Go to TMLR homepageAC$\oplus$DC search: behind the winning solution to the Flywire graph-matching challenge
Abstract: This paper describes the alternating continuous and discrete combinatorial (AC$\oplus$DC) optimizations behind the winning solution to the Flywire Ventral Nerve Cord Matching Challenge. The challenge was organized by the Princeton Neuroscience Institute and held over three months, ending on January 31, 2025. During this period, the challenge attracted teams of researchers with expertise in machine learning, high-performance computing, graph data mining, biological network analysis, and quadratic assignment problems. The goal of the challenge was to align the connectomes of a male and female fruit fly, and more specifically, to determine a one-to-one correspondence between the neurons in their ventral nerve cords. The connectomes were represented as large weighted graphs, and the challenge was posed as a problem in graph matching: how does one find a permutation that maps the nodes of one graph onto the nodes of another? The winning solution to the challenge alternated between two complementary approaches to graph matching—the first, a combinatorial optimization over the symmetric group of permutations, and the second, a continuous relaxation of this problem to the space of doubly stochastic matrices. For the latter, the doubly stochastic matrices were optimized by combining Frank-Wolfe methods with a fast preconditioner to solve the linear assignment problem at each iteration. We provide a complete implementation of these methods with a few hundred lines of code in MATLAB. Notably, this implementation obtains a winning score to the challenge in less than 15 minutes on a laptop computer.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=cNOjnx8XrR
Changes Since Last Submission: Anonymized versions of the README.txt and LICENSE.txt files have been uploaded to the code repository that is linked to the VNC Matching Challenge website.
Assigned Action Editor: ~Giannis_Nikolentzos1
Submission Number: 5649
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