Boundary Representation (B-rep) is the most commonly used data format in Computer-Aided Design (CAD) due to its analytical precision and direct support for parametric editing. However, its heterogeneous data structure— continuous parametric geometry with discrete topological graphs—poses fundamental challenges for deep learning models. Existing methods often directly predict the heterogeneous B-rep graph, relying on fixed-size padding or sequential tokenization to handle the varying cardinality of the geometric primitives. These approaches struggle with the combinatorial complexity of CAD models. The discrete, non-differentiable nature of the graph data structure prevents end-to-end optimization of the geometry and watertightness. In this work we introduce DualBrep, a novel continuous representation that unifies B-rep geometry and topology within a fully structured Euclidean domain. DualBrep encodes a CAD model using dual scalar fields: a Signed Distance Function (SDF) to represent the global shape geometry, and an Unsigned Distance Field (UDF) that implicitly encodes the topological structure via a Voronoi partitioning of the surface elements. Rather than processing these fields independently, we compress them into a single latent space. While the dual-field formulation alone already gives reconstruction a flexible, primitive-free segmentation signal that adapts to arbitrary face counts and surface types, the shared latent also makes generation tractable: a Flow Matching model can sample geometry and topology jointly from a single code, avoiding the error accumulation that plagues sequential or autoregressive B-rep predictors. Finally, we use a neural rebuilder to extract explicit B-rep models—comprising both prismatic and free-form primitives—directly from our continuous dual scalar fields. We demonstrate that DualBrep serves as a robust, unified backbone for CAD B-rep learning, achieving strong performance in both reverse engineering from raw point clouds and generative modeling via latent flow matching. Code is available at https://github.com/AutodeskAILab/DualBrep.
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The escalating energy consumption and carbon footprint of training large-scale Web AI models pose urgent challenges for sustainable development. Dataset Distillation (DD) offers a promising avenue for green AI by compressing large datasets into small synthetic ones for efficient training. However, most existing DD methods overfit to the inductive biases of specific source architectures (e.g., CNNs or ViTs), resulting in poor cross-model generalization. This limitation necessitates redundant re-distillation processes for different architectures, severely undermining the energy-saving potential of DD. To address this, we introduce Adversarial Mutual Information Distillation (AMID), a rigorous framework designed to create highly reusable and robust synthetic datasets. From an information-theoretic perspective, we cast model-agnosticism as minimizing the mutual information (MI) between the synthetic data and the specific identity of the distillation model. We convert this intractable objective into a tractable two-player adversarial game, which unifies knowledge preservation with adversarial unlearning of architectural bias. Extensive experiments on CIFAR-10 and Tiny ImageNet demonstrate that AMID achieves state-of-the-art cross-architecture generalization across diverse CNNs and ViTs. Crucially, our analysis confirms that AMID significantly reduces the computational overhead and CO2 emissions of downstream training while maintaining robust performance, paving the way for energy-efficient, transferable, and sustainable Web AI ecosystems.
Graph Neural Networks (GNNs) have achieved remarkable success across various graph-based tasks but remain highly sensitive to distribution shifts. In this work, we focus on a prevalent yet underexplored phenomenon in graph generalization, Minimal Shift Flip (MSF)—where test samples that slightly deviate from the training distribution are abruptly misclassified. To interpret this phenomenon, we revisit MSF through the lens of Sharpness-Aware Minimization (SAM), which characterizes the local stability and sharpness of the loss landscape while providing a theoretical foundation for modeling generalization error. To quantify loss sharpness, we introduce the concept of Local Robust Radius, measuring the smallest perturbation required to flip a prediction and establishing a theoretical link between local stability and generalization. Building on this perspective, we further observe a continual decrease in the robust radius during training, indicating weakened local stability and an increasingly sharp loss landscape that gives rise to MSF. To jointly solve the MSF phenomenon and the intractability of radius, we develop an energy-based formulation that is theoretically proven to be monotonically correlated with the robust radius, offering a tractable and principled objective for modeling flatness and stability. Building on these insights, we propose an energy-driven generative augmentation framework (E2A) that leverages energy-guided latent perturbations to generate pseudo-OOD samples and enhance model generalization. Extensive experiments across multiple benchmarks demonstrate that E2A consistently improves graph OOD generalization, outperforming state-of-the-art baselines. Code is available at https://github.com/anders1123/E2A
Graph generation is a fundamental problem in graph learning with broad applications across Web-scale systems, knowledge graphs, and scientific domains such as drug and material discovery. Recent approaches leverage diffusion models for step-by-step generation, yet unconditional diffusion offers little control over desired properties, often leading to unstable quality and difficulty in incorporating new objectives. Inference-time guidance methods mitigate these issues by adjusting the sampling process without retraining, but they remain inherently local, heuristic, and limited in controllability. To overcome these limitations, we propose TreeDiff, a Monte Carlo Tree Search (MCTS) guided dual-space diffusion framework for controllable graph generation. TreeDiff is a plug-and-play inference-time method that expands the search space while keeping computation tractable. Specifically, TreeDiff introduces three key designs to make it practical and scalable: (1) a macro-step expansion strategy that groups multiple denoising updates into a single transition, reducing tree depth and enabling long-horizon exploration; (2) a dual-space denoising mechanism that couples efficient latent-space denoising with lightweight discrete correction in graph space, ensuring both scalability and structural fidelity; and (3) a dual-space verifier that predicts long-term rewards from partially denoised graphs, enabling early value estimation and removing the need for full rollouts. Extensive experiments on 2D and 3D molecular generation benchmarks, under both unconditional and conditional settings, demonstrate that TreeDiff achieves state-of-the-art performance. Notably, TreeDiff exhibits favorable inference-time scaling: it continues to improve with additional computation, while existing inference-time methods plateau early under limited resources.
Climate policy analysis requires models that capture multi-gas climate effects, but such models are too slow to embed in reinforcement learning loops at scale. In collaboration with a pan-European public-sector environmental agency, we develop a multi-agent reinforcement learning (MARL) framework that integrates a higher-fidelity climate surrogate as the environment transition, enabling regional agents to learn policies under multi-gas dynamics. We train a recurrent surrogate on 20,000 multi-gas emission pathways to emulate CICERO-SCM. The surrogate achieves near-simulator accuracy (global-mean temperature RMSE ≈ 4 × 10⁻⁴ K) with ∼1000× faster one-step inference and yields >100× end-to-end MARL training speed-up. We show policy agreement with the simulator in tractable settings and propose a replay- and rank-consistency test (Kendall’s τ) for assessing policy fidelity when simulator-in-the-loop training is infeasible. This enables large-scale multi-agent policy experiments while retaining high-fidelity multi-gas climate response.
Hedonic games are a central model of coalition formation, yet most of their general subclasses are marked by negative results: stable outcomes often fail to exist, and deciding their existence is typically computationally hard. The most notable exception is the class of hedonic games with the common ranking property (HGCRP), a nontrivial subclass that guarantees both the existence and tractability of stable partitions. The common ranking property implies the top-coalition property, which in turn implies the weak top-coalition property, forming a natural hierarchy of increasingly general domains. In this paper, we extend the frontier of strong existence and tractability results beyond the HGCRP to hedonic games with the top-coalition property (HGTCP) and hedonic games with the weak top-coalition property (HGWTCP). We show that every HGWTCP instance admits a strong individually stable (SIS) partition that can be computed in polynomial time, and prove that our polynomial-time algorithm generates a partition that is both SIS and Pareto optimal (PO) if preferences are strict. These results show that strong stability and tractability results persist well beyond the common ranking framework. We further show that a contractually Nash stable (CNS) partition may fail to exist even in HGTCP, revealing a sharp contrast with HGCRP, where the existence of partitions that are both CNS and PO is guaranteed. Taken together, these results provide a comprehensive characterization of stability and efficiency in top-coalition-based hedonic games, mapping how stability guarantees evolve from HGCRP to HGWTCP.
Real-world multi-agent systems, from traffic coordination to resource allocation, are often modeled as general-sum games where individual incentives conflict with collective welfare. In these settings, the central challenge is not merely finding an equilibrium, but selecting socially desirable outcomes among many suboptimal Nash equilibria. Standard deep multi-agent reinforcement learning (MARL) methods struggle with this problem, as value-decomposition approaches are constrained by monotonicity assumptions and policy-gradient methods often converge to stable but socially inefficient equilibria. To address this limitation, we propose Phi-Actor-Critic (Phi-AC), a framework that leverages swap regret minimization to steer learning toward high-welfare correlated equilibria (CE). To make counterfactual regret estimation tractable in deep MARL, Phi-AC employs a centralized attention critic that predicts vector-valued regrets in a single forward pass, avoiding computationally expensive counterfactual simulations. We further introduce a Lagrangian-based equilibrium selection mechanism that optimizes social welfare while enforcing stability through regret constraints. Experiments on matrix games, Multi-Agent Particle Environments (MPE), and the Melting Pot Harvest scenario demonstrate that Phi-AC learns efficient and stable coordination strategies across diverse mixed-motive settings while maintaining high collective return and competitive fairness.
Temporal embeddings play a crucial role in dynamic graph neural networks (DGNNs) by capturing the temporal dynamics of interactions. However, existing Random Fourier Feature (RFF)-based methods in DGNNs directly sample Fourier frequencies from a fixed, data-independent distribution, neglecting the temporal characteristics of dynamic graphs and thereby limiting representational capacity. We propose DeepSTE, a deep spectral temporal embedding framework for dynamic graphs. DeepSTE learns RFF representations via Monte Carlo importance sampling with a tractable proposal distribution (e.g., Gaussian) to approximate the feature map of a shift-invariant or positive-definite kernel whose latent spectral density is analytically intractable. DeepSTE adopts a data-dependent scale parameter, estimated from interaction intervals, to construct the frequency proposal distribution reflecting time–frequency uncertainty. The frequency DNN and the importance-weighting DNN, initialized from the proposal distribution, are jointly optimized to model the importance-sampled spectral representation and learn adaptive temporal features. Experiments demonstrate the effectiveness of DeepSTE on dynamic link prediction and node classification tasks, while also revealing insights such as temporal embedding decay and accelerated convergence.
Knowledge Compilation transforms propositional formulas into tractable structures like decision-DNNF to support efficient reasoning. However, these representations often suffer from exponential size, and standard minimization via SAT sweeping is computationally prohibitive for large instances. In this paper, we propose a scalable minimization framework for decision-DNNF that eliminates the need for SAT solvers. We introduce a semantic hashing technique leveraging polynomial-time model counting to rapidly filter redundancies, followed by a polynomial-time verification strategy based on CNF projection. Our experimental evaluation demonstrates that this approach efficiently compresses decision-DNNF circuits while avoiding the bottleneck of NP-hard equivalence checks.
Treewidth is a fundamental graph invariant that quantifies how tree-like a given graph is. It is extensively used with dynamic programming to design fixed-parameter tractable algorithms for many NP-hard graph combinatorial optimization problems. However, despite broad theoretical applicability, treewidth dynamic programming (TDP) does not scale in practice beyond graphs with very small treewidth. Rather than applying TDP as a standalone technique, we demonstrate that TDP can serve as a broadly applicable enhancer for a wide range of graph combinatorial optimization algorithms. Our framework leverages the concept of treewidth modulators, which refer to vertex sets whose removal significantly reduces the treewidth. We further propose an empirically efficient procedure for generating such treewidth modulators. To enhance an algorithm 𝒜, we use 𝒜 to heuristically make decisions on the modulators vertices, after which the remaining decisions outside the treewidth modulators become scalable for TDP. To demonstrate the general applicability of our proposed framework. We experimented with three classic graph combinatorial optimization models: Maximum Independent Set, Minimum Vertex Cover, and Max Cut. We apply TDP to enhance algorithms across diverse paradigms, including evolutionary search, greedy heuristics, and graph-neural-network-based heuristics. For all combinations of optimization models and base algorithms, TDP significantly improves performance over the original methods. In many settings, TDP-enhanced greedy heuristics are competitive with, and sometimes clearly outperform, state-of-the-art commercial solvers.
Online planning in continuous state, action, and observation spaces remains challenging for autonomous systems. While Monte Carlo Tree Search (MCTS) scales effectively via sampling, most continuous (PO)MDP solvers do not exploit gradient-based action optimization. We propose Action-Gradient MCTS (AGMCTS), a framework that combines global tree search with local gradient-based action refinement, while maintaining consistent value estimates. We provide three key theoretical contributions: (1) an action score gradient theorem for particle belief states; (2) the Multiple Importance Sampling (MIS) Tree that supports frequent action-branch updates by reusing prior samples without introducing estimator drift; and (3) tractable action score gradients for smooth generative models using the Area Formula. Empirical results demonstrate that AGMCTS outperforms state-of-the-art sample-based solvers in multiple challenging continuous MDP and POMDP benchmarks.
Recent deep learning-based ISP methods are primarily constrained by mimicking fixed camera pipelines, consequently struggling to achieve expert-level aesthetic quality. To this end, we propose AesISP, the first expert-level aesthetic ISP framework formulated as a reward flow model. Addressing the ill-posed nature of ISP, AesISP establishes a Privileged Prior Distillation paradigm. By leveraging expert-image-guided latent proxies, we decompose the intractable task into a tractable, proxy-driven learning process. Subsequently, we propose MeanFlow++, which reformulates the flow matching objective via target-prediction parameterization and a Progressive Temporal Curriculum. By evolving from learning instantaneous to long-range average velocities, this mechanism rectifies transport trajectories and uses deterministic mapping to impose explicit constraints, anchoring the generation trajectory to the expert manifold. Finally, we introduce a multi-dimensional reward-driven reinforcement learning approach.Leveraging Group Relative Policy Optimization (GRPO) to balance trade-offs across dimensions such as color and lighting, it steers the model to converge precisely on expert-level aesthetic standards. Experiments demonstrate that AesISP outperforms state-of-the-art methods in both quantitative metrics and aesthetic quality.
As Large Language Models (LLMs) scale to handle massive context windows, achieving surgical feature-level interpretation is essential for high-stakes tasks like legal auditing and code debugging. However, existing local model-agnostic explanation methods face a critical dilemma in these scenarios: feature-based methods suffer from attribution dilution due to high feature dimensionality, which prevents them from providing faithful explanations. In this paper, we propose Focus-LIME, a coarse-to-fine framework designed to restore the tractability of surgical interpretation. Focus-LIME utilizes a proxy model to curate the perturbation neighborhood, allowing the target model to perform fine-grained attribution exclusively within the optimized context. Empirical evaluations on long-context benchmarks demonstrate that our method makes surgical explanations practical and provides faithful explanations to users.
Explainable AI (XAI) seeks to answer the question: which features of the data led a model to make its decision? Sufficient reasons are an important concept for understanding the behaviour of machine learning models, as they identify the key characteristics responsible for the prediction of an individual instance. Recent work introduced probabilistic global sufficient reasons, extending sufficient reasons from the single-instance level to all instances in the feature domain, thereby providing a global understanding of the classifier. However, prior work on this notion has been purely theoretical, without empirical evaluation. In this paper, we aim to fill this gap by developing practical methods for computing probabilistic global sufficient reasons and evaluating them on decision trees and circuit-based models.
Universal Learning of Stochastic Dynamics for Exact Belief Propagation Using Bernstein Normalizing Flows
PDF ↗Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring approximate methods. When the system model is unknown and must be learned from data, a key question arises: can we learn a model that (i) universally approximates general nonlinear stochastic dynamics, and (ii) supports analytical belief propagation? This paper establishes the theoretical foundations for a class of models that satisfy both properties. The proposed approach combines the expressiveness of normalizing flows for density estimation with the analytical tractability of Bernstein polynomials. Empirical results show the efficacy of our learned model over state-of-the art data-driven methods for belief propagation, especially for highly non-linear systems with non-additive, non-Gaussian noise.
Dynamic Bayesian networks (DBNs) are compact graphical representations used to model probabilistic systems where interdependent random variables and their distributions evolve over time. In this paper, we study the verification of the evolution of conditional-independence (CI) propositions against temporal logic specifications. To this end, we consider two specification formalisms over CI propositions: linear temporal logic (LTL), and non-deterministic Büchi automata (NBAs). This problem has two variants. Stochastic CI properties take the given concrete probability distributions into account, while structural CI properties are viewed purely in terms of the graphical structure of the DBN. We show that deciding whether a stochastic CI proposition eventually holds is at least as hard as the Skolem problem for linear recurrence sequences, which is a long-standing open problem in number theory. On the other hand, we show that verifying the evolution of structural CI propositions against LTL and NBA specifications is in PSPACE, and is hard for both NP and coNP. We also identify natural restrictions on the graphical structure of the DBN that make the verification of structural CI properties tractable.
Online planning in Markov Decision Processes (MDPs) enables agents to make sequential decisions by simulating future trajectories from the current state, making it well-suited for large-scale or dynamic environments. Sample-based methods such as Sparse Sampling and Monte Carlo Tree Search (MCTS) are widely adopted for their ability to approximate optimal actions using a generative model. However, in practical settings, the generative model is often learned from limited data, introducing approximation errors that can degrade performance or lead to unsafe behaviors. To address these challenges, Robust MDPs (RMDPs) offer a principled framework for planning under model uncertainty, yet existing approaches are typically computationally intensive and not suited for real-time use. In this work, we introduce Robust Sparse Sampling (RSS), the first online planning algorithm for RMDPs with finite-sample theoretical performance guarantees. Unlike Sparse Sampling, which estimates the nominal value function, RSS computes a robust value function by leveraging the efficiency and theoretical properties of Sample Average Approximation (SAA), enabling tractable robust policy computation in online settings. RSS is applicable to infinite or continuous state spaces, and its sample and computational complexities are independent of the state space size. We provide theoretical performance guarantees and empirically show that RSS outperforms standard Sparse Sampling in environments with uncertain dynamics.
Robust Markov decision processes (r-MDPs) extend MDPs by explicitly modelling epistemic uncertainty about transition dynamics. Learning r-MDPs from interactions with an unknown environment enables the synthesis of robust policies with provable (PAC) guarantees on performance, but this can require a large number of sample interactions. We propose novel methods for solving and learning r-MDPs based on factored state-space representations that leverage the independence between model uncertainty across system components. Although policy synthesis for factored r-MDPs leads to hard, non-convex optimisation problems, we show how to reformulate these into tractable linear programs. Building on these, we also propose methods to learn factored model representations directly. Our experimental results show that exploiting factored structure can yield dimensional gains in sample efficiency, producing more effective robust policies with tighter performance guarantees than state-of-the-art methods.
Despite the explosive growth of AI and the technologies built upon it, predicting and inferring the sub-optimal behavior of users or human collaborators remains a critical challenge. In many cases, such behaviors are not a result of irrationality, but rather a rational decision made given inherent cognitive bounds and biased beliefs about the world. In this paper, we formally introduce a class of computational-rational (CR) user models for cognitively-bounded agents acting optimally under biased beliefs. The key novelty lies in explicitly modeling how a bounded memory process leads to a dynamically inconsistent and biased belief state and, consequently, sub-optimal sequential decision-making. We address the challenge of identifying the latent user-specific bound and inferring biased belief states from passive observations on the fly. We argue that for our formalized CR model family with an explicit and parameterized cognitive process, this challenge is tractable. To support our claim, we propose an efficient online inference method based on nested particle filtering that simultaneously tracks the user's latent belief state and estimates the unknown cognitive bound from a stream of observed actions. We validate our approach in a representative navigation task using memory decay as an example of a cognitive bound. With simulations, we show that (1) our CR model generates intuitively plausible behaviors corresponding to different levels of memory capacity, and (2) our inference method accurately and efficiently recovers the ground-truth cognitive bounds from limited observations (less than 100 steps). We further demonstrate how this approach provides a principled foundation for developing adaptive AI assistants, enabling adaptive assistance that accounts for the user's memory limitations.
Expressive generative models have recently shown promise in offline reinforcement learning (RL) by capturing the complex, multimodal structure of dataset behavior. However, directly integrating these models into policy optimization introduces substantial computational and stability challenges due to the intricacies of their sampling processes. We introduce Flow Latent Policy (FLP), an offline RL framework that decouples expressivity from optimization by operating entirely in the latent space of a pre-trained, frozen flow-based behavior model. FLP learns a simple latent Gaussian policy whose samples are transformed through the flow to produce complex, behavior-aligned actions. This design enables closed-form behavior regularization via latent-space KL divergence and allows policy optimization without expensive backpropagation through the generative model. Experiments on the OGBench benchmark demonstrate that FLP achieves competitive or superior performance across diverse tasks, combining the benefits of expressive modeling and tractable optimization.