Operator Learning Using Weak Supervision from Walk-on-Spheres

Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due to higher-order derivatives. To tackle this issue, we propose an alternative approach using Monte Carlo approaches to estimate the solution to the PDE as a stochastic process for weak supervision during training. Leveraging the Walk-on-Spheres method, we introduce a learning scheme called \emph{Walk-on-Spheres Neural Operator (WoS-NO)} which uses weak supervision from WoS to train any given neural operator. We propose to amortize the cost of Monte Carlo walks across the distribution of PDE instances using stochastic representations from the WoS algorithm to generate cheap, noisy, estimates of the PDE solution during training. This is formulated into a data-free physics-informed objective where a neural operator is trained to regress against these weak supervisions, allowing the operator to learn a generalized solution map for an entire family of PDEs. This strategy does not require expensive pre-computed datasets, avoids computing higher-order derivatives for loss functions that are memory-intensive and unstable, and demonstrates zero-shot generalization to novel PDE parameters and domains. Experiments show that for the same number of training steps, our method exhibits up to 8.75$\times$ improvement in $L_2$-error compared to standard physics-informed training schemes, up to 6.31$\times$ improvement in training speed, and reductions of up to 2.97$\times$ in GPU memory consumption. We present the code at https://github.com/neuraloperator/WoS-NO

Sketch2Colab: Sketch-Conditioned Multi-Human Animation via Controllable Flow Distillation

We present Sketch2Colab, which turns storyboard-style 2D sketches into coherent, object-aware 3D multi-human motion with fine-grained control over agents, joints, timing, and contacts. Conventional diffusion-based motion generators have advanced realism; however, achieving precise adherence to rich interaction constraints typically demands extensive training and/or costly posterior guidance, and performance can degrade under strong multi-entity conditioning. Sketch2Colab instead first learns a sketch-driven diffusion prior and then distills it into an efficient rectified-flow student operating in latent space for fast, stable sampling. Differentiable energies over keyframes, trajectories, and physics-based constraints directly shape the student's transport field, steering samples toward motions that faithfully satisfy the storyboard while remaining physically plausible. To capture coordinated interaction, we augment the continuous flow with a continuous-time Markov chain (CTMC) planner that schedules discrete events such as touches, grasps, and handoffs, modulating the dynamics to produce crisp, well-phased human-object-human collaborations. Experiments on CORE4D and InterHuman show that Sketch2Colab achieves state-of-the-art constraint adherence and perceptual quality while offering significantly faster inference than diffusion-only baselines.

Physics Informed Viscous Value Representations

Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

To Move or Not to Move: Constraint-based Planning Enables Zero-Shot Generalization for Interactive Navigation

Visual navigation typically assumes the existence of at least one obstacle-free path between start and goal, which must be discovered/planned by the robot. However, in real-world scenarios, such as home environments and warehouses, clutter can block all routes. Targeted at such cases, we introduce the Lifelong Interactive Navigation problem, where a mobile robot with manipulation abilities can move clutter to forge its own path to complete sequential object- placement tasks - each involving placing an given object (eg. Alarm clock, Pillow) onto a target object (eg. Dining table, Desk, Bed). To address this lifelong setting - where effects of environment changes accumulate and have long-term effects - we propose an LLM-driven, constraint-based planning framework with active perception. Our framework allows the LLM to reason over a structured scene graph of discovered objects and obstacles, deciding which object to move, where to place it, and where to look next to discover task-relevant information. This coupling of reasoning and active perception allows the agent to explore the regions expected to contribute to task completion rather than exhaustively mapping the environment. A standard motion planner then executes the corresponding navigate-pick-place, or detour sequence, ensuring reliable low-level control. Evaluated in physics-enabled ProcTHOR-10k simulator, our approach outperforms non-learning and learning-based baselines. We further demonstrate our approach qualitatively on real-world hardware.

HCVR Scene Generation: High Compatibility Virtual Reality Environment Generation for Extended Redirected Walking

Natural walking enhances immersion in virtual environments (VEs), but physical space limitations and obstacles hinder exploration, especially in large virtual scenes. Redirected Walking (RDW) techniques mitigate this by subtly manipulating the virtual camera to guide users away from physical collisions within pre-defined VEs. However, RDW efficacy diminishes significantly when substantial geometric divergence exists between the physical and virtual environments, leading to unavoidable collisions. Existing scene generation methods primarily focus on object relationships or layout aesthetics, often neglecting the crucial aspect of physical compatibility required for effective RDW. To address this, we introduce HCVR (High Compatibility Virtual Reality Environment Generation), a novel framework that generates virtual scenes inherently optimized for alignment-based RDW controllers. HCVR first employs ENI++, a novel, boundary-sensitive metric to evaluate the incompatibility between physical and virtual spaces by comparing rotation-sensitive visibility polygons. Guided by the ENI++ compatibility map and user prompts, HCVR utilizes a Large Language Model (LLM) for context-aware 3D asset retrieval and initial layout generation. The framework then strategically adjusts object selection, scaling, and placement to maximize coverage of virtually incompatible regions, effectively guiding users towards RDW-feasible paths. User studies evaluating physical collisions and layout quality demonstrate HCVR's effectiveness with HCVR-generated scenes, resulting in 22.78 times fewer physical collisions and received 35.89\% less on ENI++ score compared to LLM-based generation with RDW, while also receiving 12.5\% higher scores on user feedback to layout design.

From Building Blocks to Planning: Multi-Step Spatial Reasoning in LLMs with Reinforcement Learning

Spatial reasoning in large language models (LLMs) has gained increasing attention due to applications in navigation and planning. Despite strong general language capabilities, LLMs still struggle with spatial transformations and multi-step planning in structured environments. We propose a two-stage approach that decomposes spatial reasoning into atomic building blocks and their composition. First, we apply supervised fine-tuning on elementary spatial transformations, such as rotation, translation, and scaling, to equip the model with basic spatial physics. We then freeze this physics-aware model and train lightweight LoRA adapters within the GRPO framework to learn policies that compose these building blocks for multi-step planning in puzzle-based environments, in a closed-loop manner. To support this pipeline, we synthesize an ASCII-art dataset and construct a corresponding ASCII-based reinforcement learning environment. Our method consistently outperforms baselines, including the generic backbone, physics-aware model, and end-to-end RL models, under both Dynamic environments with explicit state updates and Static environments where the model must rely on its internal state across steps. In addition, the proposed approach converges faster and exhibits more stable training compared to end-to-end reinforcement learning from scratch. Finally, we analyze attention patterns to assess whether fine-tuning induces meaningful improvements in spatial understanding.

I-Scene: 3D Instance Models are Implicit Generalizable Spatial Learners

Generalization remains the central challenge for interactive 3D scene generation. Existing learning-based approaches ground spatial understanding in limited scene dataset, restricting generalization to new layouts. We instead reprogram a pre-trained 3D instance generator to act as a scene level learner, replacing dataset-bounded supervision with model-centric spatial supervision. This reprogramming unlocks the generator transferable spatial knowledge, enabling generalization to unseen layouts and novel object compositions. Remarkably, spatial reasoning still emerges even when the training scenes are randomly composed objects. This demonstrates that the generator's transferable scene prior provides a rich learning signal for inferring proximity, support, and symmetry from purely geometric cues. Replacing widely used canonical space, we instantiate this insight with a view-centric formulation of the scene space, yielding a fully feed-forward, generalizable scene generator that learns spatial relations directly from the instance model. Quantitative and qualitative results show that a 3D instance generator is an implicit spatial learner and reasoner, pointing toward foundation models for interactive 3D scene understanding and generation. Project page: https://luling06.github.io/I-Scene-project/

TransLocNet: Cross-Modal Attention for Aerial-Ground Vehicle Localization with Contrastive Learning

Aerial-ground localization is difficult due to large viewpoint and modality gaps between ground-level LiDAR and overhead imagery. We propose TransLocNet, a cross-modal attention framework that fuses LiDAR geometry with aerial semantic context. LiDAR scans are projected into a bird's-eye-view representation and aligned with aerial features through bidirectional attention, followed by a likelihood map decoder that outputs spatial probability distributions over position and orientation. A contrastive learning module enforces a shared embedding space to improve cross-modal alignment. Experiments on CARLA and KITTI show that TransLocNet outperforms state-of-the-art baselines, reducing localization error by up to 63% and achieving sub-meter, sub-degree accuracy. These results demonstrate that TransLocNet provides robust and generalizable aerial-ground localization in both synthetic and real-world settings.

VLAD-Grasp: Zero-shot Grasp Detection via Vision-Language Models

Robotic grasping is a fundamental capability for autonomous manipulation; however, most existing methods rely on large-scale expert annotations and necessitate retraining to handle new objects. We present VLAD-Grasp, a Vision-Language model Assisted zero-shot approach for Detecting grasps. From a single RGB-D image, our method (1) prompts a large vision-language model to generate a goal image where a straight rod "impales" the object, representing an antipodal grasp, (2) predicts depth and segmentation to lift this generated image into 3D, and (3) aligns generated and observed object point clouds via principal component analysis and correspondence-free optimization to recover an executable grasp pose. Unlike prior work, our approach is training-free and does not rely on curated grasp datasets. Despite this, VLAD-Grasp achieves performance that is competitive with or superior to that of state-of-the-art supervised models on the Cornell and Jacquard datasets. We further demonstrate zero-shot generalization to novel real-world objects on a Franka Research 3 robot, highlighting vision-language foundation models as powerful priors for robotic manipulation.

Variational Shape Inference for Grasp Diffusion on SE(3)

Grasp synthesis is a fundamental task in robotic manipulation which usually has multiple feasible solutions. Multimodal grasp synthesis seeks to generate diverse sets of stable grasps conditioned on object geometry, making the robust learning of geometric features crucial for success. To address this challenge, we propose a framework for learning multimodal grasp distributions that leverages variational shape inference to enhance robustness against shape noise and measurement sparsity. Our approach first trains a variational autoencoder for shape inference using implicit neural representations, and then uses these learned geometric features to guide a diffusion model for grasp synthesis on the SE(3) manifold. Additionally, we introduce a test-time grasp optimization technique that can be integrated as a plugin to further enhance grasping performance. Experimental results demonstrate that our shape inference for grasp synthesis formulation outperforms state-of-the-art multimodal grasp synthesis methods on the ACRONYM dataset by 6.3%, while demonstrating robustness to deterioration in point cloud density compared to other approaches. Furthermore, our trained model achieves zero-shot transfer to real-world manipulation of household objects, generating 34% more successful grasps than baselines despite measurement noise and point cloud calibration errors.