Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length -- known as scale invariance at criticality (SIC) in the renormalization group theory. SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS) -- a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site-wise-independent conditional HB sampling. Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers. RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for 128x128 two-dimensional Ising systems.

Heterogeneous tabular data poses unique challenges in generative modelling due to its fundamentally different underlying data structure compared to homogeneous modalities, such as images and text. Although previous research has sought to adapt the successes of generative modelling in homogeneous modalities to the tabular domain, defining an effective generator for tabular data remains an open problem. One major reason is that the evaluation criteria inherited from other modalities often fail to adequately assess whether tabular generative models effectively capture or utilise the unique structural information encoded in tabular data. In this paper, we carefully examine the limitations of the prevailing evaluation framework and introduce $\textbf{TabStruct}$, a novel evaluation benchmark that positions structural fidelity as a core evaluation dimension. Specifically, TabStruct evaluates the alignment of causal structures in real and synthetic data, providing a direct measure of how effectively tabular generative models learn the structure of tabular data. Through extensive experiments using generators from eight categories on seven datasets with expert-validated causal graphical structures, we show that structural fidelity offers a task-independent, domain-agnostic evaluation dimension. Our findings highlight the importance of tabular data structure and offer practical guidance for developing more effective and robust tabular generative models. Code is available at https://github.com/SilenceX12138/TabStruct.

Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the Lilleb{\ae}lt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.

Unbiased data synthesis is crucial for evaluating causal discovery algorithms in the presence of unobserved confounding, given the scarcity of real-world datasets. A common approach, implicit parameterization, encodes unobserved confounding by modifying the off-diagonal entries of the idiosyncratic covariance matrix while preserving positive definiteness. Within this approach, state-of-the-art protocols have two distinct issues that hinder unbiased sampling from the complete space of causal models: first, the use of diagonally dominant constructions, which restrict the spectrum of partial correlation matrices; and second, the restriction of possible graphical structures when sampling bidirected edges, unnecessarily ruling out valid causal models. To address these limitations, we propose an improved explicit modeling approach for unobserved confounding, leveraging block-hierarchical ancestral generation of ground truth causal graphs. Algorithms for converting the ground truth DAG into ancestral graph is provided so that the output of causal discovery algorithms could be compared with. We prove that our approach fully covers the space of causal models, including those generated by the implicit parameterization, thus enabling more robust evaluation of methods for causal discovery and inference.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the $K$ sets of future trajectories is accurate but also encourages all $K$ sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is $\textbf{100}$ times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

Real-world decision-making problems are often marked by complex, uncertain dynamics that can shift or break under changing conditions. Traditional Model-Based Reinforcement Learning (MBRL) approaches learn predictive models of environment dynamics from queried trajectories and then use these models to simulate rollouts for policy optimization. However, such methods do not account for the underlying causal mechanisms that govern the environment, and thus inadvertently capture spurious correlations, making them sensitive to distributional shifts and limiting their ability to generalize. The same naturally holds for model-free approaches. In this work, we introduce Causal Model-Based Policy Optimization (C-MBPO), a novel framework that integrates causal learning into the MBRL pipeline to achieve more robust, explainable, and generalizable policy learning algorithms. Our approach centers on first inferring a Causal Markov Decision Process (C-MDP) by learning a local Structural Causal Model (SCM) of both the state and reward transition dynamics from trajectories gathered online. C-MDPs differ from classic MDPs in that we can decompose causal dependencies in the environment dynamics via specifying an associated Causal Bayesian Network. C-MDPs allow for targeted interventions and counterfactual reasoning, enabling the agent to distinguish between mere statistical correlations and causal relationships. The learned SCM is then used to simulate counterfactual on-policy transitions and rewards under hypothetical actions (or ``interventions"), thereby guiding policy optimization more effectively. The resulting policy learned by C-MBPO can be shown to be robust to a class of distributional shifts that affect spurious, non-causal relationships in the dynamics. We demonstrate this through some simple experiments involving near and far OOD dynamics drifts.

Probabilistic reasoning is a key aspect of both human and artificial intelligence that allows for handling uncertainty and ambiguity in decision-making. In this paper, we introduce a novel numerical reasoning task under uncertainty, focusing on estimating the k-anonymity of user-generated documents containing privacy-sensitive information. We propose BRANCH, which uses LLMs to factorize a joint probability distribution to estimate the k-value-the size of the population matching the given information-by modeling individual pieces of textual information as random variables. The probability of each factor occurring within a population is estimated using standalone LLMs or retrieval-augmented generation systems, and these probabilities are combined into a final k-value. Our experiments show that this method successfully estimates the correct k-value 67% of the time, an 11% increase compared to GPT-4o chain-of-thought reasoning. Additionally, we leverage LLM uncertainty to develop prediction intervals for k-anonymity, which include the correct value in nearly 92% of cases.

Quantification learning is the task of predicting the label distribution of a set of instances. We study this problem in the context of graph-structured data, where the instances are vertices. Previously, this problem has only been addressed via node clustering methods. In this paper, we extend the popular Adjusted Classify & Count (ACC) method to graphs. We show that the prior probability shift assumption upon which ACC relies is often not fulfilled and propose two novel graph quantification techniques: Structural importance sampling (SIS) makes ACC applicable in graph domains with covariate shift. Neighborhood-aware ACC improves quantification in the presence of non-homophilic edges. We show the effectiveness of our techniques on multiple graph quantification tasks.

We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which variables enter the governing equation of which other variables". We prove a global Markov property for cyclic SDEs, which naturally extends to partially observed cyclic SDEs, because our asymmetric independence model is closed under marginalization. We then characterize the class of graphs that encode the same set of independence relations, yielding a result analogous to the seminal 'same skeleton and v-structures' result for directed acyclic graphs (DAGs). In the fully observed case, we show that each such equivalence class of graphs has a greatest element as a parsimonious representation and develop algorithms to identify this greatest element from data. We conjecture that a greatest element also exists under partial observations, which we verify computationally for graphs with up to four nodes.

Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of probability flow ODE-based samplers in practice due to their superior sampling efficiency and precision, rigorous statistical guarantees for these methods have remained elusive in the literature. This work develops the first end-to-end theoretical framework for deterministic ODE-based samplers that establishes near-minimax optimal guarantees under mild assumptions on target data distributions. Specifically, focusing on subgaussian distributions with $\beta$-H\"older smooth densities for $\beta\leq 2$, we propose a smooth regularized score estimator that simultaneously controls both the $L^2$ score error and the associated mean Jacobian error. Leveraging this estimator within a refined convergence analysis of the ODE-based sampling process, we demonstrate that the resulting sampler achieves the minimax rate in total variation distance, modulo logarithmic factors. Notably, our theory comprehensively accounts for all sources of error in the sampling process and does not require strong structural conditions such as density lower bounds or Lipschitz/smooth scores on target distributions, thereby covering a broad range of practical data distributions.