Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers (2003.11657v2)

Abstract: 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 solvers. 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. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups. The code is available at https://github.com/martius-lab/blackbox-deep-graph-matching

• The paper introduces an end-to-end architecture that integrates combinatorial solvers for efficient optimization of keypoint correspondences.
• It leverages blackbox differentiation to provide meaningful gradient information without altering solver performance, overcoming discrete output challenges.
• Evaluation on benchmarks like SPair-71k, Pascal VOC, and Willow ObjectClass confirms state-of-the-art performance and enhanced robustness.

Overview of "Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers"

The paper "Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers" explores the integration of combinatorial optimization and deep learning to enhance the efficacy of graph matching tasks. The authors propose an end-to-end trainable architecture that incorporates unmodified combinatorial solvers, setting a precedent in leveraging heavily optimized solvers within a deep learning framework to improve performance on graph matching benchmarks.

Contributions and Approach

1. End-to-End Architecture: The proposed architecture seamlessly integrates state-of-the-art combinatorial graph matching solvers into the deep learning pipeline, allowing for efficient global optimization of keypoint correspondences while maintaining performant feature extraction capabilities. This integration is based on recent advancements in differentiating through blackbox solvers which traditionally manipulate discrete outputs from continuous inputs.
2. Use of Blackbox Differentiation: The authors build on the framework allowing differentiation through combinatorial solvers, preserving solver performance while providing meaningful gradient information for neural network training. This unique approach circumvents the challenges posed by the piecewise constant nature of most solver mappings.
3. Flexible and Robust Design: The architecture effectively utilizes global image features by adjusting the weightings of node and edge similarities, adapting to complex global patterns like viewpoint invariance and object rigidity. This ensures robustness and flexibility in handling diverse scenarios during matching.
4. Experimental Innovation: For robust evaluation, the authors introduce two experimental setups, including the challenging SPair-71k dataset and assessments avoiding common keypoint pre-filtering practices, which are aimed at improving the standardization of benchmarks.

Numerical Results

The method achieves state-of-the-art performance on classic benchmarks such as Pascal VOC and Willow ObjectClass, and outperforms existing models on SPair-71k particularly in challenging scenarios with diverse viewpoints. The architecture consistently provides higher accuracy in these benchmarks, highlighting the effectiveness of the combinatorial solver integration.

Implications

The integration of combinatorial optimization within deep learning frameworks promises to enhance the generalization capabilities of neural networks, especially in domains requiring high-level discrete decisions such as graph and hypergraph matching. The demonstrated ability to handle unfiltered keypoints suggests practical implications for real-world applications where data preprocessing adjustments are infeasible.

Future Directions

Further exploration in this area can focus on refining neural network components to yield more discriminative input costs for matching, developing more advanced solvers, and extending this approach to other combinatorial problems like multicut or max-cut in computer vision. Additionally, understanding the transferability of these hybrid methods to other domains beyond standard benchmarks remains a critical area for ongoing research.

The blend of rigorous combinatorial methods with flexible neural networks exploits the strengths of both fields, supporting theoretical advances and paving the way for practical AI applications.