Daily Papers

Vision-Language-Action (VLA) models achieve strong benchmark performance but still struggle in real-world deployment with unseen objects, background shifts, and different robot embodiments. We argue that this stems from the lack of a unified geometry-aware manipulation representation, leaving existing VLAs vulnerable to low-level trajectory supervision, misaligned 3D features, and embodiment differences. To address this, we propose GEAR-VLA, a VLA framework for learning unified geometry-aware action representations for generalizable robotic manipulation. GEAR-VLA adopts coarse-to-fine action learning, where multi-source embodied pretraining equips the VLM with embodied reasoning and discrete action understanding before latent action tokens connect action semantics to a gradient-decoupled DiT continuous action expert. It further performs semantic-aligned 3D integration by aligning a trainable 3D spatial backbone with the VLA representation while freezing the original VLM-aligned visual pathway. To share this representation across robots, GEAR-VLA uses embodiment canonicalization, where embodiment-aware states and embodiment-invariant actions confine robot differences to the low-level interface. Extensive simulation and real-world experiments demonstrate strong generalization: GEAR-VLA achieves state-of-the-art performance on LIBERO, zero-shot LIBERO-Plus, and RoboTwin 2.0, reaches 85.9% success on AgileX and 81.0% on the pretraining-unseen LDT-01 embodiment, and obtains 90.1% success on a 6,360-trial universal grasping benchmark with 212 unseen objects. Code and models will be released at https://github.com/babynabeauty/GEAR-VLA.

Object-level manipulation, relocating or reorienting objects in images or videos while preserving scene realism, is central to film post-production, AR, and creative editing. Yet existing methods struggle to jointly achieve three core goals: background preservation, geometric consistency under viewpoint shifts, and user-controllable transformations. Geometry-based approaches offer precise control but require explicit 3D reconstruction and generalize poorly; diffusion-based methods generalize better but lack fine-grained geometric control. We present Ctrl&Shift, an end-to-end diffusion framework to achieve geometry-consistent object manipulation without explicit 3D representations. Our key insight is to decompose manipulation into two stages, object removal and reference-guided inpainting under explicit camera pose control, and encode both within a unified diffusion process. To enable precise, disentangled control, we design a multi-task, multi-stage training strategy that separates background, identity, and pose signals across tasks. To improve generalization, we introduce a scalable real-world dataset construction pipeline that generates paired image and video samples with estimated relative camera poses. Extensive experiments demonstrate that Ctrl&Shift achieves state-of-the-art results in fidelity, viewpoint consistency, and controllability. To our knowledge, this is the first framework to unify fine-grained geometric control and real-world generalization for object manipulation, without relying on any explicit 3D modeling.

Manipulating objects with varying geometries and deformable objects is a major challenge in robotics. Tasks such as insertion with different objects or cloth hanging require precise control and effective modelling of complex dynamics. In this work, we frame this problem through the lens of a heterogeneous graph that comprises smaller sub-graphs, such as actuators and objects, accompanied by different edge types describing their interactions. This graph representation serves as a unified structure for both rigid and deformable objects tasks, and can be extended further to tasks comprising multiple actuators. To evaluate this setup, we present a novel and challenging reinforcement learning benchmark, including rigid insertion of diverse objects, as well as rope and cloth manipulation with multiple end-effectors. These tasks present a large search space, as both the initial and target configurations are uniformly sampled in 3D space. To address this issue, we propose a novel graph-based policy model, dubbed Heterogeneous Equivariant Policy (HEPi), utilizing SE(3) equivariant message passing networks as the main backbone to exploit the geometric symmetry. In addition, by modeling explicit heterogeneity, HEPi can outperform Transformer-based and non-heterogeneous equivariant policies in terms of average returns, sample efficiency, and generalization to unseen objects. Our project page is available at https://thobotics.github.io/hepi.

Understanding and predicting the dynamics of the physical world can enhance a robot's ability to plan and interact effectively in complex environments. While recent video generation models have shown strong potential in modeling dynamic scenes, generating videos that are both temporally coherent and geometrically consistent across camera views remains a significant challenge. To address this, we propose a 4D video generation model that enforces multi-view 3D consistency of videos by supervising the model with cross-view pointmap alignment during training. This geometric supervision enables the model to learn a shared 3D representation of the scene, allowing it to predict future video sequences from novel viewpoints based solely on the given RGB-D observations, without requiring camera poses as inputs. Compared to existing baselines, our method produces more visually stable and spatially aligned predictions across multiple simulated and real-world robotic datasets. We further show that the predicted 4D videos can be used to recover robot end-effector trajectories using an off-the-shelf 6DoF pose tracker, supporting robust robot manipulation and generalization to novel camera viewpoints.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

Effective robotic manipulation relies on a precise understanding of 3D scene geometry, and one of the most straightforward ways to acquire such geometry is through multi-view observations. Motivated by this, we present GP3 -- a 3D geometry-aware robotic manipulation policy that leverages multi-view input. GP3 employs a spatial encoder to infer dense spatial features from RGB observations, which enable the estimation of depth and camera parameters, leading to a compact yet expressive 3D scene representation tailored for manipulation. This representation is fused with language instructions and translated into continuous actions via a lightweight policy head. Comprehensive experiments demonstrate that GP3 consistently outperforms state-of-the-art methods on simulated benchmarks. Furthermore, GP3 transfers effectively to real-world robots without depth sensors or pre-mapped environments, requiring only minimal fine-tuning. These results highlight GP3 as a practical, sensor-agnostic solution for geometry-aware robotic manipulation.

Recent advances in Vision-Language-Action (VLA) models have opened new avenues for robot manipulation, yet existing methods exhibit limited efficiency and a lack of high-level knowledge and spatial awareness. To address these challenges, we propose PokeVLA, a lightweight yet powerful foundation model for embodied manipulation that effectively infuses vision-language understanding into action learning. Our framework introduces a two-stage training paradigm: first, we pre-train a compact vision-language model (PokeVLM) on a curated multimodal dataset of 2.4M samples encompassing spatial grounding, affordance, and embodied reasoning tasks; second, we inject manipulation-relevant representations into the action space through multi-view goal-aware semantics learning, geometry alignment, and a novel action expert. Extensive experiments demonstrate state-of-the-art performance on the LIBERO-Plus benchmark and in real-world deployment, outperforming comparable baselines in success rate and robustness under diverse perturbations. To foster reproducibility and community progress, we will open-source our code, model weights, and the scripts for the curated pre-training dataset. Project page: https://getterupper.github.io/PokeVLA

Recent advancements in vision-language-action (VLA) models have shown promise in robotic manipulation, yet they continue to struggle with long-horizon, multi-step tasks. Existing methods lack internal reasoning mechanisms that can identify task-relevant interaction cues or track progress within a subtask, leading to critical execution errors such as repeated actions, missed steps, and premature termination. To address these challenges, we introduce PALM, a VLA framework that structures policy learning around interaction-centric affordance reasoning and subtask progress cues. PALM distills complementary affordance representations that capture object relevance, contact geometry, spatial placements, and motion dynamics, and serve as task-relevant anchors for visuomotor control. To further stabilize long-horizon execution, PALM predicts continuous within-subtask progress, enabling seamless subtask transitions. Across extensive simulation and real-world experiments, PALM consistently outperforms baselines, achieving a 91.8% success rate on LIBERO-LONG, a 12.5% improvement in average length on CALVIN ABC->D, and a 2x improvement over real-world baselines across three long-horizon generalization settings.

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

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

3D geometric information is essential for manipulation tasks, as robots need to perceive the 3D environment, reason about spatial relationships, and interact with intricate spatial configurations. Recent research has increasingly focused on the explicit extraction of 3D features, while still facing challenges such as the lack of large-scale robotic 3D data and the potential loss of spatial geometry. To address these limitations, we propose the Lift3D framework, which progressively enhances 2D foundation models with implicit and explicit 3D robotic representations to construct a robust 3D manipulation policy. Specifically, we first design a task-aware masked autoencoder that masks task-relevant affordance patches and reconstructs depth information, enhancing the 2D foundation model's implicit 3D robotic representation. After self-supervised fine-tuning, we introduce a 2D model-lifting strategy that establishes a positional mapping between the input 3D points and the positional embeddings of the 2D model. Based on the mapping, Lift3D utilizes the 2D foundation model to directly encode point cloud data, leveraging large-scale pretrained knowledge to construct explicit 3D robotic representations while minimizing spatial information loss. In experiments, Lift3D consistently outperforms previous state-of-the-art methods across several simulation benchmarks and real-world scenarios.

The fragmentation between high-level task semantics and low-level geometric features remains a persistent challenge in robotic manipulation. While vision-language models (VLMs) have shown promise in generating affordance-aware visual representations, the lack of semantic grounding in canonical spaces and reliance on manual annotations severely limit their ability to capture dynamic semantic-affordance relationships. To address these, we propose Primitive-Aware Semantic Grounding (PASG), a closed-loop framework that introduces: (1) Automatic primitive extraction through geometric feature aggregation, enabling cross-category detection of keypoints and axes; (2) VLM-driven semantic anchoring that dynamically couples geometric primitives with functional affordances and task-relevant description; (3) A spatial-semantic reasoning benchmark and a fine-tuned VLM (Qwen2.5VL-PA). We demonstrate PASG's effectiveness in practical robotic manipulation tasks across diverse scenarios, achieving performance comparable to manual annotations. PASG achieves a finer-grained semantic-affordance understanding of objects, establishing a unified paradigm for bridging geometric primitives with task semantics in robotic manipulation.

Learning to manipulate dynamic and deformable objects from a single demonstration video holds great promise in terms of scalability. Previous approaches have predominantly focused on either replaying object relationships or actor trajectories. The former often struggles to generalize across diverse tasks, while the latter suffers from data inefficiency. Moreover, both methodologies encounter challenges in capturing invisible physical attributes, such as forces. In this paper, we propose to interpret video demonstrations through Parameterized Symbolic Abstraction Graphs (PSAG), where nodes represent objects and edges denote relationships between objects. We further ground geometric constraints through simulation to estimate non-geometric, visually imperceptible attributes. The augmented PSAG is then applied in real robot experiments. Our approach has been validated across a range of tasks, such as Cutting Avocado, Cutting Vegetable, Pouring Liquid, Rolling Dough, and Slicing Pizza. We demonstrate successful generalization to novel objects with distinct visual and physical properties.

Previous studies on robotic manipulation are based on a limited understanding of the underlying 3D motion constraints and affordances. To address these challenges, we propose a comprehensive paradigm, termed UniAff, that integrates 3D object-centric manipulation and task understanding in a unified formulation. Specifically, we constructed a dataset labeled with manipulation-related key attributes, comprising 900 articulated objects from 19 categories and 600 tools from 12 categories. Furthermore, we leverage MLLMs to infer object-centric representations for manipulation tasks, including affordance recognition and reasoning about 3D motion constraints. Comprehensive experiments in both simulation and real-world settings indicate that UniAff significantly improves the generalization of robotic manipulation for tools and articulated objects. We hope that UniAff will serve as a general baseline for unified robotic manipulation tasks in the future. Images, videos, dataset, and code are published on the project website at:https://sites.google.com/view/uni-aff/home

Generalist robot policies must follow user instructions while reasoning about how objects, cameras, and robot actions interact in the 3D physical world. Recent vision-language-action models (VLAs) and video world-action models (WAMs) inherit strong semantic or temporal priors from large-scale foundation models, but they still operate primarily on 2D image frames or 2D-derived latent spaces, leaving implicit the 3D geometry required for contact-rich manipulation. We propose the Geometric Action Model (GAM), a language-conditioned manipulation policy that directly repurposes a pretrained geometric foundation model (GFM) as a shared substrate for perception, temporal prediction, and action decoding. GAM splits the GFM at an intermediate layer: the shallow layers serve as an observation encoder, and a causal future predictor inserted at the split layer forecasts future latent tokens conditioned on language, proprioception, and action history. The predicted future tokens are then routed through the remaining GFM blocks for feature propagation and decoding, allowing a single backbone to produce both future geometry and actions. This design equips the GFM with language-conditioned temporal world modeling through minimal architectural modification while preserving its rich geometric priors. Across a broad suite of simulation and real-robot manipulation benchmarks, GAM is more accurate, more robust, faster, and lighter than current foundation-model-scale baselines.

We are surrounded by various objects with movable, articulated parts, e.g., box, handle, door. An accurate and generalizable perception of articulated parts is essential to enhance robotic manipulation capabilities. Building on this need, recent efforts in articulated parts perception have followed two main directions: One line of work uses pose-based representation, which requires high manual cost; in parallel, affordance-based methods extract future object motion from point tracking without additional manual efforts, but suffer from low-quality data. In this paper, we propose a new representation of articulated parts, Geometric Primary Structure (GPS), an abstraction of the part geometry structure to balance scalability and quality. For efficient and scalable data collection, GPS is integrated with a portable Virtual Reality (VR) device and requires only one minute to annotate one object sequence. This direct human annotation provides higher quality than the estimated affordance. With this efficient VR-GPS system, we collect 41K frames for 234 objects across six part classes, and train a generalizable GPS model with a single RGB-D object image as input. For object manipulation, we deploy a heuristic policy based on GPS prediction. Without any in-domain fine-tuning, our method achieves an 73% success rate, covering 270 initial states for 9 objects. Our code, data and reusable tool are available at https://enlighten0707.github.io/gps.

Self-supervised and language-supervised image models contain rich knowledge of the world that is important for generalization. Many robotic tasks, however, require a detailed understanding of 3D geometry, which is often lacking in 2D image features. This work bridges this 2D-to-3D gap for robotic manipulation by leveraging distilled feature fields to combine accurate 3D geometry with rich semantics from 2D foundation models. We present a few-shot learning method for 6-DOF grasping and placing that harnesses these strong spatial and semantic priors to achieve in-the-wild generalization to unseen objects. Using features distilled from a vision-language model, CLIP, we present a way to designate novel objects for manipulation via free-text natural language, and demonstrate its ability to generalize to unseen expressions and novel categories of objects.

The ability for robots to perform efficient and zero-shot grasping of object parts is crucial for practical applications and is becoming prevalent with recent advances in Vision-Language Models (VLMs). To bridge the 2D-to-3D gap for representations to support such a capability, existing methods rely on neural fields (NeRFs) via differentiable rendering or point-based projection methods. However, we demonstrate that NeRFs are inappropriate for scene changes due to their implicitness and point-based methods are inaccurate for part localization without rendering-based optimization. To amend these issues, we propose GraspSplats. Using depth supervision and a novel reference feature computation method, GraspSplats generates high-quality scene representations in under 60 seconds. We further validate the advantages of Gaussian-based representation by showing that the explicit and optimized geometry in GraspSplats is sufficient to natively support (1) real-time grasp sampling and (2) dynamic and articulated object manipulation with point trackers. With extensive experiments on a Franka robot, we demonstrate that GraspSplats significantly outperforms existing methods under diverse task settings. In particular, GraspSplats outperforms NeRF-based methods like F3RM and LERF-TOGO, and 2D detection methods.

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.

Synthesizing controllable 6-DOF object manipulation trajectories in 3D environments is essential for enabling robots to interact with complex scenes, yet remains challenging due to the need for accurate spatial reasoning, physical feasibility, and multimodal scene understanding. Existing approaches often rely on 2D or partial 3D representations, limiting their ability to capture full scene geometry and constraining trajectory precision. We present GMT, a multimodal transformer framework that generates realistic and goal-directed object trajectories by jointly leveraging 3D bounding box geometry, point cloud context, semantic object categories, and target end poses. The model represents trajectories as continuous 6-DOF pose sequences and employs a tailored conditioning strategy that fuses geometric, semantic, contextual, and goaloriented information. Extensive experiments on synthetic and real-world benchmarks demonstrate that GMT outperforms state-of-the-art human motion and human-object interaction baselines, such as CHOIS and GIMO, achieving substantial gains in spatial accuracy and orientation control. Our method establishes a new benchmark for learningbased manipulation planning and shows strong generalization to diverse objects and cluttered 3D environments. Project page: https://huajian- zeng.github. io/projects/gmt/.

Affordance, defined as the potential actions that an object offers, is crucial for robotic manipulation tasks. A deep understanding of affordance can lead to more intelligent AI systems. For example, such knowledge directs an agent to grasp a knife by the handle for cutting and by the blade when passing it to someone. In this paper, we present a streamlined affordance learning system that encompasses data collection, effective model training, and robot deployment. First, we collect training data from egocentric videos in an automatic manner. Different from previous methods that focus only on the object graspable affordance and represent it as coarse heatmaps, we cover both graspable (e.g., object handles) and functional affordances (e.g., knife blades, hammer heads) and extract data with precise segmentation masks. We then propose an effective model, termed Geometry-guided Affordance Transformer (GKT), to train on the collected data. GKT integrates an innovative Depth Feature Injector (DFI) to incorporate 3D shape and geometric priors, enhancing the model's understanding of affordances. To enable affordance-oriented manipulation, we further introduce Aff-Grasp, a framework that combines GKT with a grasp generation model. For comprehensive evaluation, we create an affordance evaluation dataset with pixel-wise annotations, and design real-world tasks for robot experiments. The results show that GKT surpasses the state-of-the-art by 15.9% in mIoU, and Aff-Grasp achieves high success rates of 95.5% in affordance prediction and 77.1% in successful grasping among 179 trials, including evaluations with seen, unseen objects, and cluttered scenes.

Semantics has enabled 3D scene understanding and affordance-driven object interaction. However, robots operating in real-world environments face a critical limitation: they cannot anticipate how objects move. Long-horizon mobile manipulation requires closing the gap between semantics, geometry, and kinematics. In this work, we present MoMa-SG, a novel framework for building semantic-kinematic 3D scene graphs of articulated scenes containing a myriad of interactable objects. Given RGB-D sequences containing multiple object articulations, we temporally segment object interactions and infer object motion using occlusion-robust point tracking. We then lift point trajectories into 3D and estimate articulation models using a novel unified twist estimation formulation that robustly estimates revolute and prismatic joint parameters in a single optimization pass. Next, we associate objects with estimated articulations and detect contained objects by reasoning over parent-child relations at identified opening states. We also introduce the novel Arti4D-Semantic dataset, which uniquely combines hierarchical object semantics including parent-child relation labels with object axis annotations across 62 in-the-wild RGB-D sequences containing 600 object interactions and three distinct observation paradigms. We extensively evaluate the performance of MoMa-SG on two datasets and ablate key design choices of our approach. In addition, real-world experiments on both a quadruped and a mobile manipulator demonstrate that our semantic-kinematic scene graphs enable robust manipulation of articulated objects in everyday home environments. We provide code and data at: https://momasg.cs.uni-freiburg.de.

In this paper, we study the problem of 3D scene geometry decomposition and manipulation from 2D views. By leveraging the recent implicit neural representation techniques, particularly the appealing neural radiance fields, we introduce an object field component to learn unique codes for all individual objects in 3D space only from 2D supervision. The key to this component is a series of carefully designed loss functions to enable every 3D point, especially in non-occupied space, to be effectively optimized even without 3D labels. In addition, we introduce an inverse query algorithm to freely manipulate any specified 3D object shape in the learned scene representation. Notably, our manipulation algorithm can explicitly tackle key issues such as object collisions and visual occlusions. Our method, called DM-NeRF, is among the first to simultaneously reconstruct, decompose, manipulate and render complex 3D scenes in a single pipeline. Extensive experiments on three datasets clearly show that our method can accurately decompose all 3D objects from 2D views, allowing any interested object to be freely manipulated in 3D space such as translation, rotation, size adjustment, and deformation.

Real-world robotic manipulation demands visuomotor policies capable of robust spatial scene understanding and strong generalization across diverse camera viewpoints. While recent advances in 3D-aware visual representations have shown promise, they still suffer from several key limitations, including reliance on multi-view observations during inference which is impractical in single-view restricted scenarios, incomplete scene modeling that fails to capture holistic and fine-grained geometric structures essential for precise manipulation, and lack of effective policy training strategies to retain and exploit the acquired 3D knowledge. To address these challenges, we present MethodName, a unified representation-policy learning framework for view-generalizable robotic manipulation. MethodName introduces a single-view 3D pretraining paradigm that leverages point cloud reconstruction and feed-forward gaussian splatting under multi-view supervision to learn holistic geometric representations. During policy learning, MethodName performs multi-step distillation to preserve the pretrained geometric understanding and effectively transfer it to manipulation skills. We conduct experiments on 12 RLBench tasks, where our approach outperforms the previous state-of-the-art method by 12.7% in average success rate. Further evaluation on six representative tasks demonstrates strong zero-shot view generalization, with success rate drops of only 22.0% and 29.7% under moderate and large viewpoint shifts respectively, whereas the state-of-the-art method suffers larger decreases of 41.6% and 51.5%.

We present a framework for visual action planning of complex manipulation tasks with high-dimensional state spaces, focusing on manipulation of deformable objects. We propose a Latent Space Roadmap (LSR) for task planning which is a graph-based structure globally capturing the system dynamics in a low-dimensional latent space. Our framework consists of three parts: (1) a Mapping Module (MM) that maps observations given in the form of images into a structured latent space extracting the respective states as well as generates observations from the latent states, (2) the LSR which builds and connects clusters containing similar states in order to find the latent plans between start and goal states extracted by MM, and (3) the Action Proposal Module that complements the latent plan found by the LSR with the corresponding actions. We present a thorough investigation of our framework on simulated box stacking and rope/box manipulation tasks, and a folding task executed on a real robot.

An open problem in mobile manipulation is how to represent objects and scenes in a unified manner, so that robots can use it both for navigating in the environment and manipulating objects. The latter requires capturing intricate geometry while understanding fine-grained semantics, whereas the former involves capturing the complexity inherit to an expansive physical scale. In this work, we present GeFF (Generalizable Feature Fields), a scene-level generalizable neural feature field that acts as a unified representation for both navigation and manipulation that performs in real-time. To do so, we treat generative novel view synthesis as a pre-training task, and then align the resulting rich scene priors with natural language via CLIP feature distillation. We demonstrate the effectiveness of this approach by deploying GeFF on a quadrupedal robot equipped with a manipulator. We evaluate GeFF's ability to generalize to open-set objects as well as running time, when performing open-vocabulary mobile manipulation in dynamic scenes.

For robots to operate in general environments like households, they must be able to perform non-prehensile manipulation actions such as toppling and rolling to manipulate ungraspable objects. However, prior works on non-prehensile manipulation cannot yet generalize across environments with diverse geometries. The main challenge lies in adapting to varying environmental constraints: within a cabinet, the robot must avoid walls and ceilings; to lift objects to the top of a step, the robot must account for the step's pose and extent. While deep reinforcement learning (RL) has demonstrated impressive success in non-prehensile manipulation, accounting for such variability presents a challenge for the generalist policy, as it must learn diverse strategies for each new combination of constraints. To address this, we propose a modular and reconfigurable architecture that adaptively reconfigures network modules based on task requirements. To capture the geometric variability in environments, we extend the contact-based object representation (CORN) to environment geometries, and propose a procedural algorithm for generating diverse environments to train our agent. Taken together, the resulting policy can zero-shot transfer to novel real-world environments and objects despite training entirely within a simulator. We additionally release a simulation-based benchmark featuring nine digital twins of real-world scenes with 353 objects to facilitate non-prehensile manipulation research in realistic domains.

Vision-Language Models (VLMs) have shown remarkable capabilities in spatial reasoning, yet they remain fundamentally limited to qualitative precision and lack the computational precision required for real-world robotics. Current approaches fail to leverage metric cues from depth sensors and camera calibration, instead reducing geometric problems to pattern recognition tasks that cannot deliver the centimeter-level accuracy essential for robotic manipulation. We present TIGeR (Tool-Integrated Geometric Reasoning), a novel framework that transforms VLMs from perceptual estimators to geometric computers by enabling them to generate and execute precise geometric computations through external tools. Rather than attempting to internalize complex geometric operations within neural networks, TIGeR empowers models to recognize geometric reasoning requirements, synthesize appropriate computational code, and invoke specialized libraries for exact calculations. To support this paradigm, we introduce TIGeR-300K, a comprehensive tool-invocation-oriented dataset covering point transformations, pose estimation, and spatial compatibility verification, complete with tool invocation sequences and intermediate computations. Through a two-stage training pipeline combining supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT) with our proposed hierarchical reward design, TIGeR achieves SOTA performance on geometric reasoning benchmarks while demonstrating centimeter-level precision in real-world robotic manipulation tasks.

We present Supermarket-6DoF, a real-world dataset of 1500 grasp attempts across 20 supermarket objects with publicly available 3D models. Unlike most existing grasping datasets that rely on analytical metrics or simulation for grasp labeling, our dataset provides ground-truth outcomes from physical robot executions. Among the few real-world grasping datasets, wile more modest in size, Supermarket-6DoF uniquely features full 6-DoF grasp poses annotated with both initial grasp success and post-grasp stability under external perturbation. We demonstrate the dataset's utility by analyzing three grasp pose representations for grasp success prediction from point clouds. Our results show that representing the gripper geometry explicitly as a point cloud achieves higher prediction accuracy compared to conventional quaternion-based grasp pose encoding.

In this paper, we question whether we have a reliable self-supervised point cloud model that can be used for diverse 3D tasks via simple linear probing, even with limited data and minimal computation. We find that existing 3D self-supervised learning approaches fall short when evaluated on representation quality through linear probing. We hypothesize that this is due to what we term the "geometric shortcut", which causes representations to collapse to low-level spatial features. This challenge is unique to 3D and arises from the sparse nature of point cloud data. We address it through two key strategies: obscuring spatial information and enhancing the reliance on input features, ultimately composing a Sonata of 140k point clouds through self-distillation. Sonata is simple and intuitive, yet its learned representations are strong and reliable: zero-shot visualizations demonstrate semantic grouping, alongside strong spatial reasoning through nearest-neighbor relationships. Sonata demonstrates exceptional parameter and data efficiency, tripling linear probing accuracy (from 21.8% to 72.5%) on ScanNet and nearly doubling performance with only 1% of the data compared to previous approaches. Full fine-tuning further advances SOTA across both 3D indoor and outdoor perception tasks.

A deep understanding of kinematic structures and movable components is essential for enabling robots to manipulate objects and model their own articulated forms. Such understanding is captured through articulated objects, which are essential for tasks such as physical simulation, motion planning, and policy learning. However, creating these models, particularly for objects with high degrees of freedom (DoF), remains a significant challenge. Existing methods typically rely on motion sequences or strong assumptions from hand-curated datasets, which hinders scalability. In this paper, we introduce Kinematify, an automated framework that synthesizes articulated objects directly from arbitrary RGB images or textual descriptions. Our method addresses two core challenges: (i) inferring kinematic topologies for high-DoF objects and (ii) estimating joint parameters from static geometry. To achieve this, we combine MCTS search for structural inference with geometry-driven optimization for joint reasoning, producing physically consistent and functionally valid descriptions. We evaluate Kinematify on diverse inputs from both synthetic and real-world environments, demonstrating improvements in registration and kinematic topology accuracy over prior work.

Robotic mapping systems typically approach building metric-semantic scene representations from the robot's own sensors and cameras. However, these "first person" maps inherit the robot's own limitations due to its embodiment or skillset, which may leave many aspects of the environment unexplored. For example, the robot might not be able to open drawers or access wall cabinets. In this sense, the map representation is not as complete, and requires a more capable robot to fill in the gaps. We narrow these blind spots in current methods by leveraging egocentric data captured as a human naturally explores a scene wearing Project Aria glasses, giving a way to directly transfer knowledge about articulation from the human to any deployable robot. We demonstrate that, by using simple heuristics, we can leverage egocentric data to recover models of articulate object parts, with quality comparable to those of state-of-the-art methods based on other input modalities. We also show how to integrate these models into 3D scene graph representations, leading to a better understanding of object dynamics and object-container relationships. We finally demonstrate that these articulated 3D scene graphs enhance a robot's ability to perform mobile manipulation tasks, showcasing an application where a Boston Dynamics Spot is tasked with retrieving concealed target items, given only the 3D scene graph as input.

Visual foundation models provide strong perceptual features for robotics, but their dense representations lack explicit object-level structure, limiting robustness and contractility in manipulation tasks. We propose STORM (Slot-based Task-aware Object-centric Representation for robotic Manipulation), a lightweight object-centric adaptation module that augments frozen visual foundation models with a small set of semantic-aware slots for robotic manipulation. Rather than retraining large backbones, STORM employs a multi-phase training strategy: object-centric slots are first stabilized through visual--semantic pretraining using language embeddings, then jointly adapted with a downstream manipulation policy. This staged learning prevents degenerate slot formation and preserves semantic consistency while aligning perception with task objectives. Experiments on object discovery benchmarks and simulated manipulation tasks show that STORM improves generalization to visual distractors, and control performance compared to directly using frozen foundation model features or training object-centric representations end-to-end. Our results highlight multi-phase adaptation as an efficient mechanism for transforming generic foundation model features into task-aware object-centric representations for robotic control.

Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches process diagrams as static images, they lack the capacity for dynamic manipulation - a core aspect of human geometric reasoning involving auxiliary line construction and affine transformations. We present GeoSketch, a neural-symbolic framework that recasts geometric reasoning as an interactive perception-reasoning-action loop. GeoSketch integrates: (1) a Perception module that abstracts diagrams into structured logic forms, (2) a Symbolic Reasoning module that applies geometric theorems to decide the next deductive step, and (3) a Sketch Action module that executes operations such as drawing auxiliary lines or applying transformations, thereby updating the diagram in a closed loop. To train this agent, we develop a two-stage pipeline: supervised fine-tuning on 2,000 symbolic-curated trajectories followed by reinforcement learning with dense, symbolic rewards to enhance robustness and strategic exploration. To evaluate this paradigm, we introduce the GeoSketch Benchmark, a high-quality set of 390 geometry problems requiring auxiliary construction or affine transformations. Experiments on strong MLLM baselines demonstrate that GeoSketch significantly improves stepwise reasoning accuracy and problem-solving success over static perception methods. By unifying hierarchical decision-making, executable visual actions, and symbolic verification, GeoSketch advances multimodal reasoning from static interpretation to dynamic, verifiable interaction, establishing a new foundation for solving complex visuospatial problems.

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

Open-Vocabulary 3D object affordance grounding aims to anticipate ``action possibilities'' regions on 3D objects with arbitrary instructions, which is crucial for robots to generically perceive real scenarios and respond to operational changes. Existing methods focus on combining images or languages that depict interactions with 3D geometries to introduce external interaction priors. However, they are still vulnerable to a limited semantic space by failing to leverage implied invariant geometries and potential interaction intentions. Normally, humans address complex tasks through multi-step reasoning and respond to diverse situations by leveraging associative and analogical thinking. In light of this, we propose GREAT (GeometRy-intEntion collAboraTive inference) for Open-Vocabulary 3D Object Affordance Grounding, a novel framework that mines the object invariant geometry attributes and performs analogically reason in potential interaction scenarios to form affordance knowledge, fully combining the knowledge with both geometries and visual contents to ground 3D object affordance. Besides, we introduce the Point Image Affordance Dataset v2 (PIADv2), the largest 3D object affordance dataset at present to support the task. Extensive experiments demonstrate the effectiveness and superiority of GREAT. The code and dataset are available at https://yawen-shao.github.io/GREAT/.

We present OAKINK2, a dataset of bimanual object manipulation tasks for complex daily activities. In pursuit of constructing the complex tasks into a structured representation, OAKINK2 introduces three level of abstraction to organize the manipulation tasks: Affordance, Primitive Task, and Complex Task. OAKINK2 features on an object-centric perspective for decoding the complex tasks, treating them as a sequence of object affordance fulfillment. The first level, Affordance, outlines the functionalities that objects in the scene can afford, the second level, Primitive Task, describes the minimal interaction units that humans interact with the object to achieve its affordance, and the third level, Complex Task, illustrates how Primitive Tasks are composed and interdependent. OAKINK2 dataset provides multi-view image streams and precise pose annotations for the human body, hands and various interacting objects. This extensive collection supports applications such as interaction reconstruction and motion synthesis. Based on the 3-level abstraction of OAKINK2, we explore a task-oriented framework for Complex Task Completion (CTC). CTC aims to generate a sequence of bimanual manipulation to achieve task objectives. Within the CTC framework, we employ Large Language Models (LLMs) to decompose the complex task objectives into sequences of Primitive Tasks and have developed a Motion Fulfillment Model that generates bimanual hand motion for each Primitive Task. OAKINK2 datasets and models are available at https://oakink.net/v2.

Despite much progress in large 3D datasets there are currently few interactive 3D object datasets, and their scale is limited due to the manual effort required in their construction. We introduce the static to openable (S2O) task which creates interactive articulated 3D objects from static counterparts through openable part detection, motion prediction, and interior geometry completion. We formulate a unified framework to tackle this task, and curate a challenging dataset of openable 3D objects that serves as a test bed for systematic evaluation. Our experiments benchmark methods from prior work and simple yet effective heuristics for the S2O task. We find that turning static 3D objects into interactively openable counterparts is possible but that all methods struggle to generalize to realistic settings of the task, and we highlight promising future work directions.

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing object geometry, thereby facilitating abstraction. In this paper, we introduce \papername, a novel approach to shape abstraction through sweep surfaces. We propose an effective parameterization for sweep surfaces, utilizing superellipses for profile representation and B-spline curves for the axis. This compact representation, requiring as few as 14 float numbers, facilitates intuitive and interactive editing while preserving shape details effectively. Additionally, by introducing a differentiable neural sweeper and an encoder-decoder architecture, we demonstrate the ability to predict sweep surface representations without supervision. We show the superiority of our model through several quantitative and qualitative experiments throughout the paper. Our code is available at https://mingrui-zhao.github.io/SweepNet/

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER.

We present BimArt, a novel generative approach for synthesizing 3D bimanual hand interactions with articulated objects. Unlike prior works, we do not rely on a reference grasp, a coarse hand trajectory, or separate modes for grasping and articulating. To achieve this, we first generate distance-based contact maps conditioned on the object trajectory with an articulation-aware feature representation, revealing rich bimanual patterns for manipulation. The learned contact prior is then used to guide our hand motion generator, producing diverse and realistic bimanual motions for object movement and articulation. Our work offers key insights into feature representation and contact prior for articulated objects, demonstrating their effectiveness in taming the complex, high-dimensional space of bimanual hand-object interactions. Through comprehensive quantitative experiments, we demonstrate a clear step towards simplified and high-quality hand-object animations that excel over the state-of-the-art in motion quality and diversity.

We present the first approach to build hierarchical task-driven 3D scene graphs of arbitrary indoor or outdoor environments using an uncalibrated monocular camera in real-time. We leverage geometric foundation models to estimate geometric attributes of the scene graph (e.g., object bounding boxes), but we also observe that traversability information (the "places" layer of a scene graph) can be directly reconstructed by adding an extra head to existing geometric foundation models, like VGGT. Our approach is task-driven in the sense that we adjust the granularity of the objects and regions in the map depending on the task; for instance, during a manipulation task, our approach is able to resolve small knobs on a stove, while during a navigation task it can focus on large objects (e.g., the entire stove). However, in a major departure from related work, we consider the realistic case where the list of tasks is not predefined and fixed, but evolves as the robot operates. This naturally allows dealing with complex loco-manipulation tasks, where the robot can dynamically adjust its representation as the task unfolds. We dub the resulting approach FOUND-IT. FOUND-IT also includes an agentic approach to query information in the scene graph. In addition to achieving 79% higher accuracy on the ASHiTA SG3D task grounding benchmark, we demonstrate FOUND-IT runs in real-time on a ground robot using a Jetson Thor. Furthermore, to highlight the robustness of our method, we demonstrate constructing 3D scene graphs on casually captured realtor apartment tours from YouTube. Code will be made available upon publication.

We propose a novel, object-agnostic method for learning a universal policy for dexterous object grasping from realistic point cloud observations and proprioceptive information under a table-top setting, namely UniDexGrasp++. To address the challenge of learning the vision-based policy across thousands of object instances, we propose Geometry-aware Curriculum Learning (GeoCurriculum) and Geometry-aware iterative Generalist-Specialist Learning (GiGSL) which leverage the geometry feature of the task and significantly improve the generalizability. With our proposed techniques, our final policy shows universal dexterous grasping on thousands of object instances with 85.4% and 78.2% success rate on the train set and test set which outperforms the state-of-the-art baseline UniDexGrasp by 11.7% and 11.3%, respectively.

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity, they are limited by slow per-scene optimization or category-specific training, which hinders their practical deployment and scalability. Hence, generalizable feed-forward 3D reconstruction has witnessed rapid development in recent years. By learning a model that maps images directly to 3D representations in a single forward pass, these methods enable efficient reconstruction and robust cross-scene generalization. Our survey is motivated by a critical observation: despite the diverse geometric output representations, ranging from implicit fields to explicit primitives, existing feed-forward approaches share similar high-level architectural patterns, such as image feature extraction backbones, multi-view information fusion mechanisms, and geometry-aware design principles. Consequently, we abstract away from these representation differences and instead focus on model design, proposing a novel taxonomy centered on model design strategies that are agnostic to the output format. Our proposed taxonomy organizes the research directions into five key problems that drive recent research development: feature enhancement, geometry awareness, model efficiency, augmentation strategies and temporal-aware models. To support this taxonomy with empirical grounding and standardized evaluation, we further comprehensively review related benchmarks and datasets, and extensively discuss and categorize real-world applications based on feed-forward 3D models. Finally, we outline future directions to address open challenges such as scalability, evaluation standards, and world modeling.

Large vision-language models have significantly advanced GUI agents, enabling executable interaction across web, mobile, and desktop interfaces. Yet these gains largely rely on a forgiving region-tolerant paradigm, where many nearby pixels inside the same component remain valid. Precise geometric construction breaks this assumption: actions must land on points in continuous canvas space rather than tolerant regions. Because geometric primitives carry ontological dependencies, a local coordinate error can induce cascading topological failures that distort downstream objects and invalidate the final construction. We identify this regime as precision-sensitive GUI tasks, requiring point-level accuracy, geometry-aware verification, and robustness to dependency-driven error propagation. To benchmark it, we introduce PAGE Bench, with 4,906 problems and over 224K process-supervised, pixel-level GUI actions. We further propose PAGER, a topology-aware agent that decomposes construction into dependency-structured planning and pixel-level execution. Pixel-grounded supervised tuning establishes executable action grammar, while precision-aligned reinforcement learning mitigates rollout-induced exposure bias through state-conditioned geometric feedback. Experiments reveal a pronounced Semantic-Execution Gap: general multimodal models can exceed 88% action type accuracy yet remain below 6% task success. PAGER closes this gap, delivering 4.1x higher task success than the strongest evaluated general baseline and raising step success rate from below 9% for GUI-specialized agents to over 62%, establishing a new state of the art for point-precise GUI control.

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at https://github.com/dyu62/PolyGNN{github.com/dyu62/PolyGNN}.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.

The development of general robotic systems capable of manipulating in unstructured environments is a significant challenge. While Vision-Language Models(VLM) excel in high-level commonsense reasoning, they lack the fine-grained 3D spatial understanding required for precise manipulation tasks. Fine-tuning VLM on robotic datasets to create Vision-Language-Action Models(VLA) is a potential solution, but it is hindered by high data collection costs and generalization issues. To address these challenges, we propose a novel object-centric representation that bridges the gap between VLM's high-level reasoning and the low-level precision required for manipulation. Our key insight is that an object's canonical space, defined by its functional affordances, provides a structured and semantically meaningful way to describe interaction primitives, such as points and directions. These primitives act as a bridge, translating VLM's commonsense reasoning into actionable 3D spatial constraints. In this context, we introduce a dual closed-loop, open-vocabulary robotic manipulation system: one loop for high-level planning through primitive resampling, interaction rendering and VLM checking, and another for low-level execution via 6D pose tracking. This design ensures robust, real-time control without requiring VLM fine-tuning. Extensive experiments demonstrate strong zero-shot generalization across diverse robotic manipulation tasks, highlighting the potential of this approach for automating large-scale simulation data generation.

Generating natural human grasps necessitates consideration of not just object geometry but also semantic information. Solely depending on object shape for grasp generation confines the applications of prior methods in downstream tasks. This paper presents a novel semantic-based grasp generation method, termed SemGrasp, which generates a static human grasp pose by incorporating semantic information into the grasp representation. We introduce a discrete representation that aligns the grasp space with semantic space, enabling the generation of grasp postures in accordance with language instructions. A Multimodal Large Language Model (MLLM) is subsequently fine-tuned, integrating object, grasp, and language within a unified semantic space. To facilitate the training of SemGrasp, we have compiled a large-scale, grasp-text-aligned dataset named CapGrasp, featuring about 260k detailed captions and 50k diverse grasps. Experimental findings demonstrate that SemGrasp efficiently generates natural human grasps in alignment with linguistic intentions. Our code, models, and dataset are available publicly at: https://kailinli.github.io/SemGrasp.

This paper presents a novel object-centric contact representation ContactGen for hand-object interaction. The ContactGen comprises three components: a contact map indicates the contact location, a part map represents the contact hand part, and a direction map tells the contact direction within each part. Given an input object, we propose a conditional generative model to predict ContactGen and adopt model-based optimization to predict diverse and geometrically feasible grasps. Experimental results demonstrate our method can generate high-fidelity and diverse human grasps for various objects. Project page: https://stevenlsw.github.io/contactgen/

Robust 3D representation learning forms the perceptual foundation of spatial intelligence, enabling downstream tasks in scene understanding and embodied AI. However, learning such representations directly from unposed multi-view images remains challenging. Recent self-supervised methods attempt to unify geometry, appearance, and semantics in a feed-forward manner, but they often suffer from weak geometry induction, limited appearance detail, and inconsistencies between geometry and semantics. We introduce UniSplat, a feed-forward framework designed to address these limitations through three complementary components. First, we propose a dual-masking strategy that strengthens geometry induction in the encoder. By masking both encoder and decoder tokens, and targeting decoder masks toward geometry-rich regions, the model is forced to infer structural information from incomplete visual cues, yielding geometry-aware representations even under unposed inputs. Second, we develop a coarse-to-fine Gaussian splatting strategy that reduces appearance-semantics inconsistencies by progressively refining the radiance field. Finally, to enforce geometric-semantic consistency, we introduce a pose-conditioned recalibration mechanism that interrelates the outputs of multiple heads by re-projecting predicted 3D point and semantic maps into the image plane using estimated camera parameters, and aligning them with corresponding RGB and semantic predictions to ensure cross-task consistency, thereby resolving geometry-semantic mismatches. Together, these components yield unified 3D representations that are robust to unposed, sparse-view inputs and generalize across diverse tasks, laying a perceptual foundation for spatial intelligence.

This paper concerns the question of how AI systems encode semantic structure into the geometric structure of their representation spaces. The motivating observation of this paper is that the natural geometry of these representation spaces should reflect the way models use representations to produce behavior. We focus on the important special case of representations that define softmax distributions. In this case, we argue that the natural geometry is information geometry. Our focus is on the role of information geometry on semantic encoding and the linear representation hypothesis. As an illustrative application, we develop "dual steering", a method for robustly steering representations to exhibit a particular concept using linear probes. We prove that dual steering optimally modifies the target concept while minimizing changes to off-target concepts. Empirically, we find that dual steering enhances the controllability and stability of concept manipulation.

We introduce the problem of material-aware part grouping in untextured meshes. Many real-world shapes, such as scales of pinecones or windows of buildings, contain repeated structures that share the same material but exhibit geometric variations. When assigning materials to such meshes, these repeated parts often require piece-by-piece manual identification and selection, which is tedious and time-consuming. To address this, we propose Material Magic Wand, a tool that allows artists to select part groups based on their estimated material properties -- when one part is selected, our algorithm automatically retrieves all other parts likely to share the same material. The key component of our approach is a part encoder that generates a material-aware embedding for each 3D part, accounting for both local geometry and global context. We train our model with a supervised contrastive loss that brings embeddings of material-consistent parts closer while separating those of different materials; therefore, part grouping can be achieved by retrieving embeddings that are close to the embedding of the selected part. To benchmark this task, we introduce a curated dataset of 100 shapes with 241 part-level queries. We verify the effectiveness of our method through extensive experiments and demonstrate its practical value in an interactive material assignment application.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

Advances in large vision-language models (VLMs) have stimulated growing interest in vision-language-action (VLA) systems for robot manipulation. However, existing manipulation datasets remain costly to curate, highly embodiment-specific, and insufficient in coverage and diversity, thereby hindering the generalization of VLA models. Recent approaches attempt to mitigate these limitations via a plan-then-execute paradigm, where high-level plans (e.g., subtasks, trace) are first generated and subsequently translated into low-level actions, but they critically rely on extra intermediate supervision, which is largely absent from existing datasets. To bridge this gap, we introduce the RoboInter Manipulation Suite, a unified resource including data, benchmarks, and models of intermediate representations for manipulation. It comprises RoboInter-Tool, a lightweight GUI that enables semi-automatic annotation of diverse representations, and RoboInter-Data, a large-scale dataset containing over 230k episodes across 571 diverse scenes, which provides dense per-frame annotations over more than 10 categories of intermediate representations, substantially exceeding prior work in scale and annotation quality. Building upon this foundation, RoboInter-VQA introduces 9 spatial and 20 temporal embodied VQA categories to systematically benchmark and enhance the embodied reasoning capabilities of VLMs. Meanwhile, RoboInter-VLA offers an integrated plan-then-execute framework, supporting modular and end-to-end VLA variants that bridge high-level planning with low-level execution via intermediate supervision. In total, RoboInter establishes a practical foundation for advancing robust and generalizable robotic learning via fine-grained and diverse intermediate representations.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

Representation learning approaches for robotic manipulation have boomed in recent years. Due to the scarcity of in-domain robot data, prevailing methodologies tend to leverage large-scale human video datasets to extract generalizable features for visuomotor policy learning. Despite the progress achieved, prior endeavors disregard the interactive dynamics that capture behavior patterns and physical interaction during the manipulation process, resulting in an inadequate understanding of the relationship between objects and the environment. To this end, we propose a general pre-training pipeline that learns Manipulation by Predicting the Interaction (MPI) and enhances the visual representation.Given a pair of keyframes representing the initial and final states, along with language instructions, our algorithm predicts the transition frame and detects the interaction object, respectively. These two learning objectives achieve superior comprehension towards "how-to-interact" and "where-to-interact". We conduct a comprehensive evaluation of several challenging robotic tasks.The experimental results demonstrate that MPI exhibits remarkable improvement by 10% to 64% compared with previous state-of-the-art in real-world robot platforms as well as simulation environments. Code and checkpoints are publicly shared at https://github.com/OpenDriveLab/MPI.

We focus on the self-supervised discovery of manipulation concepts that can be adapted and reassembled to address various robotic tasks. We propose that the decision to conceptualize a physical procedure should not depend on how we name it (semantics) but rather on the significance of the informativeness in its representation regarding the low-level physical state and state changes. We model manipulation concepts (discrete symbols) as generative and discriminative goals and derive metrics that can autonomously link them to meaningful sub-trajectories from noisy, unlabeled demonstrations. Specifically, we employ a trainable codebook containing encodings (concepts) capable of synthesizing the end-state of a sub-trajectory given the current state (generative informativeness). Moreover, the encoding corresponding to a particular sub-trajectory should differentiate the state within and outside it and confidently predict the subsequent action based on the gradient of its discriminative score (discriminative informativeness). These metrics, which do not rely on human annotation, can be seamlessly integrated into a VQ-VAE framework, enabling the partitioning of demonstrations into semantically consistent sub-trajectories, fulfilling the purpose of discovering manipulation concepts and the corresponding sub-goal (key) states. We evaluate the effectiveness of the learned concepts by training policies that utilize them as guidance, demonstrating superior performance compared to other baselines. Additionally, our discovered manipulation concepts compare favorably to human-annotated ones while saving much manual effort.

Learning long-horizon embodied behaviors from synthetic data remains challenging because generated scenes are often physically implausible, language-driven programs frequently "succeed" without satisfying task semantics, and high-level instructions require grounding into executable action sequences. To address these limitations, we introduce V-CAGE, a closed-loop framework for generating robust, semantically aligned manipulation datasets at scale. First, we propose a context-aware instantiation mechanism that enforces geometric consistency during scene synthesis. By dynamically maintaining a map of prohibited spatial areas as objects are placed, our system prevents interpenetration and ensures reachable, conflict-free configurations in cluttered environments. Second, to bridge the gap between abstract intent and low-level control, we employ a hierarchical instruction decomposition module. This decomposes high-level goals (e.g., "get ready for work") into compositional action primitives, facilitating coherent long-horizon planning. Crucially, we enforce semantic correctness through a VLM-based verification loop. Acting as a visual critic, the VLM performs rigorous rejection sampling after each subtask, filtering out "silent failures" where code executes but fails to achieve the visual goal. Experiments demonstrate that V-CAGE yields datasets with superior physical and semantic fidelity, significantly boosting the success rate and generalization of downstream policies compared to non-verified baselines.

Learning good representations is essential for latent planning with world models. While pretrained visual encoders produce strong semantic visual features, they are not tailored to planning and contain information irrelevant -- or even detrimental -- to planning. Inspired by the perceptual straightening hypothesis in human visual processing, we introduce temporal straightening to improve representation learning for latent planning. Using a curvature regularizer that encourages locally straightened latent trajectories, we jointly learn an encoder and a predictor. We show that reducing curvature this way makes the Euclidean distance in latent space a better proxy for the geodesic distance and improves the conditioning of the planning objective. We demonstrate empirically that temporal straightening makes gradient-based planning more stable and yields significantly higher success rates across a suite of goal-reaching tasks.

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

Vision-Language-Action models have achieved remarkable progress in robotic manipulation, yet they suffer from a critical limitation: a lack of 3D scene understanding. This deficiency manifests as three intertwined challenges: weak extraction of 3D spatial positions without enforcing multi-view consistency, inadequate 3D instance understanding, and fragile reasoning under occlusion. Although mature 3D perception methods exist, their direct integration into VLA pipelines is hindered by architectural incompatibility and by heavy reliance on costly instance-level annotations. To address the above challenges, we propose 3DVLA, a plug-and-play framework that injects robust 3D reasoning into pretrained VLAs without requiring extra manual labels or discarding VLM priors. Specifically, 3DVLA tackles the three challenges through: (1) pervasive 3D feature encoding with explicit multi-view consistency constraints across all modalities and a Spatially-Conditioned Geometry Aggregation method, (2) an instance estimation module with high-level instance tokens for 3D instance awareness, and (3) a masked self-supervised 3D encoding branch that retains its predictor for visual token completion to handle occlusions. We integrate 3DVLA with multiple VLA baselines and evaluate on LIBERO-Plus and RoboTwin 2.0. Results show consistent and significant gains in manipulation performance, validating both the effectiveness and plug-and-play compatibility of our approach.

Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command sequences. But these methods struggle in practical scenarios because command sequence representation does not support entity selection (e.g. faces or edges), limiting its ability to support complex editing operations such as chamfer or fillet. Further, the discretization of a continuous variable during sketch and extrude operations may result in topological errors. To address these limitations, we present Pointer-CAD, a novel LLM-based CAD generation framework that leverages a pointer-based command sequence representation to explicitly incorporate the geometric information of B-rep models into sequential modeling. In particular, Pointer-CAD decomposes CAD model generation into steps, conditioning the generation of each subsequent step on both the textual description and the B-rep generated from previous steps. Whenever an operation requires the selection of a specific geometric entity, the LLM predicts a Pointer that selects the most feature-consistent candidate from the available set. Such a selection operation also reduces the quantization error in the command sequence-based representation. To support the training of Pointer-CAD, we develop a data annotation pipeline that produces expert-level natural language descriptions and apply it to build a dataset of approximately 575K CAD models. Extensive experimental results demonstrate that Pointer-CAD effectively supports the generation of complex geometric structures and reduces segmentation error to an extremely low level, achieving a significant improvement over prior command sequence methods, thereby significantly mitigating the topological inaccuracies introduced by quantization error.

Well structured visual representations can make robot learning faster and can improve generalization. In this paper, we study how we can acquire effective object-centric representations for robotic manipulation tasks without human labeling by using autonomous robot interaction with the environment. Such representation learning methods can benefit from continuous refinement of the representation as the robot collects more experience, allowing them to scale effectively without human intervention. Our representation learning approach is based on object persistence: when a robot removes an object from a scene, the representation of that scene should change according to the features of the object that was removed. We formulate an arithmetic relationship between feature vectors from this observation, and use it to learn a representation of scenes and objects that can then be used to identify object instances, localize them in the scene, and perform goal-directed grasping tasks where the robot must retrieve commanded objects from a bin. The same grasping procedure can also be used to automatically collect training data for our method, by recording images of scenes, grasping and removing an object, and recording the outcome. Our experiments demonstrate that this self-supervised approach for tasked grasping substantially outperforms direct reinforcement learning from images and prior representation learning methods.

The generalization capabilities of robotic manipulation policies are heavily influenced by the choice of visual representations. Existing approaches typically rely on representations extracted from pre-trained encoders, using two dominant types of features: global features, which summarize an entire image via a single pooled vector, and dense features, which preserve a patch-wise embedding from the final encoder layer. While widely used, both feature types mix task-relevant and irrelevant information, leading to poor generalization under distribution shifts, such as changes in lighting, textures, or the presence of distractors. In this work, we explore an intermediate structured alternative: Slot-Based Object-Centric Representations (SBOCR), which group dense features into a finite set of object-like entities. This representation permits to naturally reduce the noise provided to the robotic manipulation policy while keeping enough information to efficiently perform the task. We benchmark a range of global and dense representations against intermediate slot-based representations, across a suite of simulated and real-world manipulation tasks ranging from simple to complex. We evaluate their generalization under diverse visual conditions, including changes in lighting, texture, and the presence of distractors. Our findings reveal that SBOCR-based policies outperform dense and global representation-based policies in generalization settings, even without task-specific pretraining. These insights suggest that SBOCR is a promising direction for designing visual systems that generalize effectively in dynamic, real-world robotic environments.

Generalizable articulated object manipulation is essential for home-assistant robots. Recent efforts focus on imitation learning from demonstrations or reinforcement learning in simulation, however, due to the prohibitive costs of real-world data collection and precise object simulation, it still remains challenging for these works to achieve broad adaptability across diverse articulated objects. Recently, many works have tried to utilize the strong in-context learning ability of Large Language Models (LLMs) to achieve generalizable robotic manipulation, but most of these researches focus on high-level task planning, sidelining low-level robotic control. In this work, building on the idea that the kinematic structure of the object determines how we can manipulate it, we propose a kinematic-aware prompting framework that prompts LLMs with kinematic knowledge of objects to generate low-level motion trajectory waypoints, supporting various object manipulation. To effectively prompt LLMs with the kinematic structure of different objects, we design a unified kinematic knowledge parser, which represents various articulated objects as a unified textual description containing kinematic joints and contact location. Building upon this unified description, a kinematic-aware planner model is proposed to generate precise 3D manipulation waypoints via a designed kinematic-aware chain-of-thoughts prompting method. Our evaluation spanned 48 instances across 16 distinct categories, revealing that our framework not only outperforms traditional methods on 8 seen categories but also shows a powerful zero-shot capability for 8 unseen articulated object categories. Moreover, the real-world experiments on 7 different object categories prove our framework's adaptability in practical scenarios. Code is released at https://github.com/GeWu-Lab/LLM_articulated_object_manipulation/tree/main.

How can we imbue robots with the ability to manipulate objects precisely but also to reason about them in terms of abstract concepts? Recent works in manipulation have shown that end-to-end networks can learn dexterous skills that require precise spatial reasoning, but these methods often fail to generalize to new goals or quickly learn transferable concepts across tasks. In parallel, there has been great progress in learning generalizable semantic representations for vision and language by training on large-scale internet data, however these representations lack the spatial understanding necessary for fine-grained manipulation. To this end, we propose a framework that combines the best of both worlds: a two-stream architecture with semantic and spatial pathways for vision-based manipulation. Specifically, we present CLIPort, a language-conditioned imitation-learning agent that combines the broad semantic understanding (what) of CLIP [1] with the spatial precision (where) of Transporter [2]. Our end-to-end framework is capable of solving a variety of language-specified tabletop tasks from packing unseen objects to folding cloths, all without any explicit representations of object poses, instance segmentations, memory, symbolic states, or syntactic structures. Experiments in simulated and real-world settings show that our approach is data efficient in few-shot settings and generalizes effectively to seen and unseen semantic concepts. We even learn one multi-task policy for 10 simulated and 9 real-world tasks that is better or comparable to single-task policies.

To achieve human-level dexterity, robots must infer spatial awareness from multimodal sensing to reason over contact interactions. During in-hand manipulation of novel objects, such spatial awareness involves estimating the object's pose and shape. The status quo for in-hand perception primarily employs vision, and restricts to tracking a priori known objects. Moreover, visual occlusion of objects in-hand is imminent during manipulation, preventing current systems to push beyond tasks without occlusion. We combine vision and touch sensing on a multi-fingered hand to estimate an object's pose and shape during in-hand manipulation. Our method, NeuralFeels, encodes object geometry by learning a neural field online and jointly tracks it by optimizing a pose graph problem. We study multimodal in-hand perception in simulation and the real-world, interacting with different objects via a proprioception-driven policy. Our experiments show final reconstruction F-scores of 81% and average pose drifts of 4.7,mm, further reduced to 2.3,mm with known CAD models. Additionally, we observe that under heavy visual occlusion we can achieve up to 94% improvements in tracking compared to vision-only methods. Our results demonstrate that touch, at the very least, refines and, at the very best, disambiguates visual estimates during in-hand manipulation. We release our evaluation dataset of 70 experiments, FeelSight, as a step towards benchmarking in this domain. Our neural representation driven by multimodal sensing can serve as a perception backbone towards advancing robot dexterity. Videos can be found on our project website https://suddhu.github.io/neural-feels/

Perceiving and manipulating 3D articulated objects in diverse environments is essential for home-assistant robots. Recent studies have shown that point-level affordance provides actionable priors for downstream manipulation tasks. However, existing works primarily focus on single-object scenarios with homogeneous agents, overlooking the realistic constraints imposed by the environment and the agent's morphology, e.g., occlusions and physical limitations. In this paper, we propose an environment-aware affordance framework that incorporates both object-level actionable priors and environment constraints. Unlike object-centric affordance approaches, learning environment-aware affordance faces the challenge of combinatorial explosion due to the complexity of various occlusions, characterized by their quantities, geometries, positions and poses. To address this and enhance data efficiency, we introduce a novel contrastive affordance learning framework capable of training on scenes containing a single occluder and generalizing to scenes with complex occluder combinations. Experiments demonstrate the effectiveness of our proposed approach in learning affordance considering environment constraints. Project page at https://chengkaiacademycity.github.io/EnvAwareAfford/

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

Language-driven dexterous grasp generation requires the models to understand task semantics, 3D geometry, and complex hand-object interactions. While vision-language models have been applied to this problem, existing approaches directly map observations to grasp parameters without intermediate reasoning about physical interactions. We present DextER, Dexterous Grasp Generation with Embodied Reasoning, which introduces contact-based embodied reasoning for multi-finger manipulation. Our key insight is that predicting which hand links contact where on the object surface provides an embodiment-aware intermediate representation bridging task semantics with physical constraints. DextER autoregressively generates embodied contact tokens specifying which finger links contact where on the object surface, followed by grasp tokens encoding the hand configuration. On DexGYS, DextER achieves 67.14% success rate, outperforming state-of-the-art by 3.83%p with 96.4% improvement in intention alignment. We also demonstrate steerable generation through partial contact specification, providing fine-grained control over grasp synthesis.

Recent advancements in implicit 3D representations and generative models have markedly propelled the field of 3D object generation forward. However, it remains a significant challenge to accurately model geometries with defined sharp features under parametric controls, which is crucial in fields like industrial design and manufacturing. To bridge this gap, we introduce a framework that employs Large Language Models (LLMs) to generate text-driven 3D shapes, manipulating 3D software via program synthesis. We present 3D-PreMise, a dataset specifically tailored for 3D parametric modeling of industrial shapes, designed to explore state-of-the-art LLMs within our proposed pipeline. Our work reveals effective generation strategies and delves into the self-correction capabilities of LLMs using a visual interface. Our work highlights both the potential and limitations of LLMs in 3D parametric modeling for industrial applications.

Nonprehensile manipulation is essential for manipulating objects that are too thin, large, or otherwise ungraspable in the wild. To sidestep the difficulty of contact modeling in conventional modeling-based approaches, reinforcement learning (RL) has recently emerged as a promising alternative. However, previous RL approaches either lack the ability to generalize over diverse object shapes, or use simple action primitives that limit the diversity of robot motions. Furthermore, using RL over diverse object geometry is challenging due to the high cost of training a policy that takes in high-dimensional sensory inputs. We propose a novel contact-based object representation and pretraining pipeline to tackle this. To enable massively parallel training, we leverage a lightweight patch-based transformer architecture for our encoder that processes point clouds, thus scaling our training across thousands of environments. Compared to learning from scratch, or other shape representation baselines, our representation facilitates both time- and data-efficient learning. We validate the efficacy of our overall system by zero-shot transferring the trained policy to novel real-world objects. Code and videos are available at https://sites.google.com/view/contact-non-prehensile.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

End-to-end manipulation policies, combined with web-scale pretrained Vision-Language Models (VLMs), show the promise for generalizable and dexterous robotic manipulation. However, they inherit two key limitations from 2D foundation models: 1) the reliance on 2D RGB inputs that ignores the intrinsically 3D nature of manipulation; and 2) the lack of spatial 3D alignment between input-output spaces as well as across diverse robot embodiments, camera setups, and trajectory datasets. In this paper, we present a series of contributions to address these issues. First, we introduce aligned vertex map and vertex spectrum -- a pixel-wise 3D representation that elevates 2D visual inputs to 3D, using camera calibration and optional depth. This novel input representation marries 3D awareness with the generalization of 2D large VLMs. Then, we propose to align the inputs and outputs of manipulation policies by expressing per-pixel 3D information of each camera view and robot actions to a shared coordinate. Based on this, we designate a canonical Bird's-Eye-View (BEV) alignment frame and innovatively propose to construct BEV images, producing a view-invariant representation robust to camera pose variations. To enable training and evaluation at scale, we develop a comprehensive data processing pipeline to perform such alignments; we also introduce a novel temporal alignment scheme for trajectories across diverse robots, human operators, and datasets. These contributions collectively mitigate input and output spatial-temporal misalignments, improving the consistency and generalization for real-world manipulation. Pretrained checkpoint, source code and data processing pipeline are available in https://hnuzhy.github.io/projects/Dex-BEV.

This work proposes a retrieve-and-transfer framework for zero-shot robotic manipulation, dubbed RAM, featuring generalizability across various objects, environments, and embodiments. Unlike existing approaches that learn manipulation from expensive in-domain demonstrations, RAM capitalizes on a retrieval-based affordance transfer paradigm to acquire versatile manipulation capabilities from abundant out-of-domain data. First, RAM extracts unified affordance at scale from diverse sources of demonstrations including robotic data, human-object interaction (HOI) data, and custom data to construct a comprehensive affordance memory. Then given a language instruction, RAM hierarchically retrieves the most similar demonstration from the affordance memory and transfers such out-of-domain 2D affordance to in-domain 3D executable affordance in a zero-shot and embodiment-agnostic manner. Extensive simulation and real-world evaluations demonstrate that our RAM consistently outperforms existing works in diverse daily tasks. Additionally, RAM shows significant potential for downstream applications such as automatic and efficient data collection, one-shot visual imitation, and LLM/VLM-integrated long-horizon manipulation. For more details, please check our website at https://yxkryptonite.github.io/RAM/.

Vision-Language-Action (VLA) models have emerged as a promising approach for enabling robots to follow language instructions and predict corresponding actions. However, current VLA models mainly rely on 2D visual inputs, neglecting the rich geometric information in the 3D physical world, which limits their spatial awareness and adaptability. In this paper, we present GeoVLA, a novel VLA framework that effectively integrates 3D information to advance robotic manipulation. It uses a vision-language model (VLM) to process images and language instructions,extracting fused vision-language embeddings. In parallel, it converts depth maps into point clouds and employs a customized point encoder, called Point Embedding Network, to generate 3D geometric embeddings independently. These produced embeddings are then concatenated and processed by our proposed spatial-aware action expert, called 3D-enhanced Action Expert, which combines information from different sensor modalities to produce precise action sequences. Through extensive experiments in both simulation and real-world environments, GeoVLA demonstrates superior performance and robustness. It achieves state-of-the-art results in the LIBERO and ManiSkill2 simulation benchmarks and shows remarkable robustness in real-world tasks requiring height adaptability, scale awareness and viewpoint invariance.

We introduce the novel task of interactive scene exploration, wherein robots autonomously explore environments and produce an action-conditioned scene graph (ACSG) that captures the structure of the underlying environment. The ACSG accounts for both low-level information (geometry and semantics) and high-level information (action-conditioned relationships between different entities) in the scene. To this end, we present the Robotic Exploration (RoboEXP) system, which incorporates the Large Multimodal Model (LMM) and an explicit memory design to enhance our system's capabilities. The robot reasons about what and how to explore an object, accumulating new information through the interaction process and incrementally constructing the ACSG. Leveraging the constructed ACSG, we illustrate the effectiveness and efficiency of our RoboEXP system in facilitating a wide range of real-world manipulation tasks involving rigid, articulated objects, nested objects, and deformable objects.

Dense hand contact estimation requires both high-level semantic understanding and fine-grained geometric reasoning of human interaction to accurately localize contact regions. Recently, multi-modal large language models (MLLMs) have demonstrated strong capabilities in understanding visual semantics, enabled by vision-language priors learned from large-scale data. However, leveraging MLLMs for dense hand contact estimation remains underexplored. There are two major challenges in applying MLLMs to dense hand contact estimation. First, encoding explicit 3D hand geometry is difficult, as MLLMs primarily operate on vision and language modalities. Second, capturing fine-grained vertex-level contact remains challenging, as MLLMs tend to focus on high-level semantics rather than detailed geometric reasoning. To address these challenges, we propose ContactPrompt, a training-free and zero-shot approach for dense hand contact estimation using MLLMs. To effectively encode 3D hand geometry, we introduce a detailed hand-part segmentation and a part-wise vertex-grid representation that provides structured, localized geometric information. To enable accurate and efficient dense contact prediction, we develop a multi-stage structured contact reasoning with part conditioning, progressively bridging global semantics and fine-grained geometry. Therefore, our method effectively leverages the reasoning capabilities of MLLMs while enabling precise dense hand contact estimation. Surprisingly, the proposed approach outperforms previous supervised methods trained on large-scale dense contact datasets without requiring any training. The codes will be released.

We study zero-shot 3D alignment of two given meshes, using a text prompt describing their spatial relation -- an essential capability for content creation and scene assembly. Earlier approaches primarily rely on geometric alignment procedures, while recent work leverages pretrained 2D diffusion models to model language-conditioned object-object spatial relationships. In contrast, we directly optimize the relative pose at test time, updating translation, rotation, and isotropic scale with CLIP-driven gradients via a differentiable renderer, without training a new model. Our framework augments language supervision with geometry-aware objectives: a variant of soft-Iterative Closest Point (ICP) term to encourage surface attachment and a penetration loss to discourage interpenetration. A phased schedule strengthens contact constraints over time, and camera control concentrates the optimization on the interaction region. To enable evaluation, we curate a benchmark containing diverse categories and relations, and compare against baselines. Our method outperforms all alternatives, yielding semantically faithful and physically plausible alignments.

This paper introduces the first text-guided work for generating the sequence of hand-object interaction in 3D. The main challenge arises from the lack of labeled data where existing ground-truth datasets are nowhere near generalizable in interaction type and object category, which inhibits the modeling of diverse 3D hand-object interaction with the correct physical implication (e.g., contacts and semantics) from text prompts. To address this challenge, we propose to decompose the interaction generation task into two subtasks: hand-object contact generation; and hand-object motion generation. For contact generation, a VAE-based network takes as input a text and an object mesh, and generates the probability of contacts between the surfaces of hands and the object during the interaction. The network learns a variety of local geometry structure of diverse objects that is independent of the objects' category, and thus, it is applicable to general objects. For motion generation, a Transformer-based diffusion model utilizes this 3D contact map as a strong prior for generating physically plausible hand-object motion as a function of text prompts by learning from the augmented labeled dataset; where we annotate text labels from many existing 3D hand and object motion data. Finally, we further introduce a hand refiner module that minimizes the distance between the object surface and hand joints to improve the temporal stability of the object-hand contacts and to suppress the penetration artifacts. In the experiments, we demonstrate that our method can generate more realistic and diverse interactions compared to other baseline methods. We also show that our method is applicable to unseen objects. We will release our model and newly labeled data as a strong foundation for future research. Codes and data are available in: https://github.com/JunukCha/Text2HOI.

Mapping high-fidelity 3D geometry to a representation that allows for intuitive edits remains an elusive goal in computer vision and graphics. The key challenge is the need to model both continuous and discrete shape variations. Current approaches, such as implicit shape representation, lack straightforward interpretable encoding, while others that employ procedural methods output coarse geometry. We present GeoCode, a technique for 3D shape synthesis using an intuitively editable parameter space. We build a novel program that enforces a complex set of rules and enables users to perform intuitive and controlled high-level edits that procedurally propagate at a low level to the entire shape. Our program produces high-quality mesh outputs by construction. We use a neural network to map a given point cloud or sketch to our interpretable parameter space. Once produced by our procedural program, shapes can be easily modified. Empirically, we show that GeoCode can infer and recover 3D shapes more accurately compared to existing techniques and we demonstrate its ability to perform controlled local and global shape manipulations.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

Representing robotic manipulation tasks as constraints that associate the robot and the environment is a promising way to encode desired robot behaviors. However, it remains unclear how to formulate the constraints such that they are 1) versatile to diverse tasks, 2) free of manual labeling, and 3) optimizable by off-the-shelf solvers to produce robot actions in real-time. In this work, we introduce Relational Keypoint Constraints (ReKep), a visually-grounded representation for constraints in robotic manipulation. Specifically, ReKep is expressed as Python functions mapping a set of 3D keypoints in the environment to a numerical cost. We demonstrate that by representing a manipulation task as a sequence of Relational Keypoint Constraints, we can employ a hierarchical optimization procedure to solve for robot actions (represented by a sequence of end-effector poses in SE(3)) with a perception-action loop at a real-time frequency. Furthermore, in order to circumvent the need for manual specification of ReKep for each new task, we devise an automated procedure that leverages large vision models and vision-language models to produce ReKep from free-form language instructions and RGB-D observations. We present system implementations on a wheeled single-arm platform and a stationary dual-arm platform that can perform a large variety of manipulation tasks, featuring multi-stage, in-the-wild, bimanual, and reactive behaviors, all without task-specific data or environment models. Website at https://rekep-robot.github.io/.

3D grasp synthesis generates grasping poses given an input object. Existing works tackle the problem by learning a direct mapping from objects to the distributions of grasping poses. However, because the physical contact is sensitive to small changes in pose, the high-nonlinear mapping between 3D object representation to valid poses is considerably non-smooth, leading to poor generation efficiency and restricted generality. To tackle the challenge, we introduce an intermediate variable for grasp contact areas to constrain the grasp generation; in other words, we factorize the mapping into two sequential stages by assuming that grasping poses are fully constrained given contact maps: 1) we first learn contact map distributions to generate the potential contact maps for grasps; 2) then learn a mapping from the contact maps to the grasping poses. Further, we propose a penetration-aware optimization with the generated contacts as a consistency constraint for grasp refinement. Extensive validations on two public datasets show that our method outperforms state-of-the-art methods regarding grasp generation on various metrics.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

We propose Text2Motion, a language-based planning framework enabling robots to solve sequential manipulation tasks that require long-horizon reasoning. Given a natural language instruction, our framework constructs both a task- and motion-level plan that is verified to reach inferred symbolic goals. Text2Motion uses feasibility heuristics encoded in Q-functions of a library of skills to guide task planning with Large Language Models. Whereas previous language-based planners only consider the feasibility of individual skills, Text2Motion actively resolves geometric dependencies spanning skill sequences by performing geometric feasibility planning during its search. We evaluate our method on a suite of problems that require long-horizon reasoning, interpretation of abstract goals, and handling of partial affordance perception. Our experiments show that Text2Motion can solve these challenging problems with a success rate of 82%, while prior state-of-the-art language-based planning methods only achieve 13%. Text2Motion thus provides promising generalization characteristics to semantically diverse sequential manipulation tasks with geometric dependencies between skills.

Manipulation has long been a challenging task for robots, while humans can effortlessly perform complex interactions with objects, such as hanging a cup on the mug rack. A key reason is the lack of a large and uniform dataset for teaching robots manipulation skills. Current robot datasets often record robot action in different action spaces within a simple scene. This hinders the robot to learn a unified and robust action representation for different robots within diverse scenes. Observing how humans understand a manipulation task, we find that understanding how the objects should move in the 3D space is a critical clue for guiding actions. This clue is embodiment-agnostic and suitable for both humans and different robots. Motivated by this, we aim to learn a 3D flow world model from both human and robot manipulation data. This model predicts the future movement of the interacting objects in 3D space, guiding action planning for manipulation. Specifically, we synthesize a large-scale 3D optical flow dataset, named ManiFlow-110k, through a moving object auto-detect pipeline. A video diffusion-based world model then learns manipulation physics from these data, generating 3D optical flow trajectories conditioned on language instructions. With the generated 3D object optical flow, we propose a flow-guided rendering mechanism, which renders the predicted final state and leverages GPT-4o to assess whether the predicted flow aligns with the task description. This equips the robot with a closed-loop planning ability. Finally, we consider the predicted 3D optical flow as constraints for an optimization policy to determine a chunk of robot actions for manipulation. Extensive experiments demonstrate strong generalization across diverse robotic manipulation tasks and reliable cross-embodiment adaptation without hardware-specific training.

Learning-based simulation of multi-object rigid-body dynamics remains difficult because contact is discontinuous and errors compound over long horizons. Most existing methods remain tied to mesh connectivity and vertex-level message passing, which limits their applicability to mesh-free inputs such as point clouds and leads to high computational cost. Efficiently modeling high-fidelity rigid-body dynamics from mesh-free representations, therefore, remains challenging. We introduce RigidFormer, an object-centric Transformer-based model that learns mesh-free rigid-body dynamics with controllable integration step sizes. RigidFormer reasons at the object level and advances each object through compact anchors; Anchor-Vertex Pooling enriches these anchors with local vertex features, retaining contact-relevant geometry without dense vertex-level interaction. We propose Anchor-based RoPE to inject anchor geometry into attention while respecting the unordered nature of objects and anchors: object-token processing is permutation-equivariant, and the mean-pooled anchor descriptor is invariant to anchor reindexing while preserving shape extent. RigidFormer further enforces rigidity by projecting updates onto the rigid-body manifold using differentiable Kabsch alignment. On standard benchmarks, RigidFormer outperforms or matches mesh-based baselines using point inputs, runs faster, generalizes to unseen point resolutions and across datasets, and scales to 200+ objects; we also show a preliminary extension to command-conditioned articulated bodies by treating body parts as interacting object-level components.

Achieving human-level dexterity in robots is a key objective in the field of robotic manipulation. Recent advancements in 3D-based imitation learning have shown promising results, providing an effective pathway to achieve this goal. However, obtaining high-quality 3D representations presents two key problems: (1) the quality of point clouds captured by a single-view camera is significantly affected by factors such as camera resolution, positioning, and occlusions caused by the dexterous hand; (2) the global point clouds lack crucial contact information and spatial correspondences, which are necessary for fine-grained dexterous manipulation tasks. To eliminate these limitations, we propose CordViP, a novel framework that constructs and learns correspondences by leveraging the robust 6D pose estimation of objects and robot proprioception. Specifically, we first introduce the interaction-aware point clouds, which establish correspondences between the object and the hand. These point clouds are then used for our pre-training policy, where we also incorporate object-centric contact maps and hand-arm coordination information, effectively capturing both spatial and temporal dynamics. Our method demonstrates exceptional dexterous manipulation capabilities with an average success rate of 90\% in four real-world tasks, surpassing other baselines by a large margin. Experimental results also highlight the superior generalization and robustness of CordViP to different objects, viewpoints, and scenarios. Code and videos are available on https://aureleopku.github.io/CordViP.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold M_h to representations and a behavior manifold M_y to output probability distributions. We then test the link M_h leftrightarrow M_y via interventions: we find that steering along M_h, which we term manifold steering, yields behavioral trajectories that follow M_y, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

Recent advancements in robotic manipulation have highlighted the potential of intermediate representations for improving policy generalization. In this work, we explore grounding masks as an effective intermediate representation, balancing two key advantages: (1) effective spatial guidance that specifies target objects and placement areas while also conveying information about object shape and size, and (2) broad generalization potential driven by large-scale vision-language models pretrained on diverse grounding datasets. We introduce RoboGround, a grounding-aware robotic manipulation system that leverages grounding masks as an intermediate representation to guide policy networks in object manipulation tasks. To further explore and enhance generalization, we propose an automated pipeline for generating large-scale, simulated data with a diverse set of objects and instructions. Extensive experiments show the value of our dataset and the effectiveness of grounding masks as intermediate guidance, significantly enhancing the generalization abilities of robot policies.

General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic embeddings and integrate them into advanced diffusion models to enable geometry-editable generation. However, these highly compact embeddings encode only high-level semantic cues and inevitably discard fine-grained appearance details. We introduce a Disentangled Geometry-editable and Appearance-preserving Diffusion (DGAD) model that first leverages semantic embeddings to implicitly capture the desired geometric transformations and then employs a cross-attention retrieval mechanism to align fine-grained appearance features with the geometry-edited representation, facilitating both precise geometry editing and faithful appearance preservation in object composition. Specifically, DGAD builds on CLIP/DINO-derived and reference networks to extract semantic embeddings and appearance-preserving representations, which are then seamlessly integrated into the encoding and decoding pipelines in a disentangled manner. We first integrate the semantic embeddings into pre-trained diffusion models that exhibit strong spatial reasoning capabilities to implicitly capture object geometry, thereby facilitating flexible object manipulation and ensuring effective editability. Then, we design a dense cross-attention mechanism that leverages the implicitly learned object geometry to retrieve and spatially align appearance features with their corresponding regions, ensuring faithful appearance consistency. Extensive experiments on public benchmarks demonstrate the effectiveness of the proposed DGAD framework.

Articulated objects are central to interactive 3D applications, including embodied AI, robotics, and VR/AR, where functional part decomposition and kinematic motion are essential. Yet producing high-fidelity articulated assets remains difficult to scale because it requires reliable part decomposition and kinematic rigging. Existing approaches largely fall into two paradigms: optimization-based reconstruction or distillation, which can be accurate but often takes tens of minutes to hours per instance, and inference-time methods that rely on template or part retrieval, producing plausible results that may not match the specific structure and appearance in the input observation. We introduce a part-centric generative framework for articulated object creation that synthesizes part geometry, composition, and articulation under explicit part-aware conditioning. Our representation models an object as a set of movable parts, each encoded by latent tokens augmented with part identity and articulation cues. Conditioned on a single image, the model generates articulated 3D assets that preserve instance-level correspondence while maintaining valid part structure and motion. The resulting approach avoids per-instance optimization, enables fast feed-forward inference, and supports controllable assembly and articulation, which are important for embodied interaction. Experiments on common articulated categories (e.g., drawers and doors) show improved input consistency, part accuracy, and articulation plausibility over optimization-based and retrieval-driven baselines, while substantially reducing inference time.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Localizing objects and parts from natural language in 3D space is essential for robotics, AR, and embodied AI, yet existing methods face a trade-off between the accuracy and geometric consistency of per-scene optimization and the efficiency of feed-forward inference. We present TrianguLang, a feed-forward framework for 3D localization that requires no camera calibration at inference. Unlike prior methods that treat views independently, we introduce Geometry-Aware Semantic Attention (GASA), which utilizes predicted geometry to gate cross-view feature correspondence, suppressing semantically plausible but geometrically inconsistent matches without requiring ground-truth poses. Validated on five benchmarks including ScanNet++ and uCO3D, TrianguLang achieves state-of-the-art feed-forward text-guided segmentation and localization, reducing user effort from O(N) clicks to a single text query. The model processes each frame at 1008x1008 resolution in sim57ms (sim18 FPS) without optimization, enabling practical deployment for interactive robotics and AR applications. Code and checkpoints are available at https://cwru-aism.github.io/triangulang/.

The pre-training of visual representations has enhanced the efficiency of robot learning. Due to the lack of large-scale in-domain robotic datasets, prior works utilize in-the-wild human videos to pre-train robotic visual representation. Despite their promising results, representations from human videos are inevitably subject to distribution shifts and lack the dynamics information crucial for task completion. We first evaluate various pre-trained representations in terms of their correlation to the downstream robotic manipulation tasks (i.e., manipulation centricity). Interestingly, we find that the "manipulation centricity" is a strong indicator of success rates when applied to downstream tasks. Drawing from these findings, we propose Manipulation Centric Representation (MCR), a foundation representation learning framework capturing both visual features and the dynamics information such as actions and proprioceptions of manipulation tasks to improve manipulation centricity. Specifically, we pre-train a visual encoder on the DROID robotic dataset and leverage motion-relevant data such as robot proprioceptive states and actions. We introduce a novel contrastive loss that aligns visual observations with the robot's proprioceptive state-action dynamics, combined with a behavior cloning (BC)-like actor loss to predict actions during pre-training, along with a time contrastive loss. Empirical results across 4 simulation domains with 20 tasks verify that MCR outperforms the strongest baseline method by 14.8%. Moreover, MCR boosts the performance of data-efficient learning with a UR5e arm on 3 real-world tasks by 76.9%. Project website: https://robots-pretrain-robots.github.io/.

We present a novel meta-learning approach for 6D pose estimation on unknown objects. In contrast to ``instance-level" and ``category-level" pose estimation methods, our algorithm learns object representation in a category-agnostic way, which endows it with strong generalization capabilities across object categories. Specifically, we employ a neural process-based meta-learning approach to train an encoder to capture texture and geometry of an object in a latent representation, based on very few RGB-D images and ground-truth keypoints. The latent representation is then used by a simultaneously meta-trained decoder to predict the 6D pose of the object in new images. Furthermore, we propose a novel geometry-aware decoder for the keypoint prediction using a Graph Neural Network (GNN), which explicitly takes geometric constraints specific to each object into consideration. To evaluate our algorithm, extensive experiments are conducted on the \linemod dataset, and on our new fully-annotated synthetic datasets generated from Multiple Categories in Multiple Scenes (MCMS). Experimental results demonstrate that our model performs well on unseen objects with very different shapes and appearances. Remarkably, our model also shows robust performance on occluded scenes although trained fully on data without occlusion. To our knowledge, this is the first work exploring cross-category level 6D pose estimation.

Visual representations are central to the learning and generalization capabilities of robotic manipulation policies. While existing methods rely on global or dense features, such representations often entangle task-relevant and irrelevant scene information, limiting robustness under distribution shifts. In this work, we investigate object-centric representations (OCR) as a structured alternative that segments visual input into a finished set of entities, introducing inductive biases that align more naturally with manipulation tasks. We benchmark a range of visual encoders-object-centric, global and dense methods-across a suite of simulated and real-world manipulation tasks ranging from simple to complex, and evaluate their generalization under diverse visual conditions including changes in lighting, texture, and the presence of distractors. Our findings reveal that OCR-based policies outperform dense and global representations in generalization settings, even without task-specific pretraining. These insights suggest that OCR is a promising direction for designing visual systems that generalize effectively in dynamic, real-world robotic environments.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.

Recent advances in imitation learning for 3D robotic manipulation have shown promising results with diffusion-based policies. However, achieving human-level dexterity requires seamless integration of geometric precision and semantic understanding. We present G3Flow, a novel framework that constructs real-time semantic flow, a dynamic, object-centric 3D semantic representation by leveraging foundation models. Our approach uniquely combines 3D generative models for digital twin creation, vision foundation models for semantic feature extraction, and robust pose tracking for continuous semantic flow updates. This integration enables complete semantic understanding even under occlusions while eliminating manual annotation requirements. By incorporating semantic flow into diffusion policies, we demonstrate significant improvements in both terminal-constrained manipulation and cross-object generalization. Extensive experiments across five simulation tasks show that G3Flow consistently outperforms existing approaches, achieving up to 68.3% and 50.1% average success rates on terminal-constrained manipulation and cross-object generalization tasks respectively. Our results demonstrate the effectiveness of G3Flow in enhancing real-time dynamic semantic feature understanding for robotic manipulation policies.

We present the HANDAL dataset for category-level object pose estimation and affordance prediction. Unlike previous datasets, ours is focused on robotics-ready manipulable objects that are of the proper size and shape for functional grasping by robot manipulators, such as pliers, utensils, and screwdrivers. Our annotation process is streamlined, requiring only a single off-the-shelf camera and semi-automated processing, allowing us to produce high-quality 3D annotations without crowd-sourcing. The dataset consists of 308k annotated image frames from 2.2k videos of 212 real-world objects in 17 categories. We focus on hardware and kitchen tool objects to facilitate research in practical scenarios in which a robot manipulator needs to interact with the environment beyond simple pushing or indiscriminate grasping. We outline the usefulness of our dataset for 6-DoF category-level pose+scale estimation and related tasks. We also provide 3D reconstructed meshes of all objects, and we outline some of the bottlenecks to be addressed for democratizing the collection of datasets like this one.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.

Significant advancements in Large Multimodal Models (LMMs) have enabled them to tackle complex problems involving visual-mathematical reasoning. However, their ability to identify geometric elements remains underexplored. To address this gap, we introduce Tangram, a novel benchmark designed to evaluate the performance of LMMs on geometric element recognition. Tangram comprises 1,080 diverse geometric diagrams sourced from primary and secondary school exams, competitions, and textbooks, ranging from simple geometric shapes to complex combinations. Each diagram is paired with four questions, resulting in 4,320 visual-question-answer pairs. Unlike existing benchmarks that emphasize higher-level cognition and reasoning, Tangram focuses on understanding geometric elements, requiring models to perform a ``simple yet challenging" counting task. Systematic evaluation of 13 prominent LMMs, such as GPT-4o and Claude 3.5 Sonnet, reveals that these models face significant challenges even in seemingly straightforward tasks. The top-performing model achieves an accuracy of only 53.0%, highlighting a substantial gap compared to human performance. These findings underscore the limitations of current multimodal AI systems in handling basic perception tasks and serve to inspire the development of the next generation of expert-level multimodal foundational models. The data and code will be released soon.

The ability of robots to interpret human instructions and execute manipulation tasks necessitates the availability of task-relevant tabletop scenes for training. However, traditional methods for creating these scenes rely on time-consuming manual layout design or purely randomized layouts, which are limited in terms of plausibility or alignment with the tasks. In this paper, we formulate a novel task, namely task-oriented tabletop scene generation, which poses significant challenges due to the substantial gap between high-level task instructions and the tabletop scenes. To support research on such a challenging task, we introduce MesaTask-10K, a large-scale dataset comprising approximately 10,700 synthetic tabletop scenes with manually crafted layouts that ensure realistic layouts and intricate inter-object relations. To bridge the gap between tasks and scenes, we propose a Spatial Reasoning Chain that decomposes the generation process into object inference, spatial interrelation reasoning, and scene graph construction for the final 3D layout. We present MesaTask, an LLM-based framework that utilizes this reasoning chain and is further enhanced with DPO algorithms to generate physically plausible tabletop scenes that align well with given task descriptions. Exhaustive experiments demonstrate the superior performance of MesaTask compared to baselines in generating task-conforming tabletop scenes with realistic layouts. Project page is at https://mesatask.github.io/

To interact with daily-life articulated objects of diverse structures and functionalities, understanding the object parts plays a central role in both user instruction comprehension and task execution. However, the possible discordance between the semantic meaning and physics functionalities of the parts poses a challenge for designing a general system. To address this problem, we propose SAGE, a novel framework that bridges semantic and actionable parts of articulated objects to achieve generalizable manipulation under natural language instructions. More concretely, given an articulated object, we first observe all the semantic parts on it, conditioned on which an instruction interpreter proposes possible action programs that concretize the natural language instruction. Then, a part-grounding module maps the semantic parts into so-called Generalizable Actionable Parts (GAParts), which inherently carry information about part motion. End-effector trajectories are predicted on the GAParts, which, together with the action program, form an executable policy. Additionally, an interactive feedback module is incorporated to respond to failures, which closes the loop and increases the robustness of the overall framework. Key to the success of our framework is the joint proposal and knowledge fusion between a large vision-language model (VLM) and a small domain-specific model for both context comprehension and part perception, with the former providing general intuitions and the latter serving as expert facts. Both simulation and real-robot experiments show our effectiveness in handling a large variety of articulated objects with diverse language-instructed goals.

Achieving generalization in robotic manipulation remains a critical challenge, particularly for unseen scenarios and novel tasks. Current Vision-Language-Action (VLA) models, while building on top of general Vision-Language Models (VLMs), still fall short of achieving robust zero-shot performance due to the scarcity and heterogeneity prevalent in embodied datasets. To address these limitations, we propose FSD (From Seeing to Doing), a novel vision-language model that generates intermediate representations through spatial relationship reasoning, providing fine-grained guidance for robotic manipulation. Our approach combines a hierarchical data pipeline for training with a self-consistency mechanism that aligns spatial coordinates with visual signals. Through extensive experiments, we comprehensively validated FSD's capabilities in both "seeing" and "doing," achieving outstanding performance across 8 benchmarks for general spatial reasoning and embodied reference abilities, as well as on our proposed more challenging benchmark VABench. We also verified zero-shot capabilities in robot manipulation, demonstrating significant performance improvements over baseline methods in both SimplerEnv and real robot settings. Experimental results show that FSD achieves 40.6% success rate in SimplerEnv and 72% success rate across 8 real-world tasks, outperforming the strongest baseline by 30%.

Learning how humans manipulate objects requires machines to acquire knowledge from two perspectives: one for understanding object affordances and the other for learning human's interactions based on the affordances. Even though these two knowledge bases are crucial, we find that current databases lack a comprehensive awareness of them. In this work, we propose a multi-modal and rich-annotated knowledge repository, OakInk, for visual and cognitive understanding of hand-object interactions. We start to collect 1,800 common household objects and annotate their affordances to construct the first knowledge base: Oak. Given the affordance, we record rich human interactions with 100 selected objects in Oak. Finally, we transfer the interactions on the 100 recorded objects to their virtual counterparts through a novel method: Tink. The recorded and transferred hand-object interactions constitute the second knowledge base: Ink. As a result, OakInk contains 50,000 distinct affordance-aware and intent-oriented hand-object interactions. We benchmark OakInk on pose estimation and grasp generation tasks. Moreover, we propose two practical applications of OakInk: intent-based interaction generation and handover generation. Our datasets and source code are publicly available at https://github.com/lixiny/OakInk.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Manipulating articulated tools, such as tweezers or scissors, has rarely been explored in previous research. Unlike rigid tools, articulated tools change their shape dynamically, creating unique challenges for dexterous robotic hands. In this work, we present a hierarchical, goal-conditioned reinforcement learning (GCRL) framework to improve the manipulation capabilities of anthropomorphic robotic hands using articulated tools. Our framework comprises two policy layers: (1) a low-level policy that enables the dexterous hand to manipulate the tool into various configurations for objects of different sizes, and (2) a high-level policy that defines the tool's goal state and controls the robotic arm for object-picking tasks. We employ an encoder, trained on synthetic pointclouds, to estimate the tool's affordance states--specifically, how different tool configurations (e.g., tweezer opening angles) enable grasping of objects of varying sizes--from input point clouds, thereby enabling precise tool manipulation. We also utilize a privilege-informed heuristic policy to generate replay buffer, improving the training efficiency of the high-level policy. We validate our approach through real-world experiments, showing that the robot can effectively manipulate a tweezer-like tool to grasp objects of diverse shapes and sizes with a 70.8 % success rate. This study highlights the potential of RL to advance dexterous robotic manipulation of articulated tools.

Handle-based mesh deformation is a classic paradigm in computer graphics which enables intuitive edits from sparse controls. Classical techniques are fast and precise, but require users to know ideal handle placement apriori, which can be unintuitive and inconsistent. Handle sets cannot be adjusted easily, as weights are typically optimized through energies defined by the handles. Modern data-driven methods, on the other hand, provide semantic edits but sacrifice fine-grained control and speed. We propose a technique that achieves the best of both worlds: deep feature proximity yields smooth, visual-aware deformation weights with no additional regularization. Importantly, these weights are computed in real-time for any surface point, unlike prior methods which require expensive optimization. We introduce barycentric feature distillation, an improved feature distillation pipeline which leverages the full visual signal from shape renders to make distillation complexity robust to mesh resolution. This enables high resolution meshes to be processed in minutes versus potentially hours for prior methods. We preserve and extend classical properties through feature space constraints and locality weighting. Our field representation enables automatic visual symmetry detection, which we use to produce symmetry-preserving deformations. We show a proof-of-concept application which can produce deformations for meshes up to 1 million faces in real-time on a consumer-grade machine. Project page at https://threedle.github.io/dfd.

Contrastive Language-Image Pre-training (CLIP) has accomplished extraordinary success for semantic understanding but inherently struggles to perceive geometric structure. Existing methods attempt to bridge this gap by querying CLIP with textual prompts, a process that is often indirect and inefficient. This paper introduces a fundamentally different approach using a dual-pathway decoder. We present SPACE-CLIP, an architecture that unlocks and interprets latent geometric knowledge directly from a frozen CLIP vision encoder, completely bypassing the text encoder and its associated textual prompts. A semantic pathway interprets high-level features, dynamically conditioned on global context using feature-wise linear modulation (FiLM). In addition, a structural pathway extracts fine-grained spatial details from early layers. These complementary streams are hierarchically fused, enabling a robust synthesis of semantic context and precise geometry. Extensive experiments on the KITTI benchmark show that SPACE-CLIP dramatically outperforms previous CLIP-based methods. Our ablation studies validate that the synergistic fusion of our dual pathways is critical to this success. SPACE-CLIP offers a new, efficient, and architecturally elegant blueprint for repurposing large-scale vision models. The proposed method is not just a standalone depth estimator, but a readily integrable spatial perception module for the next generation of embodied AI systems, such as vision-language-action (VLA) models. Our model is available at https://github.com/taewan2002/space-clip

This paper introduces H-MaP, a hybrid sequential manipulation planner that addresses complex tasks requiring both sequential actions and dynamic contact mode switches. Our approach reduces configuration space dimensionality by decoupling object trajectory planning from manipulation planning through object-based waypoint generation, informed contact sampling, and optimization-based motion planning. This architecture enables handling of challenging scenarios involving tool use, auxiliary object manipulation, and bimanual coordination. Experimental results across seven diverse tasks demonstrate H-MaP's superior performance compared to existing methods, particularly in highly constrained environments where traditional approaches fail due to local minima or scalability issues. The planner's effectiveness is validated through both simulation and real-robot experiments.

We present a system for generating indoor scenes in response to text prompts. The prompts are not limited to a fixed vocabulary of scene descriptions, and the objects in generated scenes are not restricted to a fixed set of object categories -- we call this setting indoor scene generation. Unlike most prior work on indoor scene generation, our system does not require a large training dataset of existing 3D scenes. Instead, it leverages the world knowledge encoded in pre-trained large language models (LLMs) to synthesize programs in a domain-specific layout language that describe objects and spatial relations between them. Executing such a program produces a specification of a constraint satisfaction problem, which the system solves using a gradient-based optimization scheme to produce object positions and orientations. To produce object geometry, the system retrieves 3D meshes from a database. Unlike prior work which uses databases of category-annotated, mutually-aligned meshes, we develop a pipeline using vision-language models (VLMs) to retrieve meshes from massive databases of un-annotated, inconsistently-aligned meshes. Experimental evaluations show that our system outperforms generative models trained on 3D data for traditional, closed-universe scene generation tasks; it also outperforms a recent LLM-based layout generation method on open-universe scene generation.

Recovering high-fidelity 3D hand geometry from images is a critical task in computer vision, holding significant value for domains such as robotics, animation and VR/AR. Crucially, scalable applications demand both accuracy and deployment flexibility, requiring the ability to leverage massive amounts of unstructured image data from the internet or enable deployment on consumer-grade RGB cameras without complex calibration. However, current methods face a dilemma. While single-view approaches are easy to deploy, they suffer from depth ambiguity and occlusion. Conversely, multi-view systems resolve these uncertainties but typically demand fixed, calibrated setups, limiting their real-world utility. To bridge this gap, we draw inspiration from 3D foundation models that learn explicit geometry directly from visual data. By reformulating hand reconstruction from arbitrary views as a visual-geometry grounded task, we propose a feed-forward architecture that, for the first time in literature, jointly infers 3D hand meshes and camera poses from uncalibrated views. Extensive evaluations show that our approach outperforms state-of-the-art benchmarks and demonstrates strong generalization to uncalibrated, in-the-wild scenarios. Here is the link of our project page: https://lym29.github.io/HGGT/.

Segments in computer vision are often defined by semantic considerations and are highly dependent on category-specific conventions. In contrast, developmental psychology suggests that humans perceive the world in terms of Spelke objects--groupings of physical things that reliably move together when acted on by physical forces. Spelke objects thus operate on category-agnostic causal motion relationships which potentially better support tasks like manipulation and planning. In this paper, we first benchmark the Spelke object concept, introducing the SpelkeBench dataset that contains a wide variety of well-defined Spelke segments in natural images. Next, to extract Spelke segments from images algorithmically, we build SpelkeNet, a class of visual world models trained to predict distributions over future motions. SpelkeNet supports estimation of two key concepts for Spelke object discovery: (1) the motion affordance map, identifying regions likely to move under a poke, and (2) the expected-displacement map, capturing how the rest of the scene will move. These concepts are used for "statistical counterfactual probing", where diverse "virtual pokes" are applied on regions of high motion-affordance, and the resultant expected displacement maps are used define Spelke segments as statistical aggregates of correlated motion statistics. We find that SpelkeNet outperforms supervised baselines like SegmentAnything (SAM) on SpelkeBench. Finally, we show that the Spelke concept is practically useful for downstream applications, yielding superior performance on the 3DEditBench benchmark for physical object manipulation when used in a variety of off-the-shelf object manipulation models.