Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

Rolínek, Michal; Swoboda, Paul; Zietlow, Dominik; Paulus, Anselm; Musil, Vít; Martius, Georg

doi:10.48550/arxiv.2003.11657

Cited by 3 publications

(11 citation statements)

References 43 publications

(83 reference statements)

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“…In a broader context, MAML [28,29] also has a neural module for joint initialization and a reasoning module that performs optimization steps for task-specific adaptation. Other examples include [6,30,31,32,33,34,35,36,37,38,39]. More specifically, perception and reasoning can be jointly formulated in the form…”

Section: Summary Of Resultsmentioning

confidence: 99%

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Understanding Deep Architectures with Reasoning Layer

Chen,

Zhang,

Reisinger

et al. 2020

Preprint

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Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is often unrolled, and used as a specialized layer in the deep architecture, which can be trained end-to-end with other neural components. Although such hybrid deep architectures have led to many empirical successes, the theoretical foundation of such architectures, especially the interplay between algorithm layers and other neural layers, remains largely unexplored. In this paper, we take an initial step towards an understanding of such hybrid deep architectures by showing that properties of the algorithm layers, such as convergence, stability and sensitivity, are intimately related to the approximation and generalization abilities of the end-to-end model. Furthermore, our analysis matches closely our experimental observations under various conditions, suggesting that our theory can provide useful guidelines for designing deep architectures with reasoning layers.Preprint. Under review.

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Section: Summary Of Resultsmentioning

confidence: 99%

“…Within discrete optimization methods, Evolution Strategies (ES) is a popular choice for global optimization (33)(34)(35) and has been used to map chemical space (36). ES involves a structured search that incorporates heuristics and procedures inspired by natural evolution (37).…”

Section: Inverse Designmentioning

confidence: 99%

Understanding Deep Architectures with Reasoning Layer

Chen,

Zhang,

Reisinger

et al. 2020

Preprint

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“…Recently, [2,6] showed how to efficiently differentiate through convex cone programs by applying the implicit function theorem to a residual map introduced in [27], and [1] showed how to differentiate through convex optimization problems by an automatable reduction to convex cone programs; our method for learning convex optimization models builds on this recent work. Optimization layers have been used in many applications, including control [7,11,15,3], game-playing [46,45], computer graphics [37], combinatorial tasks [58,52,53,21], automatic repair of optimization problems [14], and data fitting more generally [9,17,16,10]. Differentiable optimization for nonconvex problems is often performed numerically by differentiating each individual step of a numerical solver [33,48,32,36], although sometimes it is done implicitly; see, e.g., [7,47,4].…”

Section: Related Workmentioning

confidence: 99%

Learning Convex Optimization Models

Agrawal¹,

Barratt²,

Boyd³

2020

Preprint

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A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression. We propose a heuristic for learning the parameters in a convex optimization model from a dataset of input-output pairs, using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters. We describe three general classes of convex optimization models, maximum a posteriori (MAP) models, utility maximization models, and agent models, and present a numerical experiment for each.

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“…tion techniques [25,26,28,34] have been proposed to make it computationally tractable. Until recently, deep graph matching (DGM) methods give birth to many more flexible formulations [13,32,39,45] besides traditional QAP. DGM aims to learn the meaningful node affinity by using deep features extracted from convolutional neural network.…”

Section: Introductionmentioning

confidence: 99%

“…DGM aims to learn the meaningful node affinity by using deep features extracted from convolutional neural network. To this end, many existing DGM methods [32,39,45] primarily focus on the feature modeling and refinement for more accurate affinity construction. The feature refinement step is expected to capture the implicit structure information [39] encoded in learnable parameters.…”

Section: Introductionmentioning

confidence: 99%

Deep Graph Matching under Quadratic Constraint

Gao¹,

Wang²,

Xue³

et al. 2021

Preprint

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Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep graph matching (DGM) methods lies in their ignorance of explicit constraint of graph structures, which may lead the model to be trapped into local minimum in training. In this paper, we propose to explicitly formulate pairwise graph structures as a quadratic constraint incorporated into the DGM framework. The quadratic constraint minimizes the pairwise structural discrepancy between graphs, which can reduce the ambiguities brought by only using the extracted CNN features. Moreover, we present a differentiable implementation to the quadratic constrained-optimization such that it is compatible with the unconstrained deep learning optimizer. To give more precise and proper supervision, a well-designed false matching loss against class imbalance is proposed, which can better penalize the false negatives and false positives with less overfitting. Exhaustive experiments demonstrate that our method achieves competitive performance on real-world datasets.

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Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

Cited by 3 publications

References 43 publications

Understanding Deep Architectures with Reasoning Layer

Understanding Deep Architectures with Reasoning Layer

Learning Convex Optimization Models

Deep Graph Matching under Quadratic Constraint

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