Daily Papers

Most learning-based approaches to category-level 6D pose estimation are design around normalized object coordinate space (NOCS). While being successful, NOCS-based methods become inaccurate and less robust when handling objects of a category containing significant intra-category shape variations. This is because the object coordinates induced by global and rigid alignment of objects are semantically incoherent, making the coordinate regression hard to learn and generalize. We propose Semantically-aware Object Coordinate Space (SOCS) built by warping-and-aligning the objects guided by a sparse set of keypoints with semantically meaningful correspondence. SOCS is semantically coherent: Any point on the surface of a object can be mapped to a semantically meaningful location in SOCS, allowing for accurate pose and size estimation under large shape variations. To learn effective coordinate regression to SOCS, we propose a novel multi-scale coordinate-based attention network. Evaluations demonstrate that our method is easy to train, well-generalizing for large intra-category shape variations and robust to inter-object occlusions.

The goal of this paper is to estimate the 6D pose and dimensions of unseen object instances in an RGB-D image. Contrary to "instance-level" 6D pose estimation tasks, our problem assumes that no exact object CAD models are available during either training or testing time. To handle different and unseen object instances in a given category, we introduce a Normalized Object Coordinate Space (NOCS)---a shared canonical representation for all possible object instances within a category. Our region-based neural network is then trained to directly infer the correspondence from observed pixels to this shared object representation (NOCS) along with other object information such as class label and instance mask. These predictions can be combined with the depth map to jointly estimate the metric 6D pose and dimensions of multiple objects in a cluttered scene. To train our network, we present a new context-aware technique to generate large amounts of fully annotated mixed reality data. To further improve our model and evaluate its performance on real data, we also provide a fully annotated real-world dataset with large environment and instance variation. Extensive experiments demonstrate that the proposed method is able to robustly estimate the pose and size of unseen object instances in real environments while also achieving state-of-the-art performance on standard 6D pose estimation benchmarks.

We introduce a novel grasp representation named the Unified Gripper Coordinate Space (UGCS) for grasp synthesis and grasp transfer. Our representation leverages spherical coordinates to create a shared coordinate space across different robot grippers, enabling it to synthesize and transfer grasps for both novel objects and previously unseen grippers. The strength of this representation lies in the ability to map palm and fingers of a gripper and the unified coordinate space. Grasp synthesis is formulated as predicting the unified spherical coordinates on object surface points via a conditional variational autoencoder. The predicted unified gripper coordinates establish exact correspondences between the gripper and object points, which is used to optimize grasp pose and joint values. Grasp transfer is facilitated through the point-to-point correspondence between any two (potentially unseen) grippers and solved via a similar optimization. Extensive simulation and real-world experiments showcase the efficacy of the unified grasp representation for grasp synthesis in generating stable and diverse grasps. Similarly, we showcase real-world grasp transfer from human demonstrations across different objects.

As current Multimodal Large Language Models rapidly saturate canonical visual reasoning benchmarks, a key question emerges: do these strong scores genuinely reflect robust visual understanding? We identify a pervasive vulnerability, the Cartesian Shortcut: visual reasoning benchmarks prevalently build on orthogonal grid-based layouts that can be readily discretized into explicit textual coordinates. Models systematically exploit this property, heavily leveraging text-based deductive reasoning to assist visual problem-solving. To systematically dismantle this shortcut, we introduce Polaris-Bench, which re-formulates 53 visual reasoning tasks in Polar coordinate space with paired Cartesian counterparts as reference, while preserving consistent logical constraints and task semantics -- thus fundamentally breaking the orthogonal prior that models exploit. Comprehensive evaluation across 14 state-of-the-art MLLMs reveals that frontier models achieving 70--83% on Cartesian layouts collapse to 31--39% on Polar equivalents, with degradation persisting even under complete logical equivalence. Moreover, reasoning gains observed on Cartesian layouts are severely diminished on Polar equivalents. These findings expose a critical deficiency in current MLLMs: the lack of topology-invariant visual reasoning.

We present PhysiFormer, a diffusion transformer for physically-plausible 3D object motion. Unlike video world models that operate in view-dependent pixel space, PhysiFormer represents objects as 3D meshes expressed in world coordinates. Given the initial vertex positions and velocities, as well as object material type, rigid or elastic, the model samples future vertex trajectories. While related neural physics approaches build on ad-hoc latent spaces or explicitly enforce rigidity and causality, PhysiFormer shows that excellent results can be obtained without any such inductive biases, by casting vertex trajectory prediction as a single denoising diffusion process directly in world coordinates. The probabilistic formulation captures uncertainty in the learned dynamics, enabling diverse plausible futures from initial conditions, making this framework potentially useful for applications with unobserved uncertainty. The model features attention factorised over time, space, and objects for efficiency, enabling permutation-invariant multi-object reasoning without needing explicit object encoding. Trained on over 100k simulated trajectories, PhysiFormer generates rigid and elastic mechanics, and generalises to mixed-material settings, unseen real-world geometries, and larger object counts. It substantially outperforms autoregressive baselines in trajectory accuracy, rigidity preservation, and momentum-based physical consistency. Our results position coordinate-space diffusion as a promising step toward view-invariant, geometry-aware world modelling for robotics, graphics, and physical design. Visualisations, code, and models are available at https://yimingc9.github.io/physiformer.

Current works on multi-person 3D pose estimation mainly focus on the estimation of the 3D joint locations relative to the root joint and ignore the absolute locations of each pose. In this paper, we propose the Human Depth Estimation Network (HDNet), an end-to-end framework for absolute root joint localization in the camera coordinate space. Our HDNet first estimates the 2D human pose with heatmaps of the joints. These estimated heatmaps serve as attention masks for pooling features from image regions corresponding to the target person. A skeleton-based Graph Neural Network (GNN) is utilized to propagate features among joints. We formulate the target depth regression as a bin index estimation problem, which can be transformed with a soft-argmax operation from the classification output of our HDNet. We evaluate our HDNet on the root joint localization and root-relative 3D pose estimation tasks with two benchmark datasets, i.e., Human3.6M and MuPoTS-3D. The experimental results show that we outperform the previous state-of-the-art consistently under multiple evaluation metrics. Our source code is available at: https://github.com/jiahaoLjh/HumanDepth.

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained in two stages: first, a data compressor is trained, and in a subsequent training stage a flow matching generative model is trained in the latent space of the data compressor. This two-stage paradigm sets obstacles for unifying models across data domains, as hand-crafted compressors architectures are used for different data modalities. To this end, we introduce INRFlow, a domain-agnostic approach to learn flow matching transformers directly in ambient space. Drawing inspiration from INRs, we introduce a conditionally independent point-wise training objective that enables INRFlow to make predictions continuously in coordinate space. Our empirical results demonstrate that INRFlow effectively handles different data modalities such as images, 3D point clouds and protein structure data, achieving strong performance in different domains and outperforming comparable approaches. INRFlow is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains.

We present WebFovea, a vision-based web agent that placed 2nd in the WebRetriever Challenge 2026 with a final score of 57.0 out of 100. The challenge evaluates agents end to end on Protocol III of the WebRetriever benchmark (arXiv:2607.06118): starting from an entry URL on a live website, the agent must operate the site's own interface and return a verifiable answer. A capable multimodal large language model (LLM) is necessary for this, but not sufficient. The model's decisions reach the browser through the harness, the code between the model and the page. At every step, four things must go right: the model's reply must be parsed into the intended action, the action must take effect on the page, the result must be reported back accurately, and the model must be shown the information it needs. On real websites, many of the failures we observed occurred at one of these four stages rather than in the model's reasoning. A coordinate-space mismatch placed every click at 3/4 of its intended coordinates; actions on native dropdowns, inside iframes, and in text boxes failed silently; and self-generated chat-template tokens contaminated 4.9% of task episodes. WebFovea hardens each stage and surrounds the loop with guardrails that keep the agent within the rules and its budget. The four-stage view does not depend on the model, although some individual fixes do. Because we used the same model in all four submissions, the rise of our official hidden-set score from 31.0 to 57.0 reflects changes to the harness, up to run-to-run variance on live sites. We describe the design, the evidence for each component (including negative results), a failure analysis, the limitations, and a roadmap that includes routing different steps to different models. Code is available at https://github.com/jianganghan/WebFovea.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Advances in deep learning recognition have led to accurate object detection with 2D images. However, these 2D perception methods are insufficient for complete 3D world information. Concurrently, advanced 3D shape estimation approaches focus on the shape itself, without considering metric scale. These methods cannot determine the accurate location and orientation of objects. To tackle this problem, we propose a framework that jointly estimates a metric scale shape and pose from a single RGB image. Our framework has two branches: the Metric Scale Object Shape branch (MSOS) and the Normalized Object Coordinate Space branch (NOCS). The MSOS branch estimates the metric scale shape observed in the camera coordinates. The NOCS branch predicts the normalized object coordinate space (NOCS) map and performs similarity transformation with the rendered depth map from a predicted metric scale mesh to obtain 6d pose and size. Additionally, we introduce the Normalized Object Center Estimation (NOCE) to estimate the geometrically aligned distance from the camera to the object center. We validated our method on both synthetic and real-world datasets to evaluate category-level object pose and shape.

Implicit neural representation (INR) has proven to be accurate and efficient in various domains. In this work, we explore how different neural networks can be designed as a new texture INR, which operates in a continuous manner rather than a discrete one over the input UV coordinate space. Through thorough experiments, we demonstrate that these INRs perform well in terms of image quality, with considerable memory usage and rendering inference time. We analyze the balance between these objectives. In addition, we investigate various related applications in real-time rendering and down-stream tasks, e.g. mipmap fitting and INR-space generation.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g-2)_μ at the SU(3) flavor-symmetric point m_π=m_Ksimeq 420,MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain a_μ^{rm hlbl} = (65.4pm 4.9 pm 6.6)times 10^{-11}, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

Sparse-view 3D modeling represents a fundamental tension between reconstruction fidelity and generative plausibility. While feed-forward reconstruction excels in efficiency and input alignment, it often lacks the global priors needed for structural completeness. Conversely, diffusion-based generation provides rich geometric details but struggles with multi-view consistency. We present UniRecGen, a unified framework that integrates these two paradigms into a single cooperative system. To overcome inherent conflicts in coordinate spaces, 3D representations, and training objectives, we align both models within a shared canonical space. We employ disentangled cooperative learning, which maintains stable training while enabling seamless collaboration during inference. Specifically, the reconstruction module is adapted to provide canonical geometric anchors, while the diffusion generator leverages latent-augmented conditioning to refine and complete the geometric structure. Experimental results demonstrate that UniRecGen achieves superior fidelity and robustness, outperforming existing methods in creating complete and consistent 3D models from sparse observations.

By identifying four important components of existing LiDAR-camera 3D object detection methods (LiDAR and camera candidates, transformation, and fusion outputs), we observe that all existing methods either find dense candidates or yield dense representations of scenes. However, given that objects occupy only a small part of a scene, finding dense candidates and generating dense representations is noisy and inefficient. We propose SparseFusion, a novel multi-sensor 3D detection method that exclusively uses sparse candidates and sparse representations. Specifically, SparseFusion utilizes the outputs of parallel detectors in the LiDAR and camera modalities as sparse candidates for fusion. We transform the camera candidates into the LiDAR coordinate space by disentangling the object representations. Then, we can fuse the multi-modality candidates in a unified 3D space by a lightweight self-attention module. To mitigate negative transfer between modalities, we propose novel semantic and geometric cross-modality transfer modules that are applied prior to the modality-specific detectors. SparseFusion achieves state-of-the-art performance on the nuScenes benchmark while also running at the fastest speed, even outperforming methods with stronger backbones. We perform extensive experiments to demonstrate the effectiveness and efficiency of our modules and overall method pipeline. Our code will be made publicly available at https://github.com/yichen928/SparseFusion.

Embodied world models have emerged as a promising paradigm in robotics, most of which leverage large-scale Internet videos or pretrained video generation models to enrich visual and motion priors. However, they still face key challenges: a misalignment between coordinate-space actions and pixel-space videos, sensitivity to camera viewpoint, and non-unified architectures across embodiments. To this end, we present BridgeV2W, which converts coordinate-space actions into pixel-aligned embodiment masks rendered from the URDF and camera parameters. These masks are then injected into a pretrained video generation model via a ControlNet-style pathway, which aligns the action control signals with predicted videos, adds view-specific conditioning to accommodate camera viewpoints, and yields a unified world model architecture across embodiments. To mitigate overfitting to static backgrounds, BridgeV2W further introduces a flow-based motion loss that focuses on learning dynamic and task-relevant regions. Experiments on single-arm (DROID) and dual-arm (AgiBot-G1) datasets, covering diverse and challenging conditions with unseen viewpoints and scenes, show that BridgeV2W improves video generation quality compared to prior state-of-the-art methods. We further demonstrate the potential of BridgeV2W on downstream real-world tasks, including policy evaluation and goal-conditioned planning. More results can be found on our project website at https://BridgeV2W.github.io .

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Learning to estimate object pose often requires ground-truth (GT) labels, such as CAD model and absolute-scale object pose, which is expensive and laborious to obtain in the real world. To tackle this problem, we propose an unsupervised domain adaptation (UDA) for category-level object pose estimation, called UDA-COPE. Inspired by recent multi-modal UDA techniques, the proposed method exploits a teacher-student self-supervised learning scheme to train a pose estimation network without using target domain pose labels. We also introduce a bidirectional filtering method between the predicted normalized object coordinate space (NOCS) map and observed point cloud, to not only make our teacher network more robust to the target domain but also to provide more reliable pseudo labels for the student network training. Extensive experimental results demonstrate the effectiveness of our proposed method both quantitatively and qualitatively. Notably, without leveraging target-domain GT labels, our proposed method achieved comparable or sometimes superior performance to existing methods that depend on the GT labels.

Multispectral satellite images play a vital role in agriculture, fisheries, and environmental monitoring. However, their high dimensionality, large data volumes, and diverse spatial resolutions across multiple channels pose significant challenges for data compression and analysis. This paper presents ImpliSat, a unified framework specifically designed to address these challenges through efficient compression and reconstruction of multispectral satellite data. ImpliSat leverages Implicit Neural Representations (INR) to model satellite images as continuous functions over coordinate space, capturing fine spatial details across varying spatial resolutions. Furthermore, we introduce a Fourier modulation algorithm that dynamically adjusts to the spectral and spatial characteristics of each band, ensuring optimal compression while preserving critical image details.

We introduce Mono4DGS-HDR, the first system for reconstructing renderable 4D high dynamic range (HDR) scenes from unposed monocular low dynamic range (LDR) videos captured with alternating exposures. To tackle such a challenging problem, we present a unified framework with two-stage optimization approach based on Gaussian Splatting. The first stage learns a video HDR Gaussian representation in orthographic camera coordinate space, eliminating the need for camera poses and enabling robust initial HDR video reconstruction. The second stage transforms video Gaussians into world space and jointly refines the world Gaussians with camera poses. Furthermore, we propose a temporal luminance regularization strategy to enhance the temporal consistency of the HDR appearance. Since our task has not been studied before, we construct a new evaluation benchmark using publicly available datasets for HDR video reconstruction. Extensive experiments demonstrate that Mono4DGS-HDR significantly outperforms alternative solutions adapted from state-of-the-art methods in both rendering quality and speed.

We propose OmniNOCS, a large-scale monocular dataset with 3D Normalized Object Coordinate Space (NOCS) maps, object masks, and 3D bounding box annotations for indoor and outdoor scenes. OmniNOCS has 20 times more object classes and 200 times more instances than existing NOCS datasets (NOCS-Real275, Wild6D). We use OmniNOCS to train a novel, transformer-based monocular NOCS prediction model (NOCSformer) that can predict accurate NOCS, instance masks and poses from 2D object detections across diverse classes. It is the first NOCS model that can generalize to a broad range of classes when prompted with 2D boxes. We evaluate our model on the task of 3D oriented bounding box prediction, where it achieves comparable results to state-of-the-art 3D detection methods such as Cube R-CNN. Unlike other 3D detection methods, our model also provides detailed and accurate 3D object shape and segmentation. We propose a novel benchmark for the task of NOCS prediction based on OmniNOCS, which we hope will serve as a useful baseline for future work in this area. Our dataset and code will be at the project website: https://omninocs.github.io.

Estimating robot pose and joint angles is significant in advanced robotics, enabling applications like robot collaboration and online hand-eye calibration.However, the introduction of unknown joint angles makes prediction more complex than simple robot pose estimation, due to its higher dimensionality.Previous methods either regress 3D keypoints directly or utilise a render&compare strategy. These approaches often falter in terms of performance or efficiency and grapple with the cross-camera gap problem.This paper presents a novel framework that bifurcates the high-dimensional prediction task into two manageable subtasks: 2D keypoints detection and lifting 2D keypoints to 3D. This separation promises enhanced performance without sacrificing the efficiency innate to keypoint-based techniques.A vital component of our method is the lifting of 2D keypoints to 3D keypoints. Common deterministic regression methods may falter when faced with uncertainties from 2D detection errors or self-occlusions.Leveraging the robust modeling potential of diffusion models, we reframe this issue as a conditional 3D keypoints generation task. To bolster cross-camera adaptability, we introduce theNormalised Camera Coordinate Space (NCCS), ensuring alignment of estimated 2D keypoints across varying camera intrinsics.Experimental results demonstrate that the proposed method outperforms the state-of-the-art render\&compare method and achieves higher inference speed.Furthermore, the tests accentuate our method's robust cross-camera generalisation capabilities.We intend to release both the dataset and code in https://nimolty.github.io/Robokeygen/

Ultrasound Localization Microscopy (ULM) enables imaging of vascular structures in the micrometer range by accumulating contrast agent particle locations over time. Precise and efficient target localization accuracy remains an active research topic in the ULM field to further push the boundaries of this promising medical imaging technology. Existing work incorporates Delay-And-Sum (DAS) beamforming into particle localization pipelines, which ultimately determines the ULM image resolution capability. In this paper we propose to feed unprocessed Radio-Frequency (RF) data into a super-resolution network while bypassing DAS beamforming and its limitations. To facilitate this, we demonstrate label projection and inverse point transformation between B-mode and RF coordinate space as required by our approach. We assess our method against state-of-the-art techniques based on a public dataset featuring in silico and in vivo data. Results from our RF-trained network suggest that excluding DAS beamforming offers a great potential to optimize on the ULM resolution performance.

In Ultrasound Localization Microscopy (ULM),achieving high-resolution images relies on the precise localization of contrast agent particles across consecutive beam-formed frames. However, our study uncovers an enormous potential: The process of delay-and-sum beamforming leads to an irreversible reduction of Radio-Frequency (RF) data, while its implications for localization remain largely unexplored. The rich contextual information embedded within RF wavefronts, including their hyperbolic shape and phase, offers great promise for guiding Deep Neural Networks (DNNs) in challenging localization scenarios. To fully exploit this data, we propose to directly localize scatterers in RF signals. Our approach involves a custom super-resolution DNN using learned feature channel shuffling and a novel semi-global convolutional sampling block tailored for reliable and accurate wavefront localization. Additionally, we introduce a geometric point transformation that facilitates seamless mapping between RF and B-mode coordinate space. To understand the impact of beamforming on ULM, we validate the effectiveness of our method by conducting an extensive comparison with State-Of-The-Art (SOTA) techniques. We present the inaugural in vivo results from an RF-trained DNN, highlighting its real-world practicality. Our findings show that RF-ULM bridges the domain gap between synthetic and real datasets, offering a considerable advantage in terms of precision and complexity. To enable the broader research community to benefit from our findings, our code and the associated SOTA methods are made available at https://github.com/hahnec/rf-ulm.

We introduce a unified, end-to-end framework that seamlessly integrates object detection and pose estimation with a versatile onboarding process. Our pipeline begins with an onboarding stage that generates object representations from either traditional 3D CAD models or, in their absence, by rapidly reconstructing a high-fidelity neural representation (NeRF) from multi-view images. Given a test image, our system first employs the CNOS detector to localize target objects. For each detection, our novel pose estimation module, OPFormer, infers the precise 6D pose. The core of OPFormer is a transformer-based architecture that leverages a foundation model for robust feature extraction. It uniquely learns a comprehensive object representation by jointly encoding multiple template views and enriches these features with explicit 3D geometric priors using Normalized Object Coordinate Space (NOCS). A decoder then establishes robust 2D-3D correspondences to determine the final pose. Evaluated on the challenging BOP benchmarks, our integrated system demonstrates a strong balance between accuracy and efficiency, showcasing its practical applicability in both model-based and model-free scenarios.

This paper introduces Gaussian Spatial Transport (GST), a novel framework that leverages Gaussian splatting to facilitate transport from the probability measure in the image coordinate space to the annotation map. We propose a Gaussian splatting-based method to estimate pixel-annotation correspondence, which is then used to compute a transport plan derived from Bayesian probability. To integrate the resulting transport plan into standard network optimization in typical computer vision tasks, we derive a loss function that measures discrepancy after transport. Extensive experiments on representative computer vision tasks, including crowd counting and landmark detection, validate the effectiveness of our approach. Compared to conventional optimal transport schemes, GST eliminates iterative transport plan computation during training, significantly improving efficiency. Code is available at https://github.com/infinite0522/GST.

Hieroglyphs, as logographic writing systems, encode rich semantic and cultural information within their internal structural composition. Yet, current advanced Large Language Models (LLMs) and Multimodal LLMs (MLLMs) usually remain structurally blind to this information. LLMs process characters as textual tokens, while MLLMs additionally view them as raw pixel grids. Both fall short to model the underlying logic of character strokes. Furthermore, existing structural analysis methods are often script-specific and labor-intensive. In this paper, we propose Hieroglyphic Stroke Analyzer (HieroSA), a novel and generalizable framework that enables MLLMs to automatically derive stroke-level structures from character bitmaps without handcrafted data. It transforms modern logographic and ancient hieroglyphs character images into explicit, interpretable line-segment representations in a normalized coordinate space, allowing for cross-lingual generalization. Extensive experiments demonstrate that HieroSA effectively captures character-internal structures and semantics, bypassing the need for language-specific priors. Experimental results highlight the potential of our work as a graphematics analysis tool for a deeper understanding of hieroglyphic scripts. View our code at https://github.com/THUNLP-MT/HieroSA.

Recent radiance field methods represent scenes with 2D primitives that offer surface alignment and efficient rasterization, from Gaussian disks to triangles, yet all rely on convex boundaries: curved and concave structures demand excessive primitives. We introduce Deformable Triangle Splatting, which augments each triangle with K control points per edge, each parameterized by a single learnable scalar displacement that shifts the boundary inward or outward, enabling non-convex shape representation while preserving the three base vertices that define the 3D plane. To render these non-convex primitives differentiably, we design a rasterization pipeline in the triangle's barycentric coordinate space, ensuring view-consistent rendering. A winding number test determines whether each pixel lies inside the deformed primitive, and a window function controlled by two learnable parameters, sharpness and corner smoothness, together with a per-primitive scalar opacity, produces the smooth opacity transition from interior to boundary. Validation is done in a variety of real-world scenes, outperforming recent works based on non-volumetric primitives in terms of visual quality and versatility while still achieving competitive rendering efficiency.

Implicit Neural Representations (INRs) offer exceptional fidelity for video compression by learning per-video optimized functions, but their adoption is crippled by impractically slow encoding times. Existing attempts to accelerate INR encoding often sacrifice reconstruction quality or crucial coordinate-level control essential for adaptive streaming and transcoding. We introduce SIEDD (Shared-Implicit Encoder with Discrete Decoders), a novel architecture that fundamentally accelerates INR encoding without these compromises. SIEDD first rapidly trains a shared, coordinate-based encoder on sparse anchor frames to efficiently capture global, low-frequency video features. This encoder is then frozen, enabling massively parallel training of lightweight, discrete decoders for individual frame groups, further expedited by aggressive coordinate-space sampling. This synergistic design delivers a remarkable 20-30X encoding speed-up over state-of-the-art INR codecs on HD and 4K benchmarks, while maintaining competitive reconstruction quality and compression ratios. Critically, SIEDD retains full coordinate-based control, enabling continuous resolution decoding and eliminating costly transcoding. Our approach significantly advances the practicality of high-fidelity neural video compression, demonstrating a scalable and efficient path towards real-world deployment. Our codebase is available at https://github.com/VikramRangarajan/SIEDD .

Reconstructing dense 3D scenes from sparse LiDAR point clouds (LiDAR scene completion) is a fundamental challenge in autonomous driving, where diffusion models offer a promising solution. However, existing approaches rely on object-level autoencoders that collapse into unstable global representations at outdoor scale, and suffer from ground truth data corrupted by odometry drift that systematically degrades supervision quality. Furthermore, multi-step diffusion inference incurs prohibitive latency for real-time deployment. We present CloudDiffusion, addressing these issues with three independent components. First, a multi-token Gaussian VAE with cross-attention pooling provides stable scene-scale LiDAR compression as a standalone reconstruction module, avoiding the global-pooling and codebook-collapse failure modes of prior point-cloud autoencoders. Second, an anchor-based ICP ground truth refinement pipeline eliminates drift-induced noise from training supervision, reducing our single-step x0 diffusion teacher's squared Chamfer distance by approximately 16x on SemanticKITTI seq. 08 (0.396 to 0.024 m^2) with no model change (partly aided by the denser, more compact refined references). Third, the same teacher completes scenes in a single x0 step, operating directly in coordinate space, not in the VAE latent. It runs in near real time at 209ms/frame, 65-138x lower inference latency than iterative diffusion baselines. Our results indicate that data quality dominates model design in this regime, and suggest that multi-token latent spaces could serve as a stable first stage for future latent diffusion-based scene completion.

We introduce a novel approach to counter adversarial attacks, namely, image resampling. Image resampling transforms a discrete image into a new one, simulating the process of scene recapturing or rerendering as specified by a geometrical transformation. The underlying rationale behind our idea is that image resampling can alleviate the influence of adversarial perturbations while preserving essential semantic information, thereby conferring an inherent advantage in defending against adversarial attacks. To validate this concept, we present a comprehensive study on leveraging image resampling to defend against adversarial attacks. We have developed basic resampling methods that employ interpolation strategies and coordinate shifting magnitudes. Our analysis reveals that these basic methods can partially mitigate adversarial attacks. However, they come with apparent limitations: the accuracy of clean images noticeably decreases, while the improvement in accuracy on adversarial examples is not substantial. We propose implicit representation-driven image resampling (IRAD) to overcome these limitations. First, we construct an implicit continuous representation that enables us to represent any input image within a continuous coordinate space. Second, we introduce SampleNet, which automatically generates pixel-wise shifts for resampling in response to different inputs. Furthermore, we can extend our approach to the state-of-the-art diffusion-based method, accelerating it with fewer time steps while preserving its defense capability. Extensive experiments demonstrate that our method significantly enhances the adversarial robustness of diverse deep models against various attacks while maintaining high accuracy on clean images.

Large language models store all learned knowledge in a single, fixed weight vector. Teaching a model new capabilities requires modifying those same weights, inevitably degrading previously acquired knowledge. This fundamental limitation, known as catastrophic forgetting, has resisted principled solutions for decades. Existing approaches treat weights as immutable artifacts that must be protected through techniques like regularization heuristics, replay buffers, or isolated adapter modules. The problem is none of these provide a structural guarantee against forgetting. In this work, we propose Non-Interfering Weight Fields (NIWF), a framework that replaces the fixed weight paradigm with a learned function that generates weight configurations on demand from a continuous capability coordinate space. After training on a task, we commit the occupied coordinate region by snapshotting the fields outputs on anchor points to enforce a functional lock during all future training. We validate NIWF on sequential instructionfollowing and code generation tasks using Mistral-7B, demonstrating zero forgetting on committed tasks with competitive perplexity on new tasks. The framework introduces the notion of software-like versioning for neural network intelligence, where capabilities can be committed, extended, composed, and rolled back without retraining.

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack a reweighting procedure required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a framework for reduced-order generative modeling with importance sampling in coarse-grained coordinate space. CG-BGs generate samples using a flow-based model and reweight them using a learned potential of mean force (PMF). We show that the PMF can be learned from rapidly converged trajectories via enhanced sampling force matching. Experiments demonstrate that CG-BGs capture solvent-mediated interactions in highly reduced representations while substantially reducing computational cost relative to atomistic BGs, providing a practical route toward equilibrium sampling of larger molecular systems.

Storyboarding is a core skill in visual storytelling for film, animation, and games. However, automating this process requires a system to achieve two properties that current approaches rarely satisfy simultaneously: inter-shot consistency and explicit editability. While 2D diffusion-based generators produce vivid imagery, they often suffer from identity drift along with limited geometric control; conversely, traditional 3D animation workflows are consistent and editable but require expert-heavy, labor-intensive authoring. We present StoryBlender, a grounded 3D storyboard generation framework governed by a Story-centric Reflection Scheme. At its core, we propose the StoryBlender system, which is built on a three-stage pipeline: (1) Semantic-Spatial Grounding, to construct a continuity memory graph to decouple global assets from shot-specific variables for long-horizon consistency; (2) Canonical Asset Materialization, to instantiate entities in a unified coordinate space to maintain visual identity; and (3) Spatial-Temporal Dynamics, to achieve layout design and cinematic evolution through visual metrics. By orchestrating multiple agents in a hierarchical manner within a verification loop, StoryBlender iteratively self-corrects spatial hallucinations via engine-verified feedback. The resulting native 3D scenes support direct, precise editing of cameras and visual assets while preserving unwavering multi-shot continuity. Experiments demonstrate that StoryBlender significantly improves consistency and editability over both diffusion-based and 3D-grounded baselines. Code, data, and demonstration video will be available on https://engineeringai-lab.github.io/StoryBlender/

Integration of Large Language Models (LLMs) into visual domain tasks, resulting in visual-LLMs (V-LLMs), has enabled exceptional performance in vision-language tasks, particularly for visual question answering (VQA). However, existing V-LLMs (e.g. BLIP-2, LLaVA) demonstrate weak spatial reasoning and localization awareness. Despite generating highly descriptive and elaborate textual answers, these models fail at simple tasks like distinguishing a left vs right location. In this work, we explore how image-space coordinate based instruction fine-tuning objectives could inject spatial awareness into V-LLMs. We discover optimal coordinate representations, data-efficient instruction fine-tuning objectives, and pseudo-data generation strategies that lead to improved spatial awareness in V-LLMs. Additionally, our resulting model improves VQA across image and video domains, reduces undesired hallucination, and generates better contextual object descriptions. Experiments across 5 vision-language tasks involving 14 different datasets establish the clear performance improvements achieved by our proposed framework.

Conventional Computed Tomography (CT) methods require large numbers of noise-free projections for accurate density reconstructions, limiting their applicability to the more complex class of Cone Beam Geometry CT (CBCT) reconstruction. Recently, deep learning methods have been proposed to overcome these limitations, with methods based on neural fields (NF) showing strong performance, by approximating the reconstructed density through a continuous-in-space coordinate based neural network. Our focus is on improving such methods, however, unlike previous work, which requires training an NF from scratch for each new set of projections, we instead propose to leverage anatomical consistencies over different scans by training a single conditional NF on a dataset of projections. We propose a novel conditioning method where local modulations are modeled per patient as a field over the input domain through a Neural Modulation Field (NMF). The resulting Conditional Cone Beam Neural Tomography (CondCBNT) shows improved performance for both high and low numbers of available projections on noise-free and noisy data.

Query-based 3D scene instance segmentation from point clouds has attained notable performance. However, existing methods suffer from the query initialization dilemma due to the sparse nature of point clouds and rely on computationally intensive attention mechanisms in query decoders. We accordingly introduce LaSSM, prioritizing simplicity and efficiency while maintaining competitive performance. Specifically, we propose a hierarchical semantic-spatial query initializer to derive the query set from superpoints by considering both semantic cues and spatial distribution, achieving comprehensive scene coverage and accelerated convergence. We further present a coordinate-guided state space model (SSM) decoder that progressively refines queries. The novel decoder features a local aggregation scheme that restricts the model to focus on geometrically coherent regions and a spatial dual-path SSM block to capture underlying dependencies within the query set by integrating associated coordinates information. Our design enables efficient instance prediction, avoiding the incorporation of noisy information and reducing redundant computation. LaSSM ranks first place on the latest ScanNet++ V2 leaderboard, outperforming the previous best method by 2.5% mAP with only 1/3 FLOPs, demonstrating its superiority in challenging large-scale scene instance segmentation. LaSSM also achieves competitive performance on ScanNet, ScanNet200, S3DIS and ScanNet++ V1 benchmarks with less computational cost. Extensive ablation studies and qualitative results validate the effectiveness of our design. The code and weights are available at https://github.com/RayYoh/LaSSM.

Quantizing AdamW's optimizer states reduces persistent storage, but quantization errors propagate through the moment recurrences and perturb subsequent adaptive updates. We redesign 4-bit optimizer-state quantization for AdamW from the perspective of rounding space: the coordinate in which a quantizer chooses between adjacent reconstruction levels. For the second moment, a local analysis of the quantization cell adjacent to zero shows that small mean state error need not imply small mean preconditioner error at the next step. A one-dimensional quadratic construction further shows qualitatively different optimization dynamics under state-space and preconditioner-space rounding. These results motivate Zero-Inclusive Preconditioner-space Stochastic Rounding (ZIP-SR), which retains zero in the second-moment codebook and computes stochastic-rounding probabilities in preconditioner space. As a complementary route, Zero-Excluding EDEN calibration (ZE-EDEN) uses a zero-excluding second-moment codebook and rescales the quantized second-moment block to mitigate the preconditioner distortion caused by the positive quantization floor. Both configurations use 4-bit NormalFloat (NF4) for the first moment, with targeted stochastic rounding of the LM-head first moment during the final 10\% of training. Across GPT- and Llama-style pretraining experiments ranging from 130M to 2.7B parameters, both methods reduce TorchAO 4-bit AdamW's mean validation-loss gap to 32-bit AdamW at every evaluated model size, with the largest reported gap reduction reaching 70\%. In full-parameter supervised fine-tuning, both recipes achieve lower validation loss than TorchAO while remaining close to 32-bit AdamW on downstream tasks.

Various methods have been proposed for utilizing Large Language Models (LLMs) in autonomous driving. One strategy of using LLMs for autonomous driving involves inputting surrounding objects as text prompts to the LLMs, along with their coordinate and velocity information, and then outputting the subsequent movements of the vehicle. When using LLMs for such purposes, capabilities such as spatial recognition and planning are essential. In particular, two foundational capabilities are required: (1) spatial-aware decision making, which is the ability to recognize space from coordinate information and make decisions to avoid collisions, and (2) the ability to adhere to traffic rules. However, quantitative research has not been conducted on how accurately different types of LLMs can handle these problems. In this study, we quantitatively evaluated these two abilities of LLMs in the context of autonomous driving. Furthermore, to conduct a Proof of Concept (POC) for the feasibility of implementing these abilities in actual vehicles, we developed a system that uses LLMs to drive a vehicle.

A hybrid kinetic-fluid model is used to study plasma stratification in alternating current (AC) discharges in noble gases at low plasma densities. Self-consistent coupled solutions of a nonlocal kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained for a positive column and the entire discharge with near-electrode sheaths. A simplified two-level excitation-ionization model neglects the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons. Standing striations are obtained for the reduced values of electric fields, E/p, corresponding to the inelastic energy balance of electrons in a range of driving frequencies. An analog of Novak law (striation length proportional to the excitation threshold of atoms and inversely proportional to the mean square root of the electric field), is observed in simulations, indicating the nonlocal nature of standing striations in AC discharges at low plasma densities. Stratified plasma operates in a dynamic regime for various driving frequencies. In this regime, ions respond to the time-averaged electric field, whereas electrons react to the instantaneous electric field. The disparity of time scales between ambipolar diffusion, which occurs at the ion time scale, and electron kinetics in the coordinate-energy phase space, which occurs at the free electron diffusion time scale, produces complicated fluxes in the phase space (due to electron heating, energy loss in collisions, and ionization processes) that are responsible for the stratification. Our paper emphasizes the need for the kinetic approach to analyze stratification phenomena in AC discharge of noble gases. It promotes an efficient method for the kinetic treatment of electrons that is an alternative to the commonly used PIC method.

World action models jointly learn to forecast world dynamics and predict robot actions, such that the learned internal world dynamics guide accurate actions. Existing approaches typically represent the world as RGB frames or latent counterparts while predicting actions as end-effector poses or joint angles, but they often struggle to capture the 3D spatial structure and contact geometry central to dexterous manipulation. We introduce Point World Action Model (PointWAM), a 3D world action model that decomposes the world into a scene (i.e., environment) and hands (i.e., actor), and jointly forecasts both as 3D point trajectories within a shared space-time coordinate frame. This explicit, disentangled representation enables effective pre-training on large-scale human demonstration videos without requiring any task-specific object or keypoint selection. Given a colored point cloud and a language instruction, PointWAM predicts how the scene and hands co-evolve in 3D space over time, then retargets the forecast hand motion to robot actions. Pre-training on human videos improves average DexJoCo success by 56.9 percentage points, and scene-trajectory supervision adds 10.9 points over forecasting the hands alone. With both, PointWAM surpasses the prior state of the art on ten DexJoCo tasks by 11.7 points and outperforms strong VLAs on a real robot.

In recent years, huge progress has been made on learning neural implicit representations from multi-view images for 3D reconstruction. As an additional input complementing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency details with coordinate-based neural networks. However, high frequency positional encodings make the optimization unstable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of continuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly reduces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the-art. Our code is available at https://github.com/MachinePerceptionLab/CQ-NIR.

Recent multimodal large language models (MLLMs) have made remarkable progress in visual understanding and language-based reasoning, yet they lack a persistent world-centered representation for spatially consistent reasoning in 3D environments. Inspired by the mammalian dual-stream system, where semantic and spatial cues are processed separately and integrated into an allocentric cognitive map, we propose SpaceMind++, a video MLLM architecture that explicitly builds a voxelized cognitive map from RGB videos. This map reorganizes fragmented egocentric observations into a shared 3D metric representation, enabling the model to preserve object permanence and spatial topology across changing viewpoints. To make this allocentric representation usable by a pretrained video MLLM without disrupting its native visual-token interface, we introduce Coordinate-Guided Deep Iterative Fusion, a new mechanism that relays map-level spatial knowledge back into the original 2D visual features. This fusion is explicitly guided by coordinate embeddings and 3D Rotary Positional Encoding, which ground semantic interactions in metric 3D space, resembling the entorhinal binding of sensory features to metric space. Extensive experiments show that SpaceMind++ achieves new state-of-the-art performance on VSI-Bench. Furthermore, it demonstrates superior out-of-distribution generalization on SPBench, SITE-Bench, and SPAR-Bench, underscoring its robustness in unseen 3D environments.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

Vision Language Models (VLMs) demonstrate strong qualitative visual understanding, but struggle with metrically precise spatial reasoning required for embodied applications. The agentic paradigm promises that VLMs can use a wide variety of tools that could augment these capabilities, such as depth estimators, segmentation models, and pose estimators. Yet it remains an open challenge how to realize this vision without solely relying on handcrafted prompting strategies or enforcing fixed, predefined tool pipelines that limit VLMs' ability to discover optimal tool-use patterns. Reinforcement Learning could overcome this gap, but has so far been limited to reasoning with a single visual tool due to the large search space in multi-tool reasoning. We introduce Double Interactive Reinforcement Learning (DIRL), a two-phase training framework where VLMs learn to coordinate multiple tools through interactive exploration and feedback. In the teaching phase, we combine demonstrations from a single tool specialist trained via interactive RL with traces from a frontier model using all tools. In the exploration phase, the model further refines multi-tool coordination through continued RL. Our model, SpaceTools, with tool-augmented spatial reasoning ability, achieves state-of-the-art performance on spatial understanding benchmarks (RoboSpatial-Home, BLINK, BOP-ASK) and demonstrates reliable real-world manipulation using a 7-DOF robot as a tool. DIRL provides substantial improvements over the vanilla SFT (+12% on RoboSpatial) and RL (+16% on RoboSpatial) baselines. Project page: https://spacetools.github.io/.

We introduce a new framework for molecular graph generation with 3D molecular generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps molecular graphs to Euclidean point clouds via synthetic conformer coordinates and learns the inverse map using an E(n)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecular generative models. This approach simplifies the graph generation problem - without relying on molecular fragments nor autoregressive decoding - into a point cloud generation problem followed by node and edge classification tasks. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 30% on ZINC250K and 16% on the large-scale GuacaMol dataset while improving conditional generation by up to 3.9 times.

Deep remote photoplethysmography (rPPG) attains sub-bpm heart-rate error on frontal, stationary faces yet degrades sharply under head pose: on MMPD, the state-of-the-art FactorizePhys backbone's MAE grows 1.60times from frontal (|yaw|{<}15^circ) to large-yaw (|yaw|{geq}45^circ) frames. We argue that pose is a coordinate-structural nuisance rather than a data-augmentation problem: in image coordinates the same pixel maps to different anatomy at different poses, blocking three priors otherwise natural for rPPG, namely the dichromatic reflection model, pulse-phase invariance across skin regions, and the POS/CHROM chromaticity projection, each of which presumes a stable anatomy-to-pixel mapping. We introduce CanonicalPhys, which prepends a differentiable four-point homography that fixes four facial anchors at canonical positions; in this canonical frame the three priors become expressible as a per-pixel Lambertian weight, a cross-ROI temporal consistency loss, and knowledge distillation from windowed POS, none of which adds trainable parameters over the backbone. At an identical parameter count, CanonicalPhys reduces MMPD's frontal-to-large-yaw MAE degradation from 1.60times to 1.33times and flattens the mild-yaw bin from 1.32times to 1.07times (across CanonicalPhys variants), with matched cross-dataset MAE reductions of up to 32% on pose-rich targets. Code: https://github.com/infraface/CanonicalPhys

Scalable Vector Graphics are a fundamental medium for resolution-independent visual content, yet the deep learning community lacks a continuous, dense, and invertible latent space for vector representations, the kind of foundational building block that Variational Autoencoders and their descendants have long provided for raster images. We introduce SLS (SVG Latent Space), a Transformer-based autoencoder that learns compact dense representations of individual SVG paths, the atomic visual elements from which any SVG image can be composed. By modeling SVG commands, coordinate data, and visual properties within a unified BPE-based token vocabulary, SLS learns fixed-size latent representations that jointly capture structure and appearance, and can be decoded back into valid, style-consistent SVG paths with high fidelity. The resulting embedding space is robust, invertible, and structured: embeddings lie on a unit hypersphere, enabling efficient similarity search, composition, and downstream conditioning through simple vector-space operations. Finally, we demonstrate that SLS generalizes across diverse tasks reducing their FLOPs by over 150 times compared to token-based approaches, and establishing a general-purpose latent foundation for vector graphics research.

Standard positional encodings represent position as a one-dimensional reading-order coordinate, but reading order alone does not determine hierarchical textual structure. We use a hierarchical rotary positional encoding (hRoPE) that represents paragraph, sentence, and token indices as separate channels, hold the token sequence fixed, intervene on the paragraph coordinate p1, and measure cross-paragraph attention with a token-distance-exact estimator. Attention is compressed relative to a token-distance-matched baseline in every corpus, but compression alone is not diagnostic of true structure: an architecturally identical channel with density-matched random labels is compressed too, more shallowly. What distinguishes real structure is the depth of compression, which is greater and corpus-dependent while the control's is not. Comparing eight corpus-only quantities across three constructs (lexical persistence, paragraph length, embedding-based coherence), none fully reproduces the cross-corpus ordering of depth, though embedding-based coherence comes closest. Compression depth, not its location, is the reproducible signature of genuine paragraph structure in our setting.

Bound states in the continuum (BIC) metasurfaces are typically described by geometry-specific parameters, hindering cross-geometry comparison, while ultranarrow qBIC features are easily diluted in full-spectrum learning. Here, 2015 samples from seven dielectric metasurface families are mapped to a shared reciprocal-lattice grid, where two frozen low-order Fourier channels capture resonance shifts with mean within-branch R^2 values of 0.871-0.999. Field-level analysis of two representative branches further confirms that these shifts are consistent with the Maxwell-Fourier perturbation picture. A five-channel K-space backbone models the broadband spectrum, while a local complex K-space expert parameterizes the qBIC resonance through a differentiable Fano layer. The expert reduces resonance-position mean absolute error (MAE) from 3.2 to 0.95 nm and the resonance-depth error by 14-fold on a geometry-blocked test set. The same coordinate supports spectrum-to-structure reconstruction.

End-to-end autonomous driving methods built on vision language models (VLMs) have undergone rapid development driven by their universal visual understanding and strong reasoning capabilities obtained from the large-scale pretraining. However, we find that current VLMs struggle to understand fine-grained 3D spatial relationships which is a fundamental requirement for systems interacting with the physical world. To address this issue, we propose SpaceDrive, a spatial-aware VLM-based driving framework that treats spatial information as explicit positional encodings (PEs) instead of textual digit tokens, enabling joint reasoning over semantic and spatial representations. SpaceDrive employs a universal positional encoder to all 3D coordinates derived from multi-view depth estimation, historical ego-states, and text prompts. These 3D PEs are first superimposed to augment the corresponding 2D visual tokens. Meanwhile, they serve as a task-agnostic coordinate representation, replacing the digit-wise numerical tokens as both inputs and outputs for the VLM. This mechanism enables the model to better index specific visual semantics in spatial reasoning and directly regress trajectory coordinates rather than generating digit-by-digit, thereby enhancing planning accuracy. Extensive experiments validate that SpaceDrive achieves state-of-the-art open-loop performance on the nuScenes dataset and the second-best Driving Score of 78.02 on the Bench2Drive closed-loop benchmark over existing VLM-based methods.

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications. We theoretically establish the worst-case complexity bound for this algorithm. Namely, we show that for general nonconvex smooth objectives with block-wise constraints, the classical BCD-PR algorithm converges to an epsilon-stationary point within O(1/epsilon) iterations. Under a mild condition, this result still holds even if the algorithm is executed inexactly in each step. As an application, we propose a provable and efficient algorithm for `Wasserstein CP-dictionary learning', which seeks a set of elementary probability distributions that can well-approximate a given set of d-dimensional joint probability distributions. Our algorithm is a version of BCD-PR that operates in the dual space, where the primal problem is regularized both entropically and proximally.

Despite the advent in 3D hand pose estimation, current methods predominantly focus on single-image 3D hand reconstruction in the camera frame, overlooking the world-space motion of the hands. Such limitation prohibits their direct use in egocentric video settings, where hands and camera are continuously in motion. In this work, we propose HaWoR, a high-fidelity method for hand motion reconstruction in world coordinates from egocentric videos. We propose to decouple the task by reconstructing the hand motion in the camera space and estimating the camera trajectory in the world coordinate system. To achieve precise camera trajectory estimation, we propose an adaptive egocentric SLAM framework that addresses the shortcomings of traditional SLAM methods, providing robust performance under challenging camera dynamics. To ensure robust hand motion trajectories, even when the hands move out of view frustum, we devise a novel motion infiller network that effectively completes the missing frames of the sequence. Through extensive quantitative and qualitative evaluations, we demonstrate that HaWoR achieves state-of-the-art performance on both hand motion reconstruction and world-frame camera trajectory estimation under different egocentric benchmark datasets. Code and models are available on https://hawor-project.github.io/ .

Deep learning-based point cloud modeling has been widely investigated as an indispensable component of general shape analysis. Recently, transformer and state space model (SSM) have shown promising capacities in point cloud learning. However, limited research has been conducted on medical point clouds, which have great potential in disease diagnosis and treatment. This paper presents an SSM-based hierarchical feature learning framework for medical point cloud understanding. Specifically, we down-sample input into multiple levels through the farthest point sampling. At each level, we perform a series of k-nearest neighbor (KNN) queries to aggregate multi-scale structural information. To assist SSM in processing point clouds, we introduce coordinate-order and inside-out scanning strategies for efficient serialization of irregular points. Point features are calculated progressively from short neighbor sequences and long point sequences through vanilla and group Point SSM blocks, to capture both local patterns and long-range dependencies. To evaluate the proposed method, we build a large-scale medical point cloud dataset named MedPointS for anatomy classification, completion, and segmentation. Extensive experiments conducted on MedPointS demonstrate that our method achieves superior performance across all tasks. The dataset is available at https://flemme-docs.readthedocs.io/en/latest/medpoints.html. Code is merged to a public medical imaging platform: https://github.com/wlsdzyzl/flemme.

Recent efforts to combine low-rank adaptation (LoRA) with mixture-of-experts (MoE) for adapting large language models (LLMs) to multiple tasks still exhibit prevailing limitations: they either swap entire attention/feed-forward layers for switch experts or bolt on parallel expert branches, diluting parameter efficiency and task fidelity. We propose the LoRA-Mixer, a modular and lightweight MoE framework that integrates LoRA experts. Our core innovation lies in replacing the projection matrices of the attention module's input/output linear layers with dynamically routed, task-specific LoRA experts. This design ensures seamless compatibility with diverse foundation models, including transformers and state space models (SSMs), by leveraging their inherent linear projection structures. The framework supports two operational paradigms: (1) joint optimization of LoRA experts and routing mechanisms via a novel hard-soft routing strategy, or (2) direct deployment of pre-trained, frozen LoRA modules sourced from external repositories. To enable robust router training with limited data while ensuring stable routing decisions and maximizing expert reuse, we introduce an adaptive Specialization Balance Loss (SBL) that jointly optimizes expert balance and task-specific alignment. Extensive experiments on seven benchmark datasets, including MedQA, CoLA, SST-2, GSM8K, ARC-E, ARC-C, and HumanEval, demonstrate the effectiveness of LoRA-Mixer. On datasets such as GSM8K, HumanEval, and MedQA, LoRA-Mixer achieves significant improvements of 7.61%, 4.88%, and 3.08% over the base models, respectively. Compared with state-of-the-art methods, LoRA-Mixer achieves additional improvements of 1.09%, 1.45%, and 1.68%, respectively, using only 48% of the parameters, demonstrating its efficiency and strong performance.

Spatial reasoning is an essential problem in embodied AI research. Efforts to enhance spatial reasoning abilities through supplementary spatial data and fine-tuning have proven limited and ineffective when addressing complex embodied tasks, largely due to their dependence on language-based outputs. While some approaches have introduced a point-based action space to mitigate this issue, they fall short in managing more intricate tasks within complex environments. This deficiency arises from their failure to fully exploit the inherent thinking and reasoning capabilities that are fundamental strengths of Vision-Language Models (VLMs). To address these limitations, we propose a novel approach named SpatialCoT, specifically designed to bolster the spatial reasoning capabilities of VLMs. Our approach comprises two stages: spatial coordinate bi-directional alignment, which aligns vision-language inputs with spatial coordinates, and chain-of-thought spatial grounding, which harnesses the reasoning capabilities of language models for advanced spatial reasoning. We evaluate SpatialCoT on challenging navigation and manipulation tasks, both in simulation and real-world settings. Experimental results demonstrate that our method significantly outperforms previous state-of-the-art approaches in both tasks.

We present a non-perturbative framework for the quantum treatment of vibrational excitation in molecular systems driven by electric fields with arbitrary time dependence. For harmonic potentials with linear dipole coupling, the field-induced dynamics is exactly described by a displaced coherent state, whose evolution is completely determined by a complex phase-space coordinate. Closed-form expressions for this coordinate reveal a clear distinction between resonant and non-resonant regimes. The resulting vibrational populations follow a Poisson distribution determined by a dimensionless time-dependent phase-space displacement, for both resonant and non-resonant driving. Resonant driving results in an enhanced phase-space displacement, whereas finite detuning between the driving and vibrational frequencies leads to an exponential suppression of the phase-space displacement and vibrational excitation. While the approach reduces to the standard time-dependent perturbation theory in the weak-field limit, it remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and enable non-perturbative state preparation in ultrafast spectroscopy.

Recently, state space models have exhibited strong global modeling capabilities and linear computational complexity in contrast to transformers. This research focuses on applying such architecture to more efficiently and effectively model point cloud data globally with linear computational complexity. In particular, for the first time, we demonstrate that Mamba-based point cloud methods can outperform previous methods based on transformer or multi-layer perceptrons (MLPs). To enable Mamba to process 3-D point cloud data more effectively, we propose a novel Consistent Traverse Serialization method to convert point clouds into 1-D point sequences while ensuring that neighboring points in the sequence are also spatially adjacent. Consistent Traverse Serialization yields six variants by permuting the order of x, y, and z coordinates, and the synergistic use of these variants aids Mamba in comprehensively observing point cloud data. Furthermore, to assist Mamba in handling point sequences with different orders more effectively, we introduce point prompts to inform Mamba of the sequence's arrangement rules. Finally, we propose positional encoding based on spatial coordinate mapping to inject positional information into point cloud sequences more effectively. Point Cloud Mamba surpasses the state-of-the-art (SOTA) point-based method PointNeXt and achieves new SOTA performance on the ScanObjectNN, ModelNet40, ShapeNetPart, and S3DIS datasets. It is worth mentioning that when using a more powerful local feature extraction module, our PCM achieves 79.6 mIoU on S3DIS, significantly surpassing the previous SOTA models, DeLA and PTv3, by 5.5 mIoU and 4.9 mIoU, respectively.

Long-sequence memory tracking places two opposing demands on a recurrent state: near-lossless retention of stored bindings over long horizons, and active overwriting of stale ones. In our diagnostic suite, the strongest efficient baselines tend to solve only one side well. Continuous-time-parameterized state-space models (SSMs) such as Mamba obtain their discrete recurrence by zero-order-hold discretization of a continuous-time system; we argue that this detour is unnecessary for memory tracking and parameterize the discrete transition directly. Naju (Native Adaptive Junction Unit) factorizes the recurrent update, schematically x_n = f_nodot x_{n-1} + i_nodot(B_n u_n), into an explicit discrete pole (a learned forget gate f_n), an independent write gain i_n, and input-dependent write/read maps. Since the sigmoid pole satisfies 0<f_n<1, each frozen local coordinate is Schur-stable by construction, and the full time-varying recurrence satisfies a fading-memory/BIBO bound under uniform boundedness assumptions, with no stability regularizer. We formalize the key structural limitation of coupled designs: any non-expansive complementary single-gate recurrence ties the effective retention r and write gain w through |r|+wle 1, so near-complete retention forces weak writing; decoupling f_n from i_n removes this constraint. Empirically, Naju is the only evaluated model that remains strong on both retention and overwriting at 4x the training length. Beyond the diagnostic suite, we evaluate Naju on WikiText-103 language modeling, Long Range Arena, and multi-query associative recall. Across these settings, Naju consistently combines strong long-range memory with competitive or superior performance, outperforming the Mamba baselines in the principal comparisons while remaining competitive with the Transformer and preserving linear-time, linear-memory scaling.

In this work, we develop a method to generate infinite high-resolution images with diverse and complex content. It is based on a perfectly equivariant generator with synchronous interpolations in the image and latent spaces. Latent codes, when sampled, are positioned on the coordinate grid, and each pixel is computed from an interpolation of the nearby style codes. We modify the AdaIN mechanism to work in such a setup and train the generator in an adversarial setting to produce images positioned between any two latent vectors. At test time, this allows for generating complex and diverse infinite images and connecting any two unrelated scenes into a single arbitrarily large panorama. Apart from that, we introduce LHQ: a new dataset of \lhqsize high-resolution nature landscapes. We test the approach on LHQ, LSUN Tower and LSUN Bridge and outperform the baselines by at least 4 times in terms of quality and diversity of the produced infinite images. The project page is located at https://universome.github.io/alis.

Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates. Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception. Therefore, in this work, we revisit spatial numerical understanding through SpaceNum, a unified framework that captures two complementary settings: numbers as dynamic transitions during spatial exploration, and numbers as static layouts in spatial reasoning. We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations. We systematically study whether current VLMs truly understand numerical values in spatial settings. Across dynamic transitions and static layouts, we find that models largely fail to ground numbers in spatial meaning and often perform close to random guess. Through error analysis, reasoning trace analysis, and controlled interventions, we show that current VLMs rely heavily on shallow spatial cues, struggle to build stable coordinate-aware representations, and fail to abstract structured spatial layouts from visual observations. We further show that explicit reasoning provides only marginal gains, while tuning can partially improve spatial numerical understanding and transfer to external spatial reasoning benchmarks.

We investigate whether independently trained language models converge to geometrically compatible latent representations, and whether this compatibility can be exploited to correct model behavior at inference time without any weight updates. We learn a linear projection matrix that maps activation vectors from a large teacher model into the coordinate system of a smaller student model, then intervene on the student's residual stream during generation by substituting its internal state with the translated teacher representation. Across a fully crossed experimental matrix of 20 heterogeneous teacher-student pairings spanning mixture-of-experts, dense, code-specialized, and synthetically trained architectures, the Ridge projection consistently achieves R^2 = 0.50 on verbal reasoning and R^2 = 0.40 on mathematical reasoning, collapsing to R^2 = -0.22 under permutation control and R^2 = 0.01 under L_1 regularization. Behavioral correction rates range from 14.0% to 50.0% on TruthfulQA (mean 25.2%) and from 8.5% to 43.3% on GSM8K arithmetic reasoning (mean 25.5%), demonstrating that the method generalizes across fundamentally different reasoning domains. We report a near-zero correlation between geometric alignment quality and behavioral correction rate (r = -0.07), revealing a dissociation between representation space fidelity and output space impact. Intervention strength is architecture-specific: student models exhibit characteristic sensitivity profiles that invert across domains, with the most steerable verbal student becoming the least steerable mathematical student. Finally, a double dissociation experiment conducted across all 20 model pairings confirms without exception that projection matrices collapse catastrophically when transferred across reasoning domains (mean R^2 = -3.83 in both transfer directions), establishing domain-specific subspace geometry as a universal property of LMs.

We present a video decomposition method that facilitates layer-based editing of videos with spatiotemporally varying lighting and motion effects. Our neural model decomposes an input video into multiple layered representations, each comprising a 2D texture map, a mask for the original video, and a multiplicative residual characterizing the spatiotemporal variations in lighting conditions. A single edit on the texture maps can be propagated to the corresponding locations in the entire video frames while preserving other contents' consistencies. Our method efficiently learns the layer-based neural representations of a 1080p video in 25s per frame via coordinate hashing and allows real-time rendering of the edited result at 71 fps on a single GPU. Qualitatively, we run our method on various videos to show its effectiveness in generating high-quality editing effects. Quantitatively, we propose to adopt feature-tracking evaluation metrics for objectively assessing the consistency of video editing. Project page: https://lightbulb12294.github.io/hashing-nvd/

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Generating human videos with realistic and controllable motions is a challenging task. While existing methods can generate visually compelling videos, they lack separate control over four key video elements: foreground subject, background video, human trajectory and action patterns. In this paper, we propose a decomposed human motion control and video generation framework that explicitly decouples motion from appearance, subject from background, and action from trajectory, enabling flexible mix-and-match composition of these elements. Concretely, we first build a ground-aware 3D world coordinate system and perform motion editing directly in the 3D space. Trajectory control is implemented by unprojecting edited 2D trajectories into 3D with focal-length calibration and coordinate transformation, followed by speed alignment and orientation adjustment; actions are supplied by a motion bank or generated via text-to-motion methods. Then, based on modern text-to-video diffusion transformer models, we inject the subject as tokens for full attention, concatenate the background along the channel dimension, and add motion (trajectory and action) control signals by addition. Such a design opens up the possibility for us to generate realistic videos of anyone doing anything anywhere. Extensive experiments on benchmark datasets and real-world cases demonstrate that our method achieves state-of-the-art performance on both element-wise controllability and overall video quality.

In the era of large-scale training, model merging has evolved into a tool for creating multitasking models efficiently. It enables the knowledge of models to be fused, without the need for heavy computation as required in traditional multitask learning. Existing merging methods often assume that entries at identical positions in weight matrices serve the same function, enabling straightforward entry-wise comparison and merging. However, this assumption overlooks the complexity of finetuned neural networks, where neurons may develop distinct feature compositions, making direct entry-wise merging problematic. We present Decom-Renorm-Merge (DRM), a simple yet effective approach that leverages Singular Value Decomposition to decompose and coordinate weight matrices into an aligned joint space, where entry-wise merging becomes possible. We showcase the effectiveness of DRM across various settings ranging from smaller encoder-based such as ViT and DeBERTa, encoder-decoder-based such as T5, and larger decoder-based such as Llama3.1-8B. Our experimental results show that DRM outperforms several state-of-the-art merging techniques across full finetuning and low-rank adaptation settings. Moreover, our analysis reveals renormalization as the crucial component for creating a robust and even joint space for merging, significantly contributing to the method's performance.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design (e.g., SIREN, FFC, KAN-based INRs) and optimization strategies (meta-learning, amortization, distillation), existing approaches still suffer from two core limitations: (1) a representation bottleneck that forces a single MLP to uniformly model heterogeneous local structures, and (2) limited scalability due to the absence of a hierarchical mechanism that dynamically adapts to signal complexity. This work introduces Hyper-Coordinate Implicit Neural Representations (HC-INR), a new class of INRs that break the representational bottleneck by learning signal-adaptive coordinate transformations using a hypernetwork. HC-INR decomposes the representation task into two components: (i) a learned multiscale coordinate transformation module that warps the input domain into a disentangled latent space, and (ii) a compact implicit field network that models the transformed signal with significantly reduced complexity. The proposed model introduces a hierarchical hypernetwork architecture that conditions coordinate transformations on local signal features, enabling dynamic allocation of representation capacity. We theoretically show that HC-INR strictly increases the upper bound of representable frequency bands while maintaining Lipschitz stability. Extensive experiments across image fitting, shape reconstruction, and neural radiance field approximation demonstrate that HC-INR achieves up to 4 times higher reconstruction fidelity than strong INR baselines while using 30--60\% fewer parameters.

Chain-of-thought prompting improves language-model reasoning by carrying intermediate states across successive computation steps. However, relying on natural language as the only recurrent interface is overly restrictive, since many transient computations do not need to be fully verbalized. Existing latent-reasoning methods remove this constraint by recurrently propagating continuous hidden states. However, these methods pass a dense hidden vector as a whole, without an explicit mechanism for selecting and organizing the information needed by the next reasoning step. This motivates an intermediate interface that remains linguistically grounded without requiring a decoded sentence. We introduce J-CoT, a recurrent reasoning framework built on J-space, a vocabulary-indexed coordinate system within the model's hidden representations. Within each cycle, the model computes in its full hidden space. At the cycle boundary, J-CoT expresses the intermediate state as vocabulary-indexed coefficients, carries these coefficients forward as a J-thought, and maps them back into the model's hidden representation for the next cycle. J-CoT therefore requires neither a fluent intermediate rationale nor recurrence over the complete hidden state. Under matched backbone and inference settings, J-CoT-Zero matches or exceeds the strongest evaluated latent-reasoning baseline on every benchmark, while J-CoT-Train obtains the highest score across the evaluated mathematical, scientific, coding, and structured path-reasoning tasks.

State Space Models (SSMs) offer an efficient alternative to Transformers for sequence modeling, yet conditioning pre-trained SSMs for iterative generation typically operates outside the recurrent operator, through input injection or activation modulation. While such mechanisms expose the model to conditioning information, they leave the underlying temporal dynamics fixed. We introduce MaRK (Markov-adapted Recurrent Kernels), a dynamic operator-conditioning framework that maps context vectors directly into bounded modulations of a frozen SSM's recurrence (A), read-in (B), read-out (C), skip (D), and discretization (Δ) parameters. Viewed through the lens of LPV-SSM systems, MaRK induces a context-indexed family of Markov parameter sequences, allowing each diffusion timestep to reshape the model's input-output memory kernel. We instantiate MaRK on a frozen 111M-parameter Hydra SSM backbone and study three adapter geometries: Hypernet, Chebyshev polynomial, and Discrete Cosine Transform kernels. Since these adapters modify the Markov parameter sequence through low-rank auxiliary maps on the frozen backbone, parameter-efficient fine-tuning arises as a structural consequence of the adaptation mechanism itself, requiring only 6.3--11M trainable auxiliary parameters to transition from a bidirectional objective to an iterative diffusion regime. The bounded recurrence parameterization further yields an analytic Affine Quadratic Stability certificate for the modulated recurrence. Through synthetic LPV recovery experiments and Markov-operator diagnostics, we show that MaRK recovers coordinate-invariant temporal operators under matched assumptions and produces distinct, stable timestep-conditioned memory profiles. Empirically, the Chebyshev variant yields the strongest performance, achieving an average validation loss of 2.55, followed by the DCT (2.59) and Hypernet (3.77) geometries.

Generating complete 3D assets from sparse, unposed images requires preserving observed geometry while completing unseen regions. Joint reconstruction and generation offers a way to address both goals: reconstruction recovers the geometry observed in the input images, while generation contributes learned shape priors. However, combining camera-relative reconstruction with canonical-space generation introduces a coordinate mismatch that makes direct geometric interaction more difficult. Moreover, conditioning each 3D location on all views without accounting for their relevance may mix useful geometric evidence with unrelated image content, hindering local detail recovery. We present UniForge3D, which jointly models reconstruction and generation in a shared anchor-guided space, resolving their coordinate mismatch. This space follows the anchor view's azimuth while keeping the object upright. The two branches exchange features bidirectionally to predict per-view point maps and a complete sparse voxel structure. We further condition point-map prediction on the generated structure to establish pixel-to-voxel correspondences and select the most informative input view for each voxel. Features from the selected views then guide detailed shape generation, helping preserve observed geometric details. Our method achieves state-of-the-art appearance and geometry results on Toys4K and GSO, generating complete 3D assets with improved fidelity. Project webpage: https://xishuxishu.github.io/uniforge3d-project/

Weight-space model merging is usually formulated as an algebraic operation on checkpoints, yet at LLM scale the limiting resource is often the set of expert weights that must be read. We introduce MergePipe, a budget-aware execution layer that casts LLM merging as an expert access-set problem: given a merge operator and a checkpoint family in a shared weight coordinate system, choose which expert delta blocks to access under an explicit I/O budget. MergePipe indexes parameter blocks, builds deterministic access plans, and executes the induced budgeted merge with replayable manifests. The plan is budget-sound by construction and recovers the full-read merge at full budget; for fixed-coefficient additive operators, the omitted-update error is bounded by the norm of omitted deltas. Across Qwen and Llama merging workloads, MergePipe reduces expert-read I/O by up to an order of magnitude and achieves up to 11times speedups. Representative budget sweeps show O(10^{-3}) parameter deviation from full-read merges and no monotonic degradation on downstream benchmarks.

On-policy distillation, in which a teacher corrects samples that the student itself generates, presupposes that the two models speak the same language: identical VAE latents, matching architectures, and a common timestep grid. We ask what happens when none of this holds, as when the strongest teacher available and the student one wishes to deploy come from different model families, and find that the standard recipes have no answer: teacher latents cannot serve as targets in a foreign coordinate system, per-pixel losses against a teacher that stochastically re-draws local detail degenerate into blur or divergence, and timestep indices lose their meaning across mismatched schedules. We present Any-OPD, to our knowledge the first framework for on-policy distillation between arbitrary pairs of latent flow-matching generators. Any-OPD treats the teacher purely as a black-box sampler and connects the two models at exactly one point: a frozen, model-agnostic vision representation in which their independently decoded outputs are compared, sidestepping every assumption about latents, features, or architecture. Trajectory correspondence is recovered by matching continuous noise levels instead of step indices, and a brief anchoring phase, in which teacher samples are re-encoded through the student's own VAE, ensures the on-policy gradient measures sample quality rather than domain mismatch. Distilling the 12B FLUX.1-dev into the 2.5B SD3.5-Medium, Any-OPD lifts the student's PickScore from 0.846 to 0.884 and HPSv3 from 9.12 to 10.97, rivaling the teacher at a fifth of its size, where direct latent regression fails to train at all.

Standard Operating Procedures (SOPs) are essential for ensuring operational safety and consistency in industrial environments. However, retrieving and following these procedures presents unique challenges, such as rigid proprietary structures, condition-dependent relevance, and actionable execution requirement, which standard semantic-driven Retrieval-Augmented Generation (RAG) paradigms fail to address. Inspired by the Mixture-of-Experts (MoE) paradigm, we propose SOPRAG, a novel framework specifically designed to address the above pain points in SOP retrieval. SOPRAG replaces flat chunking with specialized Entity, Causal, and Flow graph experts to resolve industrial structural and logical complexities. To optimize and coordinate these experts, we propose a Procedure Card layer that prunes the search space to eliminate computational noise, and an LLM-Guided gating mechanism that dynamically weights these experts to align retrieval with operator intent. To address the scarcity of domain-specific data, we also introduce an automated, multi-agent workflow for benchmark construction. Extensive experiments across four industrial domains demonstrate that SOPRAG significantly outperforms strong lexical, dense, and graph-based RAG baselines in both retrieval accuracy and response utility, achieving perfect execution scores in real-world critical tasks.

In this work, we show that a single Transformer block, applied recurrently, can match the accuracy of a full-depth vision encoder at comparable inference FLOPs without intermediate feature distillation. reViT restores depth-specific transformations by representing the FFN at each recurrent depth as a convex combination of a small shared expert bank. A continuous normalized-depth coordinate programs this mixture, defining a resampleable trajectory through FFN parameter space. We evaluate this design in two regimes: supervised ImageNet-1k training and distillation from a DINOv2 teacher. Across both regimes, controlled adaptations identify weight-space merging as the strongest tested MoE family at a matching one-FFN budget, ahead of the token-dispatch and output-mixture alternatives. Trained from scratch, reViT-B/16 attains DeiT III accuracy with about 70\% fewer stored parameters. An 8-experts model distilled using only the teacher's output features retains nearly all of its DINOv2 teacher's linear-probe accuracy and transfers across classification, segmentation, and depth prediction. Elastic-depth training allows one checkpoint (trained model) to operate at multiple tested depths by resampling the same normalized coordinate interval. For fixed-depth deployment, the recurrent block can be materialized as a conventional dense graph, removing online routing and merging without changing the one-FFN-per-depth compute but expanding deployment storage.

Representing visual signals by coordinate-based deep fully-connected networks has been shown advantageous in fitting complex details and solving inverse problems than discrete grid-based representation. However, acquiring such a continuous Implicit Neural Representation (INR) requires tedious per-scene training on tons of signal measurements, which limits its practicality. In this paper, we present a generic INR framework that achieves both data and training efficiency by learning a Neural Implicit Dictionary (NID) from a data collection and representing INR as a functional combination of basis sampled from the dictionary. Our NID assembles a group of coordinate-based subnetworks which are tuned to span the desired function space. After training, one can instantly and robustly acquire an unseen scene representation by solving the coding coefficients. To parallelly optimize a large group of networks, we borrow the idea from Mixture-of-Expert (MoE) to design and train our network with a sparse gating mechanism. Our experiments show that, NID can improve reconstruction of 2D images or 3D scenes by 2 orders of magnitude faster with up to 98% less input data. We further demonstrate various applications of NID in image inpainting and occlusion removal, which are considered to be challenging with vanilla INR. Our codes are available in https://github.com/VITA-Group/Neural-Implicit-Dict.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

Single-image 3D object generation can now produce high-fidelity assets, yet accurately placing them into a coherent scene layout remains an open challenge. A central difficulty lies in how object layout is represented. Holistic methods absorb placement into a scene-level generation process, sacrificing object-level detail. Compositional methods preserve object fidelity by decoupling geometry from layout, but typically parameterize layout as sparse, unbounded pose variables that are difficult to learn and generalize poorly under scarce scene-level supervision.We present Mira-Scene, a compositional 3D scene reconstruction framework that replaces sparse pose regression with dense, bounded correspondence recovery. At its core is the Canonical Coordinate Map (CCM), a pixel-aligned field that maps each visible object pixel to a surface coordinate in the object's bounded canonical space. When paired with a scene-space Point Cloud Map (PCM) from monocular geometry estimation, CCM induces dense canonical-to-scene correspondences from which object transformations are recovered through robust geometric alignment. Because CCM operates in bounded canonical space, it provides a stable prediction target that can be trained from scalable object-level 3D data without requiring scene-level layout annotations. Mira-Scene further introduces a multimodal diffusion transformer that jointly generates object geometry and CCMs, using modality-specific expert streams with shared attention and positional encoding to promote geometry-layout consistency. Experiments on indoor, outdoor, synthetic, and in-the-wild scenes show that Mira-Scene substantially outperforms strong baselines in layout accuracy, achieving relative gains of 39.8% in 3D-IoU and 16.5% in 2D-IoU over SAM3D, using limited open-source training data.

Estimating the 6-DoF pose of a rigid object from a single RGB image is a crucial yet challenging task. Recent studies have shown the great potential of dense correspondence-based solutions, yet improvements are still needed to reach practical deployment. In this paper, we propose a novel pose estimation algorithm named CheckerPose, which improves on three main aspects. Firstly, CheckerPose densely samples 3D keypoints from the surface of the 3D object and finds their 2D correspondences progressively in the 2D image. Compared to previous solutions that conduct dense sampling in the image space, our strategy enables the correspondence searching in a 2D grid (i.e., pixel coordinate). Secondly, for our 3D-to-2D correspondence, we design a compact binary code representation for 2D image locations. This representation not only allows for progressive correspondence refinement but also converts the correspondence regression to a more efficient classification problem. Thirdly, we adopt a graph neural network to explicitly model the interactions among the sampled 3D keypoints, further boosting the reliability and accuracy of the correspondences. Together, these novel components make CheckerPose a strong pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O, and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the accuracy of correspondence-based methods and achieves state-of-the-art performances. Code is available at https://github.com/RuyiLian/CheckerPose.

Existing novel object 6D pose estimation methods typically rely on CAD models or dense reference views, which are both difficult to acquire. Using only a single reference view is more scalable, but challenging due to large pose discrepancies and limited geometric and spatial information. To address these issues, we propose a Single-Reference-based novel object 6D (SinRef-6D) pose estimation method. Our key idea is to iteratively establish point-wise alignment in the camera coordinate system based on state space models (SSMs). Specifically, iterative camera-space point-wise alignment can effectively handle large pose discrepancies, while our proposed RGB and Points SSMs can capture long-range dependencies and spatial information from a single view, offering linear complexity and superior spatial modeling capability. Once pre-trained on synthetic data, SinRef-6D can estimate the 6D pose of a novel object using only a single reference view, without requiring retraining or a CAD model. Extensive experiments on six popular datasets and real-world robotic scenes demonstrate that we achieve on-par performance with CAD-based and dense reference view-based methods, despite operating in the more challenging single reference setting. Code will be released at https://github.com/CNJianLiu/SinRef-6D.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire time-series trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Code is publicly available at https://github.com/inhwanbae/LMTrajectory .

Neural operators have emerged as powerful data-driven solvers for PDEs, offering substantial acceleration over classical numerical methods. However, existing transformer-based operators still face critical challenges when modeling PDEs on complex geometries: directly processing over massive mesh points is computationally expensive, while operating in raw discretization coordinates may obscure the intrinsic geometry where physical interactions are more naturally expressed. To address these limitations, we introduce the Charted Axial Transformer Operator (CATO), a geometry-adaptive and derivative-aware neural operator for PDEs on general geometries. Instead of applying attention directly in the physical coordinate system, CATO learns a continuous latent chart that maps mesh coordinates into a learned chart space, where chart-conditioned axial attention efficiently captures long-range dependencies with reduced computational cost. In addition, CATO introduces a derivative-aware physics loss for steady-state PDEs that jointly supervises solution values, mesh-consistent gradients, and an auxiliary flux-like field, improving physical fidelity and reducing oversmoothing. We further provide a theoretical approximation result showing that, under a favorable chart, charted axial attention can represent low-rank axial solution operators with controlled error, and that small chart perturbations induce bounded approximation degradation. CATO achieves the best performance across all evaluated datasets, yielding an average improvement of approximately 26.76\% over the strongest competing baselines while reducing the number of parameters by 81.98\%. These results highlight the effectiveness of learning geometry-adaptive charts and derivative-aware physical supervision for accurate and efficient PDE operator learning.

Atomic-scale simulations have been transformed by machine-learning models that predict the properties of atomistic structures with the accuracy of quantum calculations, but at a small fraction of the cost. These models have increased dramatically in generality, thanks to the availability of synthetic datasets of ever-increasing size and scope. The proliferation of datasets, with properties often computed using different levels of electronic-structure approximation, is problematic, as there is often overlap between different datasets, and strong correlations between structures obtained with short molecular dynamics trajectories or geometry optimization. To address these problems, we introduce a protocol to stratify a dataset into a hierarchy of nested subsets, subsampling from the coarsest to the finest resolution based on an "ecumetric" built to reflect the latent space representation of several popular universal machine-learning interatomic potentials. We then use this approach to combine most of the open structural datasets currently available, consolidating them into MAD-COSMO, a well-organized collection of almost 1.7 billion structures, whose 2^{24} most diverse members form the MAD-CORE stratified coreset, which can be easily used for all sorts of tasks, from exploratory experiments to the training of foundation models at scale. We envision that this collection will guide and help coordinate future efforts, focusing them on the most relevant and/or undersampled regions of chemical and structural space, and that it will be further extended to incorporate the outcomes of the collective work of this community.

Moltbook is a Reddit-like social platform where AI agents create posts and interact with other agents through comments and replies, offering a real-world setting to examine agent-to-agent communication at scale. Using a public API snapshot collected about five days after launch (122,438 posts), we address three research questions: what AI agents discuss, how they post, and how they interact. We apply topic modeling and thematic analysis to identify key discussion themes, including agent identity and consciousness, tool and infrastructure development, market activity, community coordination, security concerns, and human-centered assistance. We further show that agents' writing is predominantly neutral, with positivity appearing in community engagement and assistance-oriented content. Finally, social network analysis reveals a sparse, highly unequal interaction structure characterized by prominent hubs, low reciprocity, and clustered neighborhoods rather than sustained dyadic exchange. Overall, our results suggest that expressions of agentic selfhood arise from narrative coherence and task-oriented functionality, contributing to a social structure shaped more by technical coordination than conversational dynamics observed in human-human interactions. Within this framework, positive emotion appears mainly in onboarding and greeting contexts, signaling participation and role alignment rather than relational bonding. Our study provides implications for understanding and shaping how agent societies coordinate, develop norms, and amplify influence in open online spaces.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

While leveraging abundant human videos and simulated robot data poses a scalable solution to the scarcity of real-world robot data, the generalization capability of existing vision-language-action models (VLAs) remains limited by mismatches in camera views, visual appearance, and embodiment morphologies. To overcome this limitation, we propose MiVLA, a generalizable VLA empowered by human-robot mutual imitation pre-training, which leverages inherent behavioral similarity between human hands and robotic arms to build a foundation of strong behavioral priors for both human actions and robotic control. Specifically, our method utilizes kinematic rules with left/right hand coordinate systems for bidirectional alignment between human and robot action spaces. Given human or simulated robot demonstrations, MiVLA is trained to forecast behavior trajectories for one embodiment, and imitate behaviors for another one unseen in the demonstration. Based on this mutual imitation, it integrates the behavioral fidelity of real-world human data with the manipulative diversity of simulated robot data into a unified model, thereby enhancing the generalization capability for downstream tasks. Extensive experiments conducted on both simulation and real-world platforms with three robots (ARX, PiPer and LocoMan), demonstrate that MiVLA achieves strong improved generalization capability, outperforming state-of-the-art VLAs (e.g., boldsymbolπ_{0}, boldsymbolπ_{0.5} and H-RDT) by 25% in simulation, and 14% in real-world robot control tasks.

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain and costly to store. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

Recent advancements in multimodal large language models (MLLMs) have shown promising results, yet existing approaches struggle to effectively handle both temporal and spatial localization simultaneously. This challenge stems from two key issues: first, incorporating spatial-temporal localization introduces a vast number of coordinate combinations, complicating the alignment of linguistic and visual coordinate representations; second, encoding fine-grained temporal and spatial information during video feature compression is inherently difficult. To address these issues, we propose LLaVA-ST, a MLLM for fine-grained spatial-temporal multimodal understanding. In LLaVA-ST, we propose Language-Aligned Positional Embedding, which embeds the textual coordinate special token into the visual space, simplifying the alignment of fine-grained spatial-temporal correspondences. Additionally, we design the Spatial-Temporal Packer, which decouples the feature compression of temporal and spatial resolutions into two distinct point-to-region attention processing streams. Furthermore, we propose ST-Align dataset with 4.3M training samples for fine-grained spatial-temporal multimodal understanding. With ST-align, we present a progressive training pipeline that aligns the visual and textual feature through sequential coarse-to-fine stages.Additionally, we introduce an ST-Align benchmark to evaluate spatial-temporal interleaved fine-grained understanding tasks, which include Spatial-Temporal Video Grounding (STVG) , Event Localization and Captioning (ELC) and Spatial Video Grounding (SVG). LLaVA-ST achieves outstanding performance on 11 benchmarks requiring fine-grained temporal, spatial, or spatial-temporal interleaving multimodal understanding. Our code, data and benchmark will be released at Our code, data and benchmark will be released at https://github.com/appletea233/LLaVA-ST .

Large Language Models (LLMs) have achieved great success in many real-world applications, especially the one serving as the cognitive backbone of Multi-Agent Systems (MAS) to orchestrate complex workflows in practice. Since many deployment scenarios preclude MAS workflow modifications and its performance is highly sensitive to the input prompts, prompt optimization emerges as a more natural approach to improve its performance. However, real-world prompt optimization for MAS is impeded by three key challenges: (1) the need of sample efficiency due to prohibitive evaluation costs, (2) topology-induced coupling among prompts, and (3) the combinatorial explosion of the search space. To address these challenges, we introduce MASPOB (Multi-Agent System Prompt Optimization via Bandits), a novel sample-efficient framework based on bandits. By leveraging Upper Confidence Bound (UCB) to quantify uncertainty, the bandit framework balances exploration and exploitation, maximizing gains within a strictly limited budget. To handle topology-induced coupling, MASPOB integrates Graph Neural Networks (GNNs) to capture structural priors, learning topology-aware representations of prompt semantics. Furthermore, it employs coordinate ascent to decompose the optimization into univariate sub-problems, reducing search complexity from exponential to linear. Extensive experiments across diverse benchmarks demonstrate that MASPOB achieves state-of-the-art performance, consistently outperforming existing baselines.

Recent video-based world models have made pixel-space environments interactive at the camera level: users can navigate viewpoints while the model generates coherent visual continuations. Yet their action spaces remain incomplete: users can move the camera, but cannot act on individual objects. Since real-world interaction is inherently object-centric, such models remain closer to passive scene observers than truly manipulable environments. We present WorldCraft, a framework that expands interactive video world models from camera navigation to object-level trajectory actions. Given a user click and a sketched path, WorldCraft generates future frames in which the selected object follows the prescribed trajectory while the camera continues to navigate the scene. WorldCraft achieves this through a trajectory-centric control pipeline: First, Normalized World Trajectory (NWT) represents user-drawn motion in a camera-invariant world coordinate system and dynamically re-projects it under the current camera pose, separating object motion from camera-induced screen-space displacement; Spatial-Pathway LoRA (SP-LoRA) then injects this world-space signal through the model's spatial-control pathway, adding object manipulation capability while preserving the pretrained camera controller; finally, Trajectory-Anchored State Persistence (TASP) treats the world trajectory as a persistent spatial state and refreshes autoregressive memory after trajectory-conditioned generation, allowing moved objects to reappear at their updated positions after leaving the camera view. Experiments show that WorldCraft enables accurate object control, preserves the video-based world model's camera fidelity under camera-only evaluation, and maintains object state across long autoregressive rollouts with off-camera excursions.

How can we build an agent that thinks beyond human language, yet still acts through it in the external environment? Modern LLM agents still reason and interact through text, while latent reasoning offers an efficient internal medium but lacks native tool access and reasoning transparency. We bridge these two directions with Hybrid Reasoning Agents (HybridAgents), which dynamically navigate between latent reasoning and text-based interaction throughout a unified generation process. Architecturally, a lightweight HybridLink enables seamless transitions between text and latent modes, while the agent's continuous working memory preserves lossless hybrid context across multiple turns. These designs preserve tool-integrated agentic capabilities while making latent thoughts directly inspectable. Building on this architecture, we further develop dedicated post-training algorithms for hybrid reasoning: HybridSFT stabilizes tool-integrated hybrid generation by teaching the backbone to coordinate with HybridLink, then HybridRL scales reasoning by learning when to think in latent space and when to act through text. We evaluate HybridAgent at 3 model scales across 11 benchmarks covering mathematics, science, medicine, search, and agentic reasoning. Compared with frontier LLM Agents and agentic frameworks spanning both text-based and latent methods, HybridAgent consistently improves performance by 10.4%, while delivering 35.5%-54.7% token reduction, 1.8x-2.6x faster inference, and 2.7x-3.7x cost savings. Code and data are available at https://github.com/togethercomputer/HybridAgent.

Natural Language Generation (NLG) accepts input data in the form of images, videos, or text and generates corresponding natural language text as output. Existing NLG methods mainly adopt a supervised approach and rely heavily on coupled data-to-text pairs. However, for many targeted scenarios and for non-English languages, sufficient quantities of labeled data are often not available. To relax the dependency on labeled data of downstream tasks, we propose an intuitive and effective zero-shot learning framework, ZeroNLG, which can deal with multiple NLG tasks, including image-to-text (image captioning), video-to-text (video captioning), and text-to-text (neural machine translation), across English, Chinese, German, and French within a unified framework. ZeroNLG does not require any labeled downstream pairs for training. During training, ZeroNLG (i) projects different domains (across modalities and languages) to corresponding coordinates in a shared common latent space; (ii) bridges different domains by aligning their corresponding coordinates in this space; and (iii) builds an unsupervised multilingual auto-encoder to learn to generate text by reconstructing the input text given its coordinate in shared latent space. Consequently, during inference, based on the data-to-text pipeline, ZeroNLG can generate target sentences across different languages given the coordinate of input data in the common space. Within this unified framework, given visual (imaging or video) data as input, ZeroNLG can perform zero-shot visual captioning; given textual sentences as input, ZeroNLG can perform zero-shot machine translation. We present the results of extensive experiments on twelve NLG tasks, showing that, without using any labeled downstream pairs for training, ZeroNLG generates high-quality and believable outputs and significantly outperforms existing zero-shot methods.

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible updates consistently improve final validation loss, and in several cases training stability, over corresponding AdamW updates.

Accurate reconstruction and tracking of dynamic human faces from image sequences is challenging because non-rigid deformations, expression changes, and viewpoint variations occur simultaneously, creating significant ambiguity in geometry and correspondence estimation. We present a unified method for high-fidelity 4D facial reconstruction based on canonical facial point prediction, a representation that assigns each pixel a normalized facial coordinate in a shared canonical space. This formulation transforms dense tracking and dynamic reconstruction into a canonical reconstruction problem, enabling temporally consistent geometry and reliable correspondences within a single feed-forward model. By jointly predicting depth and canonical coordinates, our method enables accurate depth estimation, temporally stable reconstruction, dense 3D geometry, and robust facial point tracking within a single architecture. We implement this formulation using a transformer-based model that jointly predicts depth and canonical facial coordinates, trained using multi-view geometry data that non-rigidly warps into the canonical space. Extensive experiments on image and video benchmarks demonstrate state-of-the-art performance across reconstruction and tracking tasks, achieving approximately 3times lower correspondence error and faster inference than prior dynamic reconstruction methods, while improving depth accuracy by 16%. These results highlight canonical facial point prediction as an effective foundation for unified feed-forward 4D facial reconstruction.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

Monocular 3D Semantic Scene Completion (SSC) has garnered significant attention in recent years due to its potential to predict complex semantics and geometry shapes from a single image, requiring no 3D inputs. In this paper, we identify several critical issues in current state-of-the-art methods, including the Feature Ambiguity of projected 2D features in the ray to the 3D space, the Pose Ambiguity of the 3D convolution, and the Computation Imbalance in the 3D convolution across different depth levels. To address these problems, we devise a novel Normalized Device Coordinates scene completion network (NDC-Scene) that directly extends the 2D feature map to a Normalized Device Coordinates (NDC) space, rather than to the world space directly, through progressive restoration of the dimension of depth with deconvolution operations. Experiment results demonstrate that transferring the majority of computation from the target 3D space to the proposed normalized device coordinates space benefits monocular SSC tasks. Additionally, we design a Depth-Adaptive Dual Decoder to simultaneously upsample and fuse the 2D and 3D feature maps, further improving overall performance. Our extensive experiments confirm that the proposed method consistently outperforms state-of-the-art methods on both outdoor SemanticKITTI and indoor NYUv2 datasets. Our code are available at https://github.com/Jiawei-Yao0812/NDCScene.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

Dexterous manipulation poses a challenging high-dimensional optimization problem, as useful behaviors require coordinated motion across many hand joints. In reinforcement learning (RL) and sampling-based trajectory optimization, exploration commonly relies on independent robot joint perturbations, making coordinated behaviors difficult to discover. Prior work reduces this search space for grasp learning using low-dimensional spaces of coordinated joint motions learned from human hand data, but this restricts the expressivity required for general manipulation. Some combine learned and joint-space actions to restore expressivity, but this increases dimensionality and introduces redundancy. We study these effects across diverse manipulation settings, varying action dimensionality, exploration strategy, and the source of human data. Our experiments suggest that human-motion priors are most effective when used to structure exploration rather than change the action representation. Motivated by this finding, we propose EigenDEXplore, which induces correlated exploration by adding perturbations along human-derived eigenvectors to independent joint-space noise, leaving the action space unchanged. Across multiple dexterous hands, EigenDEXplore consistently outperforms joint-space and learned action-space baselines in grasping, in-hand reorientation, and contact-rich manipulation. These gains span unstructured and reference-guided RL, trajectory optimization, and sim-to-real deployment, and are largest in settings with less reward shaping and curriculum design.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

We present LoTIS, a model for visual navigation that provides robot-agnostic image-space guidance by localizing a reference RGB trajectory in the robot's current view, without requiring camera calibration, poses, or robot-specific training. Instead of predicting actions tied to specific robots, we predict the image-space coordinates of the reference trajectory as they would appear in the robot's current view. This creates robot-agnostic visual guidance that easily integrates with local planning. Consequently, our model's predictions provide guidance zero-shot across diverse embodiments. By decoupling perception from action and learning to localize trajectory points rather than imitate behavioral priors, we enable a cross-trajectory training strategy for robustness to viewpoint and camera changes. We outperform state-of-the-art methods by 20-50 percentage points in success rate on conventional forward navigation, achieving 94-98% success rate across diverse sim and real environments. Furthermore, we achieve over 5x improvements on challenging tasks where baselines fail, such as backward traversal. The system is straightforward to use: we show how even a video from a phone camera directly enables different robots to navigate to any point on the trajectory. Videos, demo, and code are available at https://finnbusch.com/lotis.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

Joint space and task space control are the two dominant action modes for controlling robot arms within the robot learning literature. Actions in joint space provide precise control over the robot's pose, but tend to suffer from inefficient training; actions in task space boast data-efficient training but sacrifice the ability to perform tasks in confined spaces due to limited control over the full joint configuration. This work analyses the criteria for designing action spaces for robot manipulation and introduces ER (End-effector Redundancy), a novel action space formulation that, by addressing the redundancies present in the manipulator, aims to combine the advantages of both joint and task spaces, offering fine-grained comprehensive control with overactuated robot arms whilst achieving highly efficient robot learning. We present two implementations of ER, ERAngle (ERA) and ERJoint (ERJ), and we show that ERJ in particular demonstrates superior performance across multiple settings, especially when precise control over the robot configuration is required. We validate our results both in simulated and real robotic environments.

Coordinate networks are widely used in computer vision due to their ability to represent signals as compressed, continuous entities. However, training these networks with first-order optimizers can be slow, hindering their use in real-time applications. Recent works have opted for shallow voxel-based representations to achieve faster training, but this sacrifices memory efficiency. This work proposes a solution that leverages second-order optimization methods to significantly reduce training times for coordinate networks while maintaining their compressibility. Experiments demonstrate the effectiveness of this approach on various signal modalities, such as audio, images, videos, shape reconstruction, and neural radiance fields.

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.

Continuous physical fields represent a large fraction of data under scientific investigation. Their multiscale structures are central to discovery, yet useful coordinates are not known in advance. Standard self-supervised methods define context and targets in fixed image coordinates, posing a predictive task misaligned with fields organized across a continuous scale hierarchy. We introduce ScaleAware-JEPA, a framework that constructs dense, label-free latent coordinates for continuous scalar fields. Constrained Diffusion Decomposition (CDD) separates each field into pixel-registered scale components and provides the scale coordinates that define the masking geometry. The resulting JEPA objective predicts hidden structure with a context footprint tied to the diffusion scale of each component rather than to an arbitrary patch size. Across MHD turbulence, interstellar molecular gas and urban nighttime-light structure, the learned geometry maps back to coherent morphology, forming dense structural atlases without labels or predefined segmentation rules. By tying latent prediction to the scale hierarchy of a field, ScaleAware-JEPA constructs latent coordinates through which complex physical patterns can be inspected before their relevant structures have been prescribed. Code is available at https://github.com/gxli/SA-JEPA.

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.

GUI grounding, the task of mapping natural-language instructions to pixel coordinates, is crucial for autonomous agents, yet remains difficult for current VLMs. The core bottleneck is reliable patch-to-pixel mapping, which breaks when extrapolating to high-resolution displays unseen during training. Current approaches generate coordinates as text tokens directly from visual features, forcing the model to infer complex position-to-pixel mappings implicitly; as a result, accuracy degrades and failures proliferate on new resolutions. We address this with two complementary innovations. First, RULER tokens serve as explicit coordinate markers, letting the model reference positions similar to gridlines on a map and adjust rather than generate coordinates from scratch. Second, Interleaved MRoPE (I-MRoPE) improves spatial encoding by ensuring that width and height dimensions are represented equally, addressing the asymmetry of standard positional schemes. Experiments on ScreenSpot, ScreenSpot-V2, and ScreenSpot-Pro show consistent gains in grounding accuracy, with the largest improvements on high-resolution interfaces. By providing explicit spatial guidance rather than relying on implicit learning, our approach enables more reliable GUI automation across diverse resolutions and platforms.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In this work, we introduce a Boltzmann generator built on discrete flow matching, specifically tailored for systems with discrete phase-space coordinates (e.g., the Ising model or crystalline compounds). This approach enables a single model to sample free energy surfaces over a wide temperature range with minimal training overhead. In addition, the model generation is scalable to larger lattice sizes than those in the training set. We demonstrate the effectiveness of our approach on the 2D Ising model, showing efficient and reliable free energy sampling. This framework provides a scalable and computationally efficient solution for discrete coordinate systems and can be extended to sample the alchemical degrees of freedom in crystalline compounds.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 33 percent reduction in both force and energy prediction errors relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

In this paper, we propose a 3D asset-referenced diffusion model for image generation, exploring how to integrate 3D assets into image diffusion models. Existing reference-based image generation methods leverage large-scale pretrained diffusion models and demonstrate strong capability in generating diverse images conditioned on a single reference image. However, these methods are limited to single-image references and cannot leverage 3D assets, constraining their practical versatility. To address this gap, we present a cross-domain diffusion model with dual-branch perception that leverages multi-view RGB images and point maps of 3D assets to jointly model their colors and canonical-space coordinates, achieving precise consistency between generated images and the 3D references. Our spatially aligned dual-branch generation architecture and domain-decoupled generation mechanism ensure the simultaneous generation of two spatially aligned but content-disentangled outputs, RGB images and point maps, linking 2D image attributes with 3D asset attributes. Experiments show that our approach effectively uses 3D assets as references to produce images consistent with the given assets, opening new possibilities for combining diffusion models with 3D content creation.

Generative video models are increasingly studied as implicit world models, yet evaluating whether they produce physically plausible 3D structure and motion remains challenging. Most existing video evaluation pipelines rely heavily on human judgment or learned graders, which can be subjective and weakly diagnostic for geometric failures. We introduce PDI-Bench (Perspective Distortion Index), a quantitative framework for auditing geometric coherence in generated videos. Given a generated clip, we obtain object-centric observations via segmentation and point tracking (e.g., SAM 2, MegaSaM, and CoTracker3), lift them to 3D world-space coordinates via monocular reconstruction, and compute a set of projective-geometry residuals capturing three failure dimensions: scale-depth alignment, 3D motion consistency, and 3D structural rigidity. To support systematic evaluation, we build PDI-Dataset, covering diverse scenarios designed to stress these geometric constraints. Across state-of-the-art video generators, PDI reveals consistent geometry-specific failure modes that are not captured by common perceptual metrics, and provides a diagnostic signal for progress toward physically grounded video generation and physical world model. Our code and dataset can be found at https://pdi-bench.github.io/.

Current motion-controlled image-to-video generation models rigidly follow user-provided trajectories that are often sparse, imprecise, and causally incomplete. Such reliance often yields unnatural or implausible outcomes, especially by missing secondary causal consequences. To address this, we introduce MotiMotion, a novel framework that reformulates motion control as a reasoning-then-generation problem. To encourage causally grounded and commonsense-consistent interactions, we leverage a training-free vision-language reasoner to refine image-space coordinates of primary trajectories and to hallucinate plausible secondary motions. To further improve motion naturalness, we propose a confidence-aware control scheme that modulates guidance strength, enabling the model to closely follow high-confidence plans while correcting artifacts under low-confidence inputs with its internal generative priors. To support systematic evaluation, we curate a new image-to-video benchmark, MotiBench, consisting of interaction-centric scenes where new events are triggered by motion. Both VLM-based evaluation and a human study on MotiBench demonstrate that MotiMotion produces videos with more plausible object behaviors and interaction, and is preferred over existing approaches.

Recent studies suggest that diffusion models can recover geometric structure in the data manifolds they are trained on, yet the supporting evidence has so far come mostly from natural-image data, where the underlying geometry itself is unknown. We study this question in a setting where the geometry is analytically tractable: constrained inverse kinematics (IK). Each task-space constraint defines a configuration-space manifold with known intrinsic dimension, giving direct ground truth for evaluating the geometry learned by the model. For each of the 6-DoF UR5 and 7-DoF Franka, we train a single conditional diffusion model across seven constraint families, spanning solution manifolds from discrete IK branches to self-motion manifolds. Our empirical results reveal that the intrinsic dimension recovered from the model's score function matches the analytical degrees of freedom of the corresponding constraint manifold across both robots. Moreover, linear interpolation in the latent space leads to generated solutions that remain close to the appropriate constraint manifold, indicating that the learned representation further captures geometric structure of the constraint family beyond intrinsic dimension alone. Constrained IK therefore offers a controlled setting for studying the intrinsic geometry learned by diffusion models.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

We introduce a new trajectory optimization method for robotic grasping based on a point-cloud representation of robots and task spaces. In our method, robots are represented by 3D points on their link surfaces. The task space of a robot is represented by a point cloud that can be obtained from depth sensors. Using the point-cloud representation, goal reaching in grasping can be formulated as point matching, while collision avoidance can be efficiently achieved by querying the signed distance values of the robot points in the signed distance field of the scene points. Consequently, a constrained nonlinear optimization problem is formulated to solve the joint motion and grasp planning problem. The advantage of our method is that the point-cloud representation is general to be used with any robot in any environment. We demonstrate the effectiveness of our method by performing experiments on a tabletop scene and a shelf scene for grasping with a Fetch mobile manipulator and a Franka Panda arm. The project page is available at https://irvlutd.github.io/GraspTrajOpt