Forexample,nested MC (NMC) can only achieve, at best, a rate ofO(T 1/3) in the total computational costT [33], comparedwithO(T 1/2)forconventionalMC.

Graph Neural Networks (GNNs) are valuable intellectual property, yet many watermarks rely on backdoor triggers that break under common model edits and create ownership ambiguity. We present InvGNN-WM, which ties ownership to a model's implicit perception of a graph invariant, enabling trigger-free, black-box verification with negligible task impact. A lightweight head predicts normalized algebraic connectivity on an owner-private carrier set; a sign-sensitive decoder outputs bits, and a calibrated threshold controls the false-positive rate. Across diverse node and graph classification datasets and backbones, InvGNN-WM matches clean accuracy while yielding higher watermark accuracy than trigger- and compression-based baselines. It remains strong under unstructured pruning, fine-tuning, and post-training quantization; plain knowledge distillation (KD) weakens the mark, while KD with a watermark loss (KD+WM) restores it. We provide guarantees for imperceptibility and robustness, and we prove that exact removal is NP-complete.

Grand Theft Auto made him a legend. In July this year workers at Build a Rocket Boy, a video game studio in Edinburgh, were called to an all-staff meeting. Their first ever game, a sci-fi adventure called MindsEye, had been released three weeks earlier - and it had been a total disaster. Critics and players called it broken, buggy, and the worst game of 2025. Addressing staff via video link, the company's boss, Leslie Benzies, assured them there was a plan to get things back on track and said the negativity they'd seen was uncalled for.

Deep Reinforcement Learning (DRL) controllers for quadrupedal locomotion have demonstrated impressive performance on challenging terrains, allowing robots to execute complex skills such as climbing, running, and jumping. However, existing blind locomotion controllers often struggle to ensure safety and efficient traversal through risky gap terrains, which are typically highly complex, requiring robots to perceive terrain information and select appropriate footholds during locomotion accurately. Meanwhile, existing perception-based controllers still present several practical limitations, including a complex multi-sensor deployment system and expensive computing resource requirements. This paper proposes a DRL controller named MAstering Risky Gap Terrains (MARG), which integrates terrain maps and proprioception to dynamically adjust the action and enhance the robot's stability in these tasks. During the training phase, our controller accelerates policy optimization by selectively incorporating privileged information (e.g., center of mass, friction coefficients) that are available in simulation but unmeasurable directly in real-world deployments due to sensor limitations. We also designed three foot-related rewards to encourage the robot to explore safe footholds. More importantly, a terrain map generation (TMG) model is proposed to reduce the drift existing in mapping and provide accurate terrain maps using only one LiDAR, providing a foundation for zero-shot transfer of the learned policy. The experimental results indicate that MARG maintains stability in various risky terrain tasks.

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types of convex free energies. These approximations are efficient but can fail if the model is complex and highly interactive. In this work, we analyze two classes of approximations that include the above methods as special cases: first, if the model parameters are changed; and second, if the entropy approximation is changed. We discuss benefits and drawbacks of either approach, and deduce from this analysis how a free energy approximation should ideally be constructed. Based on our observations, we propose approximations that automatically adapt to a given model and demonstrate their effectiveness for a range of difficult problems.

In this paper, we present ReeFRAME, a scalable Reeb graph-based framework designed to analyze vast volumes of GPS-enabled human trajectory data generated at 1Hz frequency. ReeFRAME models Patterns-of-life (PoL) at both the population and individual levels, utilizing Multi-Agent Reeb Graphs (MARGs) for population-level patterns and Temporal Reeb Graphs (TERGs) for individual trajectories. The framework's linear algorithmic complexity relative to the number of time points ensures scalability for anomaly detection. We validate ReeFRAME on six large-scale anomaly detection datasets, simulating real-time patterns with up to 500,000 agents over two months.

Abstract-- We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and conditioning onto axis-aligned manifolds are well-established procedures, doing so onto non-axis-aligned manifolds is not as well understood. We demonstrate the utility of our expressions through three applications: 1) approximation of the projected normal distribution, where the quality of our linearized approximation increases as problem nonlinearity decreases; 2) covariance extraction in Koopman SLAM, where our covariances are shown to be consistent on a real-world dataset; and 3) covariance extraction in constrained GTSAM, where our covariances are shown to be consistent in simulation. Figure 1: Marginalizing and conditioning Gaussians onto manifolds defined by linear constraints using Table II. Gaussians have rank-2 covariances, lying on the constraint plane.

Research on Out-Of-Distribution (OOD) detection focuses mainly on building scores that efficiently distinguish OOD data from In Distribution (ID) data. On the other hand, Conformal Prediction (CP) uses non-conformity scores to construct prediction sets with probabilistic coverage guarantees. In this work, we propose to use CP to better assess the efficiency of OOD scores. Specifically, we emphasize that in standard OOD benchmark settings, evaluation metrics can be overly optimistic due to the finite sample size of the test dataset. Based on the work of (Bates et al., 2022), we define new conformal AUROC and conformal FRP@TPR95 metrics, which are corrections that provide probabilistic conservativeness guarantees on the variability of these metrics. We show the effect of these corrections on two reference OOD and anomaly detection benchmarks, OpenOOD (Yang et al., 2022) and ADBench (Han et al., 2022). We also show that the benefits of using OOD together with CP apply the other way around by using OOD scores as non-conformity scores, which results in improving upon current CP methods. One of the key messages of these contributions is that since OOD is concerned with designing scores and CP with interpreting these scores, the two fields may be inherently intertwined.

Training dynamic agents from datasets of expert examples, known as imitation learning, promises to take advantage of the plentiful demonstrations available in the modern data environment, in an analogous manner to the recent successes of language models conducting unsupervised learning on enormous corpora of text [68, 71]. Imitation learning is especially exciting in robotics, where mass stores of pre-recorded demonstrations on Youtube [1] or cheaply collected simulated trajectories [43, 20] can be converted into learned robotic policies. For imitation learning to be a viable path toward generalist robotic behavior, it needs to be able to both represent and execute the complex behaviors exhibited in the demonstrated data. An approach that has shown tremendous promise is generative behavior cloning: fitting generative models, such as diffusion models [2, 19, 34], to expert demonstrations with pure supervised learning. In this paper, we ask: Under what conditions can generative behavior cloning imitate arbitrarily complex expert behavior? In this paper, we are interested in how algorithmic choices interface with the dynamics of the agent's environment to render imitation possible. The key challenge separating imitation learning from vanilla supervised learning is one of compounding error: when the learner executes the trained behavior in its environment, small mistakes can accumulate into larger ones; this in turn may bring the agent to regions of state space not seen during training, leading to larger-still deviations from intended trajectories.