提出Graph Energy Matching (GEM)方法，基于JKO传输映射优化视角学习置换不变势能，通过能量基切换策略实现离散图的高质量生成，在分子图基准上匹配或超越离散扩散模型。
摘要：
离散数据（如图）的生成建模支撑着许多科学和工业应用，包括分子发现和材料设计。在这些领域中，概率推理尤其有价值，因为它能够实现可组合生成和原则性地融入期望的约束，例如结构或功能属性。能量基模型通过捕获相对似然并在推理过程中直接施加约束来支持可组合推理，自然符合这一目标。然而，离散能量基模型通常难以实现高效高质量的采样，因为支持区域外的区域常包含虚假局部最小值，会困住采样器并导致训练不稳定，从而与离散扩散模型相比存在保真度差距。为了解决这一差距，我们引入了Graph Energy Matching (GEM)，这是一种受Jordan-Kinderlehrer-Otto (JKO)传输映射优化视角启发的离散生成框架。GEM学习一个置换不变势能，同时引导从噪声到高似然图区域的离散传输，并在这些区域内细化样本。我们进一步引入了一种利用能量基切换策略的采样协议，无缝衔接快速的梯度引导传输和用于有效探索的局部混合机制。在分子图基准上，GEM在大多数报告指标上匹配或超越了强离散扩散基线。除了提高生成质量，GEM的相对似然建模还支持定向探索，促进组合生成、属性约束采样以及图之间的插值。项目页面：https://michalbalcerak.ai/graph-energy-matching/。
英文摘要：
Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan-Kinderlehrer-Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs. Project page: https://michalbalcerak.ai/graph-energy-matching/.
TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models
Department of Statistics and Actuarial Science University of Iowa（统计与精算科学系，爱荷华大学）；Departments of Data Science and AI, and Applied Mathematics The Hong Kong Polytechnic University（数据科学与人工智能系、应用数学系，香港理工大学）
Equivariant Flow Matching with Hybrid Probability Transport
Institute of AI Industry Research(AIR), Tsinghua University（清华大学人工智能产业研究院（AIR））；Stanford University（斯坦福大学）；Beijing Academy of Artificial Intelligence（北京智源人工智能研究院）
Improving Molecular Graph Generation with Flow Matching and Optimal Transport
Institute of Computing Technology（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Central China Research Institute for Artificial Intelligence Technologies（华中人工智能技术研究院）；Western Institute of Computing Technology（西部计算技术研究院）；Phil Rivers Technology（菲尔里弗斯科技公司）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions
Universiti Sains Malaysia（马来西亚理科大学）；The Chinese University of Hong Kong Shenzhen（香港中文大学（深圳））；Shenzhen Loop Area Institute（深圳河套学院）；Shenzhen Research Institute of Big Data（深圳大数据研究院）；University of Electronic Science and Technology of China（电子科技大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Multiscale Supervised Unbalanced Optimal Transport Flow Matching
Center for Quantitative Biology, Peking University（北京大学定量生物学中心）；National Engineering Laboratory for Big Data Analysis and Applications, Beijing, China（大数据分析与应用国家工程实验室）；AI for Science Institute, Beijing, China（人工智能科学研究院）
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Artificial Intelligence Research Institute（人工智能研究院）
Schrödinger Bridges (SB) have recently gained the attention of the ML community as a promising extension of classic diffusion models which is also interconnected to the Entropic Optimal Transport (EOT). Recent solvers for SB exploit the pervasive bridge matching procedures. Such procedures aim to recover a stochastic process transporting the mass between distributions given only a transport plan between them. In particular, given the EOT plan, these procedures can be adapted to solve SB. This fact is heavily exploited by recent works giving rise to matching-based SB solvers. The cornerstone he…
Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；Centre for Frontier AI Research, Agency for Science, Technology and Research（新加坡科技研究局前沿人工智能研究中心）；Dalian Jiaotong University（大连交通大学）
SMART: Semantic Matching Contrastive Learning for Partially View-Aligned Clustering
College of Computer Science and Technology, Huaqiao University（华侨大学计算机科学与技术学院）；Department of Computer Science, Shantou University（汕头大学计算机科学系）；Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University（西南大学电子信息工程学院非线性电路与智能信息处理重点实验室）；School of Computer Science and Engineering, South China University of Technology（华南理工大学计算机科学与工程学院）；Department of Computer Science, City University of Hong Kong（香港城市大学计算机科学系）
University of Maryland（马里兰大学）；Texas A&M University（得克萨斯农工大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the shuffled network to averages of the networks in the vertex-aligned collection at different levels of granularity. We demonstrate both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to cluster-averages can yield higher fidelity matching performance th…
Georgia Institute of Technology（佐治亚理工学院）；Georgia State University（佐治亚州立大学）
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching contexts. We emphasize that the discrete optimal transport plays the role of a variational principle which gives rise to an optimization-based framework for modeling the observed empirical matching data. Our formulation leads to a non-convex optimization problem which can be solved efficiently by an alternating optimization method. A key novel aspect of our form…
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations research, computer vision, neuroscience, and more. However, current state-of-the-art algorithms are inefficient in matching very large graphs, though they produce good accuracy. The main computational bottleneck of these algorithms is the linear assignment problem, which must be solved at each iteration. In this paper, we leverage the recent advances in the field of…
Bilingual lexicons form a critical component of various natural language processing applications, including unsupervised and semisupervised machine translation and crosslingual information retrieval. We improve bilingual lexicon induction performance across 40 language pairs with a graph-matching method based on optimal transport. The method is especially strong with low amounts of supervision.
Microsoft Research（微软研究院）；IBM Research（IBM研究院）；CSAIL, MIT（麻省理工学院计算机科学与人工智能实验室）
This paper focuses on the problem of unsupervised alignment of hierarchical data such as ontologies or lexical databases. This is a problem that appears across areas, from natural language processing to bioinformatics, and is typically solved by appeal to outside knowledge bases and label-textual similarity. In contrast, we approach the problem from a purely geometric perspective: given only a vector-space representation of the items in the two hierarchies, we seek to infer correspondences across them. Our work derives from and interweaves hyperbolic-space representations for hierarchical data…
Criteo AI Lab（Criteo人工智能实验室）；Ecole Polytechnique（巴黎综合理工学院）；INSA de Rouen Normandie（鲁昂国立应用科学学院）；Université Technologique de Compiègne（贡比涅技术大学）；Université de Rouen Normandie（鲁昂诺曼底大学）；Université de Bretagne Sud（南布列塔尼大学）
We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. For this sake, we propose a learning problem that minimizes importance weighted loss in the source domain and a Wasserstein distance between weighted marginals. For a proper weighting, we provide an estimator of target label proportion by blen…
Many-to-Many Matching via Sparsity Controlled Optimal Transport
Qiushi Academy for Advanced Studies, Zhejiang University（浙江大学求是高等研究院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Kyoto University（京都大学）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Zhejiang Laboratory（浙江实验室）
Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text pieces, such as tokens or sentences, as a justification for the downstream prediction. Our approach employs optimal transport (OT) to find a minimal cost alignment between the inputs. However, directly applying OT often produces dense and therefore uninterpretable alignments. To overcome this limitation, we introduce novel constrained variants of the OT prob…
Cluster-Aware Matching via Laplacian Optimal Transport
Department of Applied Mathematics, Tel Aviv University（特拉维夫大学应用数学系）；Department of Statistics, Columbia University（哥伦比亚大学统计系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
What is a good matching of probability measures? A counterfactual lens on transport maps
Institut Elie Cartan de Lorraine, Université de Lorraine（伊莱·卡坦研究所（洛林）、洛林大学）；Université Paris-Saclay, CNRS, Inria, Laboratoire de mathématiques d’Orsay（巴黎-萨克雷大学、国家科学研究中心、法国国家信息与自动化技术研究院、奥赛数学实验室）
