Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic generative flow networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.

Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a very large number of parameters or a complicated geometry. Microcanonical Langevin Monte Carlo (MCLMC) has been recently proposed as an alternative which shows striking gains in efficiency over NUTS, especially for high-dimensional problems. However, it produces biased samples, with a bias that is hard to control in general. We introduce the Metropolis-Adjusted Microcanonical sampler (MAMS), which relies on the same dynamics as MCLMC, but introduces a Metropolis-Hastings step and thus produces asymptotically unbiased samples. We develop an automated tuning scheme for the hyperparameters of the algorithm, making it applicable out of the box. We demonstrate that MAMS outperforms NUTS across the board on benchmark problems of varying complexity and dimensionality, achieving up to a factor of seven speedup.

In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to shortest paths. We prove that, if the total flow is minimized, forward and backward policies traverse the environment graph exclusively along shortest paths between the initial and terminal states. Building on this result, we show that the pathfinding problem in an arbitrary graph can be solved by training a non-acyclic GFlowNet with flow regularization. We experimentally demonstrate the performance of our method in pathfinding in permutation environments and in solving Rubik's Cubes. For the latter problem, our approach shows competitive results with state-of-the-art machine learning approaches designed specifically for this task in terms of the solution length, while requiring smaller search budget at test-time.

As Reinforcement Learning (RL) agents are increasingly deployed in real-world applications, ensuring their behavior is transparent and trustworthy is paramount. A key component of trust is explainability, yet much of the work in Explainable RL (XRL) focuses on local, single-step decisions. This paper addresses the critical need for explaining an agent's long-term behavior through trajectory-level analysis. We introduce a novel framework that ranks entire trajectories by defining and aggregating a new state-importance metric. This metric combines the classic Q-value difference with a "radical term" that captures the agent's affinity to reach its goal, providing a more nuanced measure of state criticality. We demonstrate that our method successfully identifies optimal trajectories from a heterogeneous collection of agent experiences. Furthermore, by generating counterfactual rollouts from critical states within these trajectories, we show that the agent's chosen path is robustly superior to alternatives, thereby providing a powerful "Why this, and not that?" explanation. Our experiments in standard OpenAI Gym environments validate that our proposed importance metric is more effective at identifying optimal behaviors compared to classic approaches, offering a significant step towards trustworthy autonomous systems.

Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The underlying challenge is that the optimization formulation becomes brittle and numerically unstable with changing scales, especially under potentially nonlinear constraints that impose dynamic restrictions, due to the kernel-based formulation. This paper proposes to address this problem via the development of a scale-agnostic and adaptive ergodic coverage optimization method based on the maximum mean discrepancy metric (MMD). Our approach allows the optimizer to solve for the scale of differential constraints while annealing the hyperparameters to best suit the problem domain and ensure physical consistency. We also derive a variation of the ergodic metric in the log space, providing additional numerical conditioning without loss of performance. We compare our approach with existing coverage planning methods and demonstrate the utility of our approach on a wide range of coverage problems.

Humans build viewpoint-independent cognitive maps through navigation, enabling intuitive reasoning about object permanence and spatial relations. We argue that multimodal large language models (MLLMs), despite extensive video training, lack this fundamental spatial reasoning capability, a critical limitation for embodied applications. To demonstrate these limitations and drive research, we introduce REM (Reasoning over Embodied Multi-Frame Trajectories), a benchmark using controllable 3D environments for long-horizon embodied spatial reasoning. REM systematically evaluates key aspects like object permanence/distinction, spatial relationships, and numerical tracking across dynamic embodied viewpoints. Our evaluation shows that the best-performing current models exhibit promising overall performance, but become increasingly unreliable at even moderate complexity levels easily handled by humans. These findings highlight challenges MLLMs face in developing robust spatial representations from sequential visual input. Consequently, REM provides targeted metrics and diagnostics to foster improved spatial understanding in future models.

Consider a dataset where data is collected on multiple features of multiple individuals over multiple times.

Long-horizon planning is crucial in complex environments, but diffusion-based planners like Diffuser are limited by the trajectory lengths observed during training. This creates a dilemma: long trajectories are needed for effective planning, yet they degrade model performance. In this paper, we introduce this extendable long-horizon planning challenge and propose a two-phase solution. First, Progressive Trajectory Extension incrementally constructs longer trajectories through multi-round compositional stitching. Second, the Hierarchical Multiscale Diffuser enables efficient training and inference over long horizons by reasoning across temporal scales. To avoid the need for multiple separate models, we propose Adaptive Plan Pondering and the Recursive HM-Diffuser, which unify hierarchical planning within a single model. Experiments show our approach yields strong performance gains, advancing scalable and efficient decision-making over long-horizons.

In this work, we study the problem of offline safe imitation learning (IL). In many real-world settings, online interactions can be risky, and accurately specifying the reward and the safety cost information at each timestep can be difficult. However, it is often feasible to collect trajectories reflecting undesirable or risky behavior, implicitly conveying the behavior the agent should avoid. We refer to these trajectories as non-preferred trajectories. Unlike standard IL, which aims to mimic demonstrations, our agent must also learn to avoid risky behavior using non-preferred trajectories. In this paper, we propose a novel approach, SafeMIL, to learn a parame-terized cost that predicts if the state-action pair is risky via Multiple Instance Learning. The learned cost is then used to avoid non-preferred behaviors, resulting in a policy that prioritizes safety. We empirically demonstrate that our approach can learn a safer policy that satisfies cost constraints without degrading the reward performance, thereby outperforming several baselines.