.5%, respectively. These findings show that closing the modality gap is pivotal for effective coupling between multimodal encoders and LLMs, and diffusion-based modality bridging offers a promising direction beyond knowledge-retrieval-centric designs. Code will be released upon acceptance https://github.com/DevKiHyun/Diffusion-Link

As models and data scale, independently trained networks often induce analogous notions of similarity. But, matching similarities is weaker than establishing an explicit correspondence between the representation spaces, especially for multimodal models, where consistency must hold not only within each modality, but also for the learned image-text coupling. We therefore ask: given two independently trained multimodal contrastive models (with encoders (f, g) and (f,g)) -- trained on different distributions and with different architectures -- does a systematic geometric relationship exist between their embedding spaces? If so, what form does it take, and does it hold uniformly across modalities? In this work, we show that across model families such as CLIP, SigLIP, and FLAVA, this geometric relationship is well approximated by an orthogonal map (up to a global mean shift), i.e., there exists an orthogonal map Q where Q^top Q = I such that f(x)approx Q f(x) for paired images x. Strikingly, the same Q simultaneously aligns the text encoders i.e., g(y)approx Q g(y) for texts y. Theoretically, we prove that if the multimodal kernel agrees across models on a small anchor set i.e. langle f(x), g(y)rangle approx langle f(x), g(y)rangle, then the two models must be related by a single orthogonal map Q and the same Q maps images and text across models. More broadly, this finding enables backward-compatible model upgrades, avoiding costly re-embedding, and has implications for the privacy of learned representations. Our project page: https://canonical-multimodal.github.io/

Realistic sound simulation plays a critical role in many applications. A key element in sound simulation is the room impulse response (RIR), which characterizes how sound propagates within a given space. Recent studies have applied neural implicit methods to learn RIR using context information collected from the environment, such as scene images. However, these approaches do not effectively leverage explicit geometric information from the environment. To further exploit neural implicit models with direct geometric features, we present MiNAF, which queries a rough room mesh at given locations and extracts distance distributions as an explicit representation of local context. Our approach demonstrates that incorporating explicit local geometric features can better guide the model in generating more accurate RIR predictions. Through comparisons with conventional and state-of-the-art methods, we show that MiNAF performs competitively across various evaluation metrics.

3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representations automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet -- a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.

Multimodal Large Language Models (MLLMs) that directly process RGB inputs for tasks like 3D localization and navigation have shown remarkable potential. However, we argue that these RGB-only approaches are fundamentally flawed in their ability to generalize across cameras. By ignoring camera parameters, they entangle an object's physical properties with the camera's perspective, creating an irresolvable ambiguity. We show this leads MLLMs to overfit to the training camera distribution, rather than learning true and generalizable 3D geometric principles. To address this, we propose Camera-Aware MLLM framework for spatial MLLMs. It learns generalizable spatial reasoning by: (i) injecting camera intrinsics via a dense embedding that conditions each visual token; (ii) introducing a camera-aware data augmentation strategy that synthetically varies camera parameters, forcing the model to disentangle camera properties from scene content; and (iii) distilling geometric priors from a 3D vision foundation model. Extensive experiments demonstrate that camera-aware MLLMs substantially outperform their naive counterparts, particularly in cross-camera generalization tests on spatially-grounded tasks, indicating that camera-awareness is not only beneficial but also a prerequisite for robust and generalizable spatial intelligence in MLLMs.

Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We study this question through statistical provability: the probability of reaching a verified proof within a budget on a specified stream of theorem instances. We model formal proof search as a finite-horizon reachability MDP with deterministic verifier dynamics, and show that under a faithful state abstraction the optimal success probability coincides with ordinary syntactic provability. We then analyze a simple but practically important pipeline: depth-wise offline action-value regression followed by greedy test-time proving. Our main theorem bounds the provability gap between the learned prover and the optimal prover by an occupancy-weighted sum of uniform action-value errors; in the common uniform-error reading, the leading complexity multiplier is the learned prover's average truncated proof length. The error decomposes into approximation error, geometric coverage of the training distribution, and Monte Carlo label noise, and improves to a fast rate under an action-gap margin condition. The result gives a component-sensitive account of why verifier feedback, retrieval, representation geometry, and proof-shortening mechanisms help on biased theorem workloads, without contradicting classical worst-case hardness.

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: https://github.com/thiamine128/PriorEdit3D.

Metamaterials are artificially engineered structures whose mechanical and physical behaviors are strongly shaped by geometry rather than composition. Voxel representation provides a unified format for metamaterial geometry generation, as it can express diverse classes such as truss, shell, and porous structures within a single cubic discretization. However, voxel-based generation faces a plausibility-novelty trade-off: staying close to known geometries helps preserve geometric regularities, while moving away from them is necessary for novelty but may produce degenerate geometries. To address this challenge, we propose REGDIFF, a generative framework that couples voxel representation with latent space regulation and guided diffusion. REGDIFF introduces a repel-and-sink (RAS) mechanism to smooth the latent distribution of plausible geometries, and short-range repulsion (SRR) guidance to discourage generation overly close to known samples while maintaining geometric plausibility. We further contribute a voxel-based benchmark covering truss- and shell-type metamaterial geometries, together with an evaluation module for geometric plausibility, novelty, and diversity. Experiments show that REGDIFF outperforms voxel-based generative baselines, achieving +8.9% in geometric plausibility, +46.4% in novelty, and +128.6% in diversity on average across two datasets. These results suggest that REGDIFF is a strong geometry candidate generator for downstream evaluation. Our code is provided at https://github.com/wzhan24/ReGDiff.

Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect do interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.

We present Diffusion Soup, a compartmentalization method for Text-to-Image Generation that averages the weights of diffusion models trained on sharded data. By construction, our approach enables training-free continual learning and unlearning with no additional memory or inference costs, since models corresponding to data shards can be added or removed by re-averaging. We show that Diffusion Soup samples from a point in weight space that approximates the geometric mean of the distributions of constituent datasets, which offers anti-memorization guarantees and enables zero-shot style mixing. Empirically, Diffusion Soup outperforms a paragon model trained on the union of all data shards and achieves a 30% improvement in Image Reward (.34 to .44) on domain sharded data, and a 59% improvement in IR (.37 to .59) on aesthetic data. In both cases, souping also prevails in TIFA score (respectively, 85.5 to 86.5 and 85.6 to 86.8). We demonstrate robust unlearning -- removing any individual domain shard only lowers performance by 1% in IR (.45 to .44) -- and validate our theoretical insights on anti-memorization using real data. Finally, we showcase Diffusion Soup's ability to blend the distinct styles of models finetuned on different shards, resulting in the zero-shot generation of hybrid styles.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

Large language models (LLMs) are increasingly utilized for machine translation, yet their predictions often exhibit uncertainties that hinder interpretability and user trust. Effectively visualizing these uncertainties can enhance the usability of LLM outputs, particularly in contexts where translation accuracy is critical. This paper addresses two primary objectives: (1) providing users with token-level insights into model confidence and (2) developing a web-based visualization tool to quantify and represent translation uncertainties. To achieve these goals, we utilized the T5 model with the WMT19 dataset for translation tasks and evaluated translation quality using established metrics such as BLEU, METEOR, and ROUGE. We introduced three novel uncertainty quantification (UQ) metrics: (1) the geometric mean of token probabilities, (2) the arithmetic mean of token probabilities, and (3) the arithmetic mean of the kurtosis of token distributions. These metrics provide a simple yet effective framework for evaluating translation performance. Our analysis revealed a linear relationship between the traditional evaluation metrics and our UQ metrics, demonstrating the validity of our approach. Additionally, we developed an interactive web-based visualization that uses a color gradient to represent token confidence. This tool offers users a clear and intuitive understanding of translation quality while providing valuable insights into model performance. Overall, we show that our UQ metrics and visualization are both robust and interpretable, offering practical tools for evaluating and accessing machine translation systems.

Learning robotic manipulation policies directly in the real world can be expensive and time-consuming. While reinforcement learning (RL) policies trained in simulation present a scalable alternative, effective sim-to-real transfer remains challenging, particularly for tasks that require precise dynamics. To address this, we propose Phys2Real, a real-to-sim-to-real RL pipeline that combines vision-language model (VLM)-inferred physical parameter estimates with interactive adaptation through uncertainty-aware fusion. Our approach consists of three core components: (1) high-fidelity geometric reconstruction with 3D Gaussian splatting, (2) VLM-inferred prior distributions over physical parameters, and (3) online physical parameter estimation from interaction data. Phys2Real conditions policies on interpretable physical parameters, refining VLM predictions with online estimates via ensemble-based uncertainty quantification. On planar pushing tasks of a T-block with varying center of mass (CoM) and a hammer with an off-center mass distribution, Phys2Real achieves substantial improvements over a domain randomization baseline: 100% vs 79% success rate for the bottom-weighted T-block, 57% vs 23% in the challenging top-weighted T-block, and 15% faster average task completion for hammer pushing. Ablation studies indicate that the combination of VLM and interaction information is essential for success. Project website: https://phys2real.github.io/ .

Endeavors have been recently made to transfer knowledge from the labeled pinhole image domain to the unlabeled panoramic image domain via Unsupervised Domain Adaptation (UDA). The aim is to tackle the domain gaps caused by the style disparities and distortion problem from the non-uniformly distributed pixels of equirectangular projection (ERP). Previous works typically focus on transferring knowledge based on geometric priors with specially designed multi-branch network architectures. As a result, considerable computational costs are induced, and meanwhile, their generalization abilities are profoundly hindered by the variation of distortion among pixels. In this paper, we find that the pixels' neighborhood regions of the ERP indeed introduce less distortion. Intuitively, we propose a novel UDA framework that can effectively address the distortion problems for panoramic semantic segmentation. In comparison, our method is simpler, easier to implement, and more computationally efficient. Specifically, we propose distortion-aware attention (DA) capturing the neighboring pixel distribution without using any geometric constraints. Moreover, we propose a class-wise feature aggregation (CFA) module to iteratively update the feature representations with a memory bank. As such, the feature similarity between two domains can be consistently optimized. Extensive experiments show that our method achieves new state-of-the-art performance while remarkably reducing 80% parameters.

3D-aware face generators are typically trained on 2D real-life face image datasets that primarily consist of near-frontal face data, and as such, they are unable to construct one-quarter headshot 3D portraits with complete head, neck, and shoulder geometry. Two reasons account for this issue: First, existing facial recognition methods struggle with extracting facial data captured from large camera angles or back views. Second, it is challenging to learn a distribution of 3D portraits covering the one-quarter headshot region from single-view data due to significant geometric deformation caused by diverse body poses. To this end, we first create the dataset 360{\deg}-Portrait-HQ (360{\deg}PHQ for short) which consists of high-quality single-view real portraits annotated with a variety of camera parameters (the yaw angles span the entire 360{\deg} range) and body poses. We then propose 3DPortraitGAN, the first 3D-aware one-quarter headshot portrait generator that learns a canonical 3D avatar distribution from the 360{\deg}PHQ dataset with body pose self-learning. Our model can generate view-consistent portrait images from all camera angles with a canonical one-quarter headshot 3D representation. Our experiments show that the proposed framework can accurately predict portrait body poses and generate view-consistent, realistic portrait images with complete geometry from all camera angles.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

With the rapid development of speech generation technology, discrete codec representations have been widely used because they provide a stable prediction paradigm. In expressive speech generation, however, the quantization bottleneck of discrete codecs results in information gaps in fine-grained prosody, timbre, pronunciation, and frame-to-frame continuity. Continuous representations (e.g., VAE latents), by eliminating this constraint, have emerged as a more effective alternative for autoregressive modeling. Yet when continuous representations are used as autoregressive prediction targets, prediction errors can accumulate along the generation chain, causing latent drift and degrading long-form stability. To mitigate this problem, we propose SphereVAE, which constrains the VAE latent space to the unit hypersphere. SphereVAE defines a Power Spherical posterior on the hypersphere and regularizes the latent distribution toward a uniform prior, so that information is encoded mainly by directional variation, providing a bounded geometric target for autoregressive prediction and reducing the risk of norm drift. SphereVAE underperforms the standard VAE on reconstruction metrics due to reduced latent freedom. However, when integrated into VoxCPM for zero-shot TTS and long-text generation, it yields lower content error rates with comparable speaker similarity, and shows more stable long-range speaker consistency. These results indicate that an appropriate latent geometric constraint can effectively mitigate autoregressive error accumulation and drift in speech generation.

Activation steering methods are widely used to control large language model (LLM) behavior and are often interpreted as revealing meaningful internal representations. This interpretation assumes that steering directions are identifiable and uniquely recoverable from input-output behavior. We show that, under white-box single-layer access, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we find that orthogonal perturbations achieve near-equivalent efficacy with negligible effect sizes across multiple models and traits, with pre-trained semantic classifiers confirming equivalence at the output level. We estimate null-space dimensionality via SVD of activation covariance matrices and validate that equivalence holds robustly throughout the operationally relevant steering range. Critically, we show that non-identifiability is a robust geometric property that persists across diverse prompt distributions. These findings reveal fundamental interpretability limits and highlight the need for structural constraints beyond behavioral testing to enable reliable alignment interventions.

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.