Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to Riemannian manifolds remain challenging due to the curved geometry. In this work, we propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling while respecting the intrinsic manifold constraint imposed by the Riemannian geometry. Leveraging the covariant derivative and exponential-map-based parameterization, we derive the closed-form solutions for both discrete-and continuous-time training objectives for RCM. We then demonstrate theoretical equivalence between the two variants of RCM: Riemannian consistency distillation (RCD) that relies on a teacher model to approximate the marginal vector field, and Riemannian consistency training (RCT) that utilizes the conditional vector field for training. We further propose a simplified training objective that eliminates the need for the complicated differential calculation. Finally, we provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles.

This paper introduces a novel iterative method for missing data imputation that sequentially reduces the mutual information between data and the corresponding missingness mask. Inspired by GAN-based approaches that train generators to decrease the predictability of missingness patterns, our method explicitly targets this reduction in mutual information.

In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games--one in continuous and one in discrete time--with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone--underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty.

Verifiers can improve language model (LM) capabilities by providing feedback or selecting the best response from a pool of generated candidates. Currently, high-quality verifiers are either unscalable (e.g., humans) or limited in utility (e.g., tools like Lean for formal proofs). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers. To help close this gap, we introduce WEAVER, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. First we find that weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in the verifiers. To reduce the dependency on labeled data, WEAVER leverages weak supervision to estimate each verifier's accuracy and combines their outputs into a unified score that better reflects true response quality.

Modern reinforcement learning (RL) algorithms have found success by using probabilistic models, such as transformers, energy-based models, and diffusion/flowbased models. To this end, researchers often choose to pay the price of accommodating these models into their algorithms - diffusion models are expressive, but are computationally intensive due to their reliance on solving differential equations, while autoregressive transformer models are scalable but typically require learning discrete representations. Normalizing flows (NFs), by contrast, seem to provide an appealing alternative, as they enable likelihoods and sampling without solving differential equations or autoregressive architectures. However, their potential in RL has received limited attention, partly due to the prevailing belief that normalizing flows lack sufficient expressivity. We show that this is not the case. Building on recent work in NFs, we propose a single NF architecture which integrates seamlessly into RL algorithms, serving as a policy, Q-function, and occupancy measure. Our approach leads to much simpler algorithms, and achieves higher performance in imitation learning, offline, goal conditioned RL and unsupervised RL.1

Recent advancements in diffusion policies have demonstrated promising performance in decision-making tasks. To align these policies with human preferences, a common approach is incorporating Preference-based Reinforcement Learning (PbRL) into policy tuning. However, since preference data is practically collected from populations with different backgrounds, a key challenge lies in handling the inherent uncertainties in people's preferences during policy updates. To address this challenge, we propose the Diff-UAPA algorithm, designed for uncertainty-aware preference alignment in diffusion policies. Specifically, Diff-UAPA introduces a novel iterative preference alignment framework in which the diffusion policy adapts incrementally to preferences from different user groups. To accommodate this online learning paradigm, Diff-UAPA employs a maximum posterior objective, which aligns the diffusion policy with regret-based preferences under the guidance of an informative Beta prior. This approach enables direct optimization of the diffusion policy without specifying any reward functions, while effectively mitigating the influence of inconsistent preferences across different user groups. We conduct extensive experiments across both simulated and real-world robotics tasks, and diverse human preference configurations, demonstrating the robustness and reliability of Diff-UAPA in achieving effective preference alignment.

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.

A longstanding goal in safe reinforcement learning (RL) is a method to ensure the safety of a policy throughout the entire process, from learning to operation. However, existing safe RL paradigms inherently struggle to achieve this objective. We propose a method, called Provably Lifetime Safe RL (PLS), that integrates offline safe RL with safe policy deployment to address this challenge. Our proposed method learns a policy offline using return-conditioned supervised learning and then deploys the resulting policy while cautiously optimizing a limited set of parameters, known as target returns, using Gaussian processes (GPs). Theoretically, we justify the use of GPs by analyzing the mathematical relationship between target and actual returns. We then prove that PLS finds near-optimal target returns while guaranteeing safety with high probability. Empirically, we demonstrate that PLS outperforms baselines both in safety and reward performance, thereby achieving the longstanding goal to obtain high rewards while ensuring the safety of a policy throughout the lifetime from learning to operation.

Human behavior is characterized by continuous learning to reduce uncertainties about the world in pursuit of goals. When trying to understand such behavior from observations, it is essential to account for this adaptive nature and reason about the uncertainties that may have led to seemingly suboptimal decisions. Nevertheless, most inverse approaches to sequential decision-making focus on inferring cost functions underlying stationary behavior or are limited to low-dimensional tasks. In this paper, we address this gap by considering the problem of inferring an agent's knowledge or awareness about the environment based on a given trajectory. We assume that the agent aims to reach a goal in an environment they only partially know, and integrates new information into their plan as they act. We propose a Bayesian approach to infer their latent knowledge state, leveraging an approximate navigation model that optimistically incorporates partial information while accounting for uncertainty. By combining sample-based Bayesian inference with dynamic graph algorithms, we achieve an efficient method for computing posterior beliefs about the agent's knowledge. Empirical validation using simulated behavioral data and human data from an online experiment demonstrates that our model effectively captures human navigation under uncertainty and reveals interpretable insights into their environmental knowledge.

The widespread use of generative models has created a feedback loop, in which each version of a model is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation in performance caused by repeated training on synthetic data. However, different analyses in the literature have reached different conclusions as to the severity of model collapse. As such, it remains unclear how concerning this phenomenon is, and under which assumptions it can be avoided. To address this, we theoretically study model collapse for maximum likelihood estimation (MLE), in a natural setting where synthetic data is gradually added to the original data set. Under standard assumptions (similar to those long used for proving asymptotic consistency and normality of MLE), we establish non-asymptotic bounds showing that collapse can be avoided even as the fraction of real data vanishes. On the other hand, we prove that some assumptions (beyond MLE consistency) are indeed necessary: Without them, model collapse can occur arbitrarily quickly, even when the original data is still present in the training set. To the best of our knowledge, these are the first rigorous examples of iterative generative modeling with accumulating data that rapidly leads to model collapse.