A neural algorithm for computing bipartite matchings

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 121; no. 37; p. e2321032121
• Main Authors: Dasgupta, Sanjoy, Meirovitch, Yaron, Zheng, Xingyu, Bush, Inle, Lichtman, Jeff W., Navlakha, Saket
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 10.09.2024
• Subjects: Algorithms; Animals; Biological Sciences; Combinatorial analysis; Computation; Computer Sciences; Fibers; Graph theory; Humans; Matching; Models, Neurological; Motor neurons; Motor Neurons - physiology; Muscles; Neural networks; Neural Networks, Computer; Neurons; Neuroscience; Physical Sciences; neural algorithm; neural-inspired computing; neuromuscular circuit; bipartite matching; circuit development
• ISSN: 0027-8424; 1091-6490; 1091-6490
• DOI: 10.1073/pnas.2321032121

SignificanceFinding bipartite matchings is one of the oldest and most well-studied problems in computer science. This problem comes up in many guises, such as when matching donors to recipients for organ transplants, advertisers to advertising slots in marketing applications, or drivers to passengers on ride-sharing services. By studying the development of the neuromuscular circuit-a key circuit for motor control with a bipartite architecture-we found an algorithm for the bipartite matching problem. This algorithm achieves near-optimal performance, despite being fully distributed and privacy-preserving. Biologically, this algorithm demonstrates how matching architectures can scalably and robustly emerge over development despite significant variation in circuit sizes and wiring patterns. Thus, we uncovered a unique connection between computer science and neuroscience. Finding optimal bipartite matchings—e.g., matching medical students to hospitals for residency, items to buyers in an auction, or papers to reviewers for peer review—is a fundamental combinatorial optimization problem. We found a distributed algorithm for computing matchings by studying the development of the neuromuscular circuit. The neuromuscular circuit can be viewed as a bipartite graph formed between motor neurons and muscle fibers. In newborn animals, neurons and fibers are densely connected, but after development, each fiber is typically matched (i.e., connected) to exactly one neuron. We cast this synaptic pruning process as a distributed matching (or assignment) algorithm, where motor neurons “compete” with each other to “win” muscle fibers. We show that this algorithm is simple to implement, theoretically sound, and effective in practice when evaluated on real-world bipartite matching problems. Thus, insights from the development of neural circuits can inform the design of algorithms for fundamental computational problems.