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Learning Combinatorial Solver for Graph Matching

Tao Wang, He Liu, Yidong Li, Yi Jin, Xiaohui Hou, Haibin Ling
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
combinatorial solver.  ...  In this paper we propose a fully trainable framework for graph matching, in which learning of affinities and solving for combinatorial optimization are not explicitly separated as in many previous arts  ...  In contrast, our method is able to learn not only the affinity function but also the combinatorial solver for graph matching.  ... 
doi:10.1109/cvpr42600.2020.00759 dblp:conf/cvpr/WangLLJHL20 fatcat:dp5itqktsrcu7lnypwe6rd5jhy

Deep graph matching meets mixed-integer linear programming: Relax at your own risk ? [article]

Zhoubo Xu, Puqing Chen, Romain Raveaux, Xin Yang, Huadong Liu
2022 arXiv   pre-print
Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no research to explain what role the graph matching algorithm plays in the model.  ...  This quality level controls the quality of the solutions provided by the graph matching solver. In addition, several relaxations of the graph matching problem are put to the test.  ...  For the first time, an exact graph matching solver is embedded into a deep learning architecture.  ... 
arXiv:2108.00394v5 fatcat:vsxmrrvuerev5hpcett7zafuqq

Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers [article]

Michal Rolínek, Paul Swoboda, Dominik Zietlow, Anselm Paulus, Vít Musil, Georg Martius
2020 arXiv   pre-print
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial  ...  Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence  ...  Conclusion We have demonstrated that deep learning architectures that integrate combinatorial graph matching solvers perform well on deep graph matching benchmarks.  ... 
arXiv:2003.11657v2 fatcat:7vmpyk23rjhjbkfioryiwisjc4

Variational Bayes in Private Settings (VIPS) (Extended Abstract)

James R. Foulds, Mijung Park, Kamalika Chaudhuri, Max Welling
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method.  ...  overcome this by combining: (1) an improved composition method, called the moments accountant, and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning  ...  Towards Learning of Graph Matching Overview. For generality, we discuss graphs with weighted edges and labeled nodes.  ... 
doi:10.24963/ijcai.2020/694 dblp:conf/ijcai/YanYH20 fatcat:pc4nelo7gzfmvmsiym3ohwspxa

Differentiation of Blackbox Combinatorial Solvers [article]

Marin Vlastelica and Anselm Paulus and Vít Musil and Georg Martius and Michal Rolínek
2020 arXiv   pre-print
Achieving fusion of deep learning with combinatorial algorithms promises transformative changes to artificial intelligence.  ...  In particular, we incorporate the Gurobi MIP solver, Blossom V algorithm, and Dijkstra's algorithm into architectures that extract suitable features from raw inputs for the traveling salesman problem,  ...  ACKNOWLEDGEMENT We thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Marin Vlastelica.  ... 
arXiv:1912.02175v2 fatcat:uasyrwlozzehleotno3omrkdh4

Differentiable Combinatorial Losses through Generalized Gradients of Linear Programs [article]

Xi Gao, Han Zhang, Aliakbar Panahi, Tom Arodz
2020 arXiv   pre-print
Here, we show how to perform gradient descent over combinatorial optimization algorithms that involve continuous parameters, for example edge weights, and can be efficiently expressed as linear programs  ...  The natural training-time loss would involve a combinatorial problem -- dynamic programming-based global sequence alignment -- but solutions to combinatorial problems are not differentiable with respect  ...  for each bag size with the combinatorial loss based on weighted bipartite graph matching, using cross-entropy as the loss defining the edge weights C jk .  ... 
arXiv:1910.08211v4 fatcat:lwhtkafsefhalcpqyrffos6hr4

USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems [article]

Guangmo Tong
2022 arXiv   pre-print
For learning foundations, we present learning-error analysis under the PAC-Bayesian framework using a new margin-based analysis.  ...  Our main deliverable is a universal solver that is able to handle abstract undetermined stochastic combinatorial optimization problems.  ...  Another significance of USCO-Solver lies in our use of combinatorial kernels, which suggests a novel and principled way for incorporating an approximation algorithm into a learning process.  ... 
arXiv:2107.07508v3 fatcat:przlwuabgrad3giwsqfpl2azs4

Revocable Deep Reinforcement Learning with Affinity Regularization for Outlier-Robust Graph Matching [article]

Chang Liu, Runzhong Wang, Zetian Jiang, Junchi Yan, Lingxiao Huang, Pinyan Lu
2021 arXiv   pre-print
We propose a deep reinforcement learning (RL) based approach RGM for weighted graph matching, whose sequential node matching scheme naturally fits with the strategy for selective inlier matching against  ...  In this paper, we are focused on learning the back-end solver for the most general form of GM: the Lawler's QAP, whose input is the affinity matrix.  ...  Meanwhile, there emerge seminal works for differentiable learning of combinatorial tasks [16] and specifically tuned model for graph matching [16] whereby the learning-free solvers can be integrated  ... 
arXiv:2012.08950v3 fatcat:6zq32rcqlnatlcnkbw7ssi4s3u

Deep Latent Graph Matching

Tianshu Yu, Runzhong Wang, Junchi Yan, Baoxin Li
2021 International Conference on Machine Learning  
Deep learning for graph matching (GM) has emerged as an important research topic due to its superior performance over traditional methods and insights it provides for solving other combinatorial problems  ...  While recent deep methods for GM extensively investigated effective node/edge feature learning or downstream GM solvers given such learned features, there is little existing work questioning if the fixed  ...  Recent works in tackling combinatorial problem with deep learning (Huang et al., 2019; Kool & Welling, 2018 ) also inspired development of combinatorial deep solvers for GM problems formulated by both  ... 
dblp:conf/icml/YuWYL21 fatcat:e442umcg7vgs3muownqyifl5f4

Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching [article]

Runzhong Wang, Junchi Yan, Xiaokang Yang
2021 arXiv   pre-print
For pure QAP tasks on synthetic data and QAPLIB benchmark, our method can perform competitively and even surpass state-of-the-art graph matching and QAP solvers with notable less time cost.  ...  The association graph is learned by an embedding network for vertex classification, followed by Sinkhorn normalization and a cross-entropy loss for end-to-end learning.  ...  We also note one recent important work on learning for graph matching, namely Learning Combinatorial Solver (LCS) [32] .  ... 
arXiv:1911.11308v3 fatcat:texrw5wc5bfzpd5rkiotxn4joe

A General Large Neighborhood Search Framework for Solving Integer Linear Programs [article]

Jialin Song, Ravi Lanka, Yisong Yue, Bistra Dilkina
2020 arXiv   pre-print
This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways.  ...  We show that one can learn a good neighborhood selector using imitation and reinforcement learning techniques.  ...  Acknowledgement We thank the anonymous reviewers for their suggestions for improvements.  ... 
arXiv:2004.00422v3 fatcat:w4rfod67pfgqhlquol3mbamvju

The SAT+CAS method for combinatorial search with applications to best matrices

Curtis Bright, Dragomir Ž. Đoković, Ilias Kotsireas, Vijay Ganesh
2019 Annals of Mathematics and Artificial Intelligence  
We describe how the SAT+CAS method has been previously used to resolve many open problems from graph theory, combinatorial design theory, and number theory, showing that the method has broad applications  ...  In this paper, we provide an overview of the SAT+CAS method that combines satisfiability checkers (SAT solvers) and computer algebra systems (CAS) to resolve combinatorial conjectures, and present new  ...  ., a matching of the graph) is found by the SAT solver the matching is passed to a CAS to verify that it can be extended into a Hamiltonian cycle.  ... 
doi:10.1007/s10472-019-09681-3 fatcat:paxe7oruzfeypf7cd2d6b75slu

Learning Combinatorial Embedding Networks for Deep Graph Matching [article]

Runzhong Wang, Junchi Yan, Xiaokang Yang
2019 arXiv   pre-print
It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching.  ...  To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching.  ...  ) approaches for deep combinatorial learning of graph matching.  ... 
arXiv:1904.00597v3 fatcat:yide642jdrhetkobnzmy6k7ppy

Combinatorial optimization and reasoning with graph neural networks [article]

Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, Petar Veličković
2021 arXiv   pre-print
However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by  ...  enhancing exact solvers.  ...  Fey et al. (2020); Li et al. (2019) investigate using GNNs for graph matching.  ... 
arXiv:2102.09544v2 fatcat:eweej3mq2bbohaifazeghswcpi

Combinatorial Learning of Robust Deep Graph Matching: an Embedding based Approach

Runzhong Wang, Junchi Yan, Xiaokang Yang
2020 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The learning is supervised by combinatorial permutation loss over nodes.  ...  This paper resorts to deep neural networks to learn the node and edge feature, as well as the affinity model for graph matching in an end-to-end fashion.  ...  Learning-free Graph Matching Over the decades, the majority line of research on graph matching are focused solving the constrained combinatorial optimization problem for graph matching, which assumes the  ... 
doi:10.1109/tpami.2020.3005590 pmid:32750800 fatcat:5ykitchzznfkzg6pafruoc7h34
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