Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into single fixed-curvature manifolds or discrete product spaces, struggle to capture this diversity. We introduce Adaptive Riemannian Graph Neural Networks (ARGNN), a novel framework that learns a continuous and anisotropic Riemannian metric tensor field over the graph. It allows each node to determine its optimal local geometry, enabling the model to fluidly adapt to the graph's structural landscape. Our core innovation is an efficient parameterization of the node-wise metric tensor, specializing to a learnable diagonal form that captures directional geometric information while maintaining computational tractability. To ensure geometric regularity and stable training, we integrate a Ricci flow-inspired regularization that smooths the learned manifold. Theoretically, we establish the rigorous geometric evolution convergence guarantee for ARGNN and provide a continuous generalization that unifies prior fixed or mixed-curvature GNNs. Empirically, our method demonstrates superior performance on both homophilic and heterophilic benchmark datasets with the ability to capture diverse structures adaptively. Moreover, the learned geometries both offer interpretable insights into the underlying graph structure and empirically corroborate our theoretical analysis.
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Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can often lead to overfitting, especially when data is limited. We analyze PC overfitting from a log-likelihood-landscape perspective and show that it is often caused by convergence to sharp optima that generalize poorly. Inspired by sharpness aware minimization in neural networks, we propose a Hessian-based regularizer for training PCs. As a key contribution, we show that the trace of the Hessian of the log-likelihood--a sharpness proxy that is typically intractable in deep neural networks--can be computed efficiently for PCs. Minimizing this Hessian trace induces a gradient-norm-based regularizer that yields simple closed-form parameter updates for EM, and integrates seamlessly with gradient based learning methods. Experiments on synthetic and real-world datasets demonstrate that our method consistently guides PCs toward flatter minima, improving generalization performance.
Machine learning models now drive many critical decisions, making explanations of their reasoning essential. Recent work analyzes the complexity of exact explanations in transparent models, but these explanations are often too large for practical use. This has motivated research into probabilistic alternatives. We study probabilistic extensions that allow controlled uncertainty while maintaining rigorous foundations. We analyze three basic model types: decision trees, decision lists, and decision sets. We introduce algorithms for computing both local and global probabilistic explanations for these models. Our main result shows that computing minimum-size probabilistic explanations is fixed-parameter tractable when parameterized by structural properties---specifically, the number of terms for decision lists and decision sets and the minimum of the number of positive and the number of negative leaves.
Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.
Detecting unobserved confounders is crucial for reliable causal inference in observational studies. Existing methods require either linearity assumptions or multiple heterogeneous environments, limiting applicability to nonlinear single-environment settings. To bridge this gap, we propose Kernel Regression Confounder Detection (KRCD), a novel method for detecting unobserved confounding in nonlinear observational data under single-environment conditions. KRCD leverages reproducing kernel Hilbert spaces to model complex dependencies. By comparing standard and higher-order kernel regressions, we derive a test statistic whose significant deviation from zero indicates unobserved confounding. Theoretically, we prove two key results: First, in infinite samples, regression coefficients coincide if and only if no unobserved confounders exist. Second, finite-sample differences converge to zero-mean Gaussian distributions with tractable variance. Extensive experiments on synthetic benchmarks and the Twins dataset demonstrate that KRCD not only outperforms existing baselines but also achieves superior computational efficiency.
One of the most important queries in knowledge compilation is weighted model counting (WMC), which has been applied to probabilistic inference on various models, such as Bayesian networks. In practical situations on inference tasks, the model's parameters have uncertainty because they are often learned from data, and thus we want to compute the degree of uncertainty in the inference outcome. One possible approach is to regard the inference outcome as a random variable by introducing distributions for the parameters and evaluate the variance of the outcome. Unfortunately, the tractability of computing such a variance is hardly known. Motivated by this, we consider the problem of computing the variance of WMC and investigate this problem's tractability. First, we derive a polynomial time algorithm to evaluate the WMC variance when the input is given as a structured d-DNNF. Second, we prove the hardness of this problem for structured DNNFs, d-DNNFs, and FBDDs, which is intriguing because the latter two allow polynomial time WMC algorithms. Finally, we show an application that measures the uncertainty in the inference of Bayesian networks. We empirically show that our algorithm can evaluate the variance of the marginal probability on real-world Bayesian networks and analyze the impact of the variances of parameters on the variance of the marginal.
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. Conditioning WFOMC on evidence—fixing the truth values of a set of ground literals—has been shown impossible in time polynomial in the domain size (unless ♯P ⊆ FP) even for fragments of logic that are otherwise tractable for WFOMC without evidence. In this work, we address the barrier by restricting the binary evidence to the case where the underlying Gaifman graph has bounded treewidth. We present a polynomial-time algorithm in the domain size for computing WFOMC for the two-variable fragments ??² and ?² conditioned on such binary evidence. Furthermore, we show the applicability of our algorithm in combinatorial problems by solving the stable seating arrangement problem on bounded-treewidth graphs of bounded degree, which was an open problem. We also conducted experiments to show the scalability of our algorithm compared to the existing model counting solvers.
Ensuring alignment with human values is essential for modern large language models (LLMs), especially amid growing concerns around AI safety and social impact. Yet achieving such alignment remains challenging due to the limited, noisy, and often conflicting nature of human feedback from diverse annotators. Most existing approaches, such as Direct Preference Optimization (DPO), assume consistent and conflict-free supervision, overlooking the ambiguity, inconsistency, and value trade-offs inherent in real-world preferences—often leading to reduced robustness and exclusion of minority views. To address this, we propose FGD-Align, a novel pluralistic alignment framework grounded in Fuzzy Group Decision-Making theory. Our approach rigorously models and aggregates human preferences while retaining the complexity of real-world value trade-offs. Unlike traditional methods that rely on coarse-grained preference pairs, FGD-Align introduces fuzzy preference modeling via triangular fuzzy numbers to capture nuanced, multi-criteria human judgments. We further develop a new training objective, Probabilistic Fuzzy DPO, which incorporates fuzzy preference strength as adaptive loss weights and gradient filters, enhancing robustness to ambiguity and inconsistency in feedback. Comprehensive experiments demonstrate that FGD-Align consistently outperforms both DPO variants and advanced preference aggregation methods in terms of preference accuracy and robustness to ambiguity. It achieves superior alignment stability and better preserves minority preferences, all with minimal computational overhead. Our work bridges the gap between algorithmic tractability and the nuanced landscape of human values, enabling more scalable, inclusive, and socially-aware AI alignment.
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.
Dividing Indivisible Items for the Benefit of All: It Is Hard to Be Fair Without Social Awareness
PDF ↗In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items that, at the same time, maximize social impact. In this model, each agent is associated with two additive functions that define their value and social impact for each item. The goal is to allocate items so that the social impact is maximized while maintaining some fairness criterion. We reveal that the complexity of the problem heavily depends on whether the agents are socially aware, i.e., they take into consideration the social impact functions. For socially unaware agents, we prove that the problem is NP-hard for a variety of fairness notions, and that it is tractable only for very restricted cases, e.g., if for every agent valuation equals social impact and it is binary. On the other hand, social awareness allows for fair allocations that maximize social impact, and such allocations can be computed in polynomial time. Interestingly, the problem becomes again intractable as soon as the definition of social awareness is relaxed.
Time-inconsistent behavior, such as procrastination or abandonment of long-term goals, arises when agents evaluate immediate outcomes disproportionately higher than future ones. This leads to globally suboptimal behavior, where plans are frequently revised or abandoned entirely. In the influential model of Kleinberg and Oren (2014) such behavior is modeled by a present-biased agent navigating a task graph toward a goal, making locally optimal decisions at each step based on discounted future costs. As a result, the agent may repeatedly deviate from initially intended plans. Recent work by Belova et al. (2024) introduced a two-agent extension of this model, where a fully-aware principal attempts to guide the present-biased agent through a specific set of critical tasks without causing abandonment. This captures a rich class of principal–agent dynamics in behavioral settings. In this paper, we provide a comprehensive algorithmic characterization of this problem. We analyze its computational complexity through the framework of parameterized algorithms, focusing on graph parameters that naturally emerge in this setting, such as treewidth, vertex cover, and feedback vertex set. Our main result is a fixed-parameter tractable algorithm when parameterized by the treewidth of the task graph and the number of distinct (v,t)-path costs. Our algorithm encaptures several input settings, such as bounded edge costs and restricted task graph structure. We demonstrate that our main result yields efficient algorithms for a number of such configurations. We complement this with tight hardness results, that highlight the extreme difficulty of the problem even on simplest graphs with bounded number of nodes and constant parameter values, and motivate our choice of parameters. We delineate tractable and intractable regions of the problem landscape, which include answers to open questions of Belova et al. (2024).
We study the computational complexity of explaining preference data through Boolean attribute models (BAMs), motivated by extensive research involving attribute models and their promise in understanding preference structure and enabling more efficient decision-making processes. In a BAM, each alternative possesses a subset of binary attributes, each voter cares about a subset of attributes, and voters prefer alternatives with more of their desired attributes. In the BAM problem, we are given a preference profile and want to know whether there is a k-attribute model explaining the profile. We establish a complexity dichotomy for the number of attributes k: BAM is linear-time solvable for k≤2 but NP-complete for k≥3. The problem remains hard even when preference orders have length two. On the positive side, BAM becomes fixed-parameter tractable when parameterized by the number of alternatives m. For the special case of two voters, we provide a linear-time algorithm. We also analyze variants where partial information is given: When voter preferences over attributes are known (BAM With Cares) or when alternative attributes are specified (BAM With Has), showing that for most parameters BAM With Cares is more difficult whereas BAM With Has is more tractable except for being NP-hard even for one voter.
Humans exhibit time-inconsistent behavior, in which planned actions diverge from executed actions. Understanding time inconsistency and designing appropriate interventions is a key research challenge in computer science and behavioral economics. Previous work focuses on progress-based tasks and derives a closed-form description of agent behavior, from which they obtain optimal intervention strategies. They model time-inconsistency using the β–δ discounting (quasi-hyperbolic discounting), but the analysis is limited to the case δ = 1. In this paper, we relax that constraint and show that a closed-form description of agent behavior remains possible for the general case 0 < δ ≤ 1. Based on this result, we derive the conditions under which agents abandon tasks and develop efficient methods for computing optimal interventions. Our analysis reveals that agent behavior and optimal interventions depend critically on the value of δ, suggesting that fixing δ = 1 in many prior studies may unduly simplify real-world decision-making processes.
Diffusion probabilistic models have set a new standard for generative fidelity but are hindered by a slow iterative sampling process. A powerful training-free strategy to accelerate this process is Schedule Optimization, which aims to find an optimal distribution of timesteps for a fixed and small Number of Function Evaluations (NFE) to maximize sample quality. To this end, a successful schedule optimization method must adhere to four core principles: effectiveness, adaptivity, practical robustness, and computational efficiency. However, existing paradigms struggle to satisfy these principles simultaneously, motivating the need for a more advanced solution. To overcome these limitations, we propose the Hierarchical-Schedule-Optimizer (HSO), a novel and efficient bi-level optimization framework. HSO reframes the search for a globally optimal schedule into a more tractable problem by iteratively alternating between two synergistic levels: an upper-level global search for an optimal initialization strategy and a lower-level local optimization for schedule refinement. This process is guided by two key innovations: the Midpoint Error Proxy (MEP), a solver-agnostic and numerically stable objective for effective local optimization, and the Spacing-Penalized Fitness (SPF) function, which ensures practical robustness by penalizing pathologically close timesteps. Extensive experiments show that HSO sets a new state-of-the-art for training-free sampling in the extremely low-NFE regime. For instance, with an NFE of just 5, HSO achieves a remarkable FID of 11.94 on LAION-Aesthetics with Stable Diffusion v2.1. Crucially, this level of performance is attained not through costly retraining, but with a one-time optimization cost of less than 8 seconds, presenting a highly practical and efficient paradigm for diffusion model acceleration.
AnchorHOI: Zero-shot Generation of 4D Human-Object Interaction via Anchor-based Prior Distillation
PDF ↗Despite significant progress in text-driven 4D human-object interaction (HOI) generation with supervised methods, the scalability remains limited by the scarcity of large-scale 4D HOI datasets. To overcome this, recent approaches attempt zero-shot 4D HOI generation with pre-trained image diffusion models. However, interaction cues are minimally distilled during the generation process, restricting their applicability across diverse scenarios. In this paper, we propose AnchorHOI, a novel framework that thoroughly exploits hybrid priors by incorporating video diffusion models beyond image diffusion models, advancing 4D HOI generation. Nevertheless, directly optimizing high-dimensional 4D HOI with such priors remains challenging, particularly for human pose and compositional motion. To address this challenge, AnchorHOI introduces an anchor-based prior distillation strategy, which constructs interaction-aware anchors and then leverages them to guide generation in a tractable two-step process. Specifically, two tailored anchors are designed for 4D HOI generation: anchor Neural Radiance Fields (NeRFs) for expressive interaction composition, and anchor keypoints for realistic motion synthesis. Extensive experiments demonstrate that AnchorHOI outperforms previous methods with superior diversity and generalization.
Vision-language models (VLMs) achieve strong multimodal performance, yet how computation is organized across populations of neurons remains poorly understood. In this work, we study VLMs through the lens of neural topology, representing each layer as a within-layer correlation graph derived from neuron-neuron co-activations. This view allows us to ask whether population-level structure is behaviorally meaningful, how it changes across modalities and depth, and whether it identifies causally influential internal components under intervention. We show that correlation topology carries recoverable behavioral signal; moreover, cross-modal structure progressively consolidates with depth around a compact set of recurrent hub neurons, whose targeted perturbation materially alters model output. Neural topology thus emerges as a meaningful intermediate scale for VLM interpretability: richer than local attribution, more tractable than full circuit recovery, and empirically tied to multimodal behavior. Code is publicly available at https://github.com/he-h/vlm-graph-probing.
Despite significant progress in text-to-image generation, aligning outputs with complex prompts remains challenging, particularly for fine-grained semantics and spatial relations. This difficulty stems from the feed-forward nature of generation, which requires anticipating alignment without fully understanding the output. In contrast, evaluating generated images is more tractable. Motivated by this asymmetry, we propose xLARD, a self-correcting framework that uses multimodal large language models to guide generation through Explainable Latent Rewards. xLARD introduces a lightweight corrector that refines latent representations based on structured feedback from model-generated references. A key component is a differentiable mapping from latent edits to interpretable reward signals, enabling continuous latent-level guidance from non-differentiable image-level evaluations. This mechanism allows the model to understand, assess, and correct itself during generation. Experiments across diverse generation and editing tasks show that xLARD improves semantic alignment and visual fidelity while maintaining generative priors, offering a data-efficient and generalizable solution to bridging the gap between comprehension and synthesis.
Stochastic human motion prediction aims to forecast future motion distributions. Although recent studies have achieved strong performance in terms of accuracy and diversity, they often overlook plausibility (e.g., resulting in physically unrealistic predictions) and uncertainty quantification, which is essential for real-world applications and downstream tasks. To address these issues, we propose a latent flow-based model equipped with a data-driven Gaussian mixture prior that more effectively disentangles diverse human behaviors than conventional single-modal priors. This prior is derived from patterns in the training data without requiring additional annotations. Furthermore, the fully invertible nature of our model enables natural uncertainty quantification through tractable likelihood computation. Experiments on the Human3.6M and AMASS datasets demonstrate that our approach achieves state-of-the-art performance in both accuracy and plausibility, while also providing reliable uncertainty estimates.
Registration of multiview point clouds typically depends on extensive pairwise matching to build a pose graph for global synchronization, which is computationally expensive and ill-posed without holistic geometric constraints. In this paper, we propose FUSER, the first feed-forward multi-view registration transformer that processes all scans jointly in a unified, compact latent space to directly predict global poses without any pairwise estimation. To maintain tractability, FUSER employs a sparse 3D CNN to encode each scan into low-resolution superpoint features preserving absolute translation cues, followed by a Geometric Alternating Attention module for efficient intra- and inter-scan reasoning. Particularly, we transfer 2D attention priors from off-the-shelf foundation models (i.e., \pi^3) to enhance 3D feature attention. Building upon FUSER and its estimates, we further introduce FUSER-DF, an SE(3) diffusion refinement framework to correct FUSER's estimates through a denoising process over the joint SE(3)^N space. Here, FUSER serves as a surrogate multiview register to model the denoiser, and a prior-conditioned SE(3)^N variational lower bound is derived for denoising supervision. Extensive experiments on 3DMatch and ScanNet confirm the superior registration accuracy and efficiency of our method.
What makes a good viewpoint? The quality of the data used to learn 3D reconstructions is crucial for enabling efficient and accurate scene modeling. We study the active view selection problem and develop a principled analysis that yields a simple and interpretable criterion for selecting informative camera poses. Our key insight is that informative views can be obtained by minimizing a tractable approximation of the Fisher Information Gain, which reduces to favoring viewpoints that cover geometry that has been insufficiently observed by past cameras. This leads to a lightweight coverage-based view selection metric that avoids expensive transmittance estimation and is robust to noise and training dynamics. We call this metric CONVERGE (Coverage Optimized Novel Viewset Estimation for Reconstructing Geometry Efficiently). We integrate our method into the Nerfstudio framework and evaluate it on real datasets within fixed and embodied data acquisition scenarios. Across multiple datasets and radiance-field baselines, our method consistently improves reconstruction quality compared to state-of-the-art active view selection methods.