Superpixel graphs (statistics in Table S1) gain from all augmentations except attribute masking as shown in Figure S1. D Difficulty of Contrastive T asks v.s. Pairing "Identical" stands for a no-augmentation baseline for contrastive The baseline training-from-scratch accuracy is 79.71%. Performance on contrastive learning with different implemented subgraph. For subgraph, we propose the following variants with difficulty levels.

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets whose samples lie on low-dimensional manifolds requires robust techniques capable of separating meaningful signal from noise. We propose a principled framework for statistical inference of similarity and alignment between distributions supported on manifolds underlying high-dimensional datasets in the presence of heterogeneous noise. The key idea is to link the low-rank structure of observed data matrices to their underlying manifold geometry. By analyzing the spectrum of the sample covariance under a manifold signal-plus-noise model, we develop a scale-invariant distance measure between datasets based on their principal variance structures. We further introduce a consistent estimator for this distance and a statistical test for manifold alignability, and establish their asymptotic properties using random matrix theory. The proposed framework accommodates heterogeneous noise across datasets and offers an efficient, theoretically grounded approach for comparing high-dimensional datasets with low-dimensional manifold structures. Through extensive simulations and analyses of multi-sample single-cell datasets, we demonstrate that our method achieves superior robustness and statistical power compared with existing approaches.

Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner.

The accompanying tool, available open source, can be found at https://github.com/meelgroup/teq.

Inferring an adversary's goals from exhibited behavior is crucial for counterplanning and non-cooperative multi-agent systems in domains like cybersecurity, military, and strategy games. Deep Inverse Reinforcement Learning (IRL) methods based on maximum entropy principles show promise in recovering adversaries' goals but are typically offline, require large batch sizes with gradient descent, and rely on first-order updates, limiting their applicability in real-time scenarios. We propose an online Recursive Deep Inverse Reinforcement Learning (RDIRL) approach to recover the cost function governing the adversary actions and goals. Specifically, we minimize an upper bound on the standard Guided Cost Learning (GCL) objective using sequential second-order Newton updates, akin to the Extended Kalman Filter (EKF), leading to a fast (in terms of convergence) learning algorithm. We demonstrate that RDIRL is able to recover cost and reward functions of expert agents in standard and adversarial benchmark tasks. Experiments on benchmark tasks show that our proposed approach outperforms several leading IRL algorithms.

Superpixel graphs (statistics in Table S1) gain from all augmentations except attribute masking as shown in Figure S1. D Difficulty of Contrastive T asks v.s. Pairing "Identical" stands for a no-augmentation baseline for contrastive The baseline training-from-scratch accuracy is 79.71%. Performance on contrastive learning with different implemented subgraph. For subgraph, we propose the following variants with difficulty levels.

Abstract--We present a method for formal safety verification of learning-based generative motion planners. Generative motion planners (GMPs) offer advantages over traditional planners, but verifying the safety and dynamic feasibility of their outputs is difficult since neural network verification (NNV) tools scale only to a few hundred neurons, while GMPs often contain millions. T o preserve GMP expressiveness while enabling verification, our key insight is to imitate the GMP by stabilizing references sampled from the GMP with a small neural tracking controller and then applying NNV to the closed-loop dynamics. This yields reachable sets that rigorously certify closed-loop safety, while the controller enforces dynamic feasibility. Building on this, we construct a library of verified GMP references and deploy them online in a way that imitates the original GMP distribution whenever it is safe to do so, improving safety without retraining. We evaluate across diverse planners, including diffusion, flow matching, and vision-language models, improving safety in simulation (on ground robots and quadcopters) and on hardware (differential-drive robot). Motion planning has been transformed by generative models like diffusion and conditional flow matching (CFM) [1], [2], which learn multimodal trajectory distributions and enable generative motion planners (GMPs) that produce diverse plans from inputs like language or images [3]-[6].

Abstract--Neural-based motion planning methods have achieved remarkable progress for robotic manipulators, yet a fundamental challenge lies in simultaneously accounting for both the robot's physical shape and the surrounding environment when generating safe and feasible motions. Moreover, existing approaches often rely on simplified robot models or focus primarily on obstacle representation, which can lead to incomplete collision detection and degraded performance in cluttered scenes. T o address these limitations, we propose spatial anchor-based motion policy (SAMP), a unified framework that simultaneously encodes the environment and the manipulator using signed distance field (SDF) anchored on a shared spatial grid. SAMP incorporates a dedicated robot SDF network that captures the manipulator's precise geometry, enabling collision-aware reasoning beyond coarse link approximations. These representations are fused on spatial anchors and used to train a neural motion policy that generates smooth, collision-free trajectories in the proposed efficient feature alignment strategy. Experiments conducted in both simulated and real-world environments consistently show that SAMP outperforms existing methods, delivering an 11 % increase in success rate and a 7 % reduction in collision rate. Efficient computation of collision-free motions remains a fundamental challenge in robotic planning. Traditional motion planning methods for robots typically operate in configuration space, which execute a projection of obstacles in the workspace and perform collision checks during path search with sampling-based methods or trajectory optimization [1], [2], [3].

Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner.