High-order attention-shifting networks for relational structure matching

The Hopfield-Tank optimization network has been applied to the model-image matching problem in computer vision using a graph matching formulation. However, the network has been criticized for unreliable convergence to feasible solutions and for poor solution quality, and the graph matching formulation is unable to represent matching problems with multiple object types, and multiple relations, and high-order relations. The Hopfield-Tank network dynamics is generalized to provide a basis for reliable convergence to feasible solutions, for finding high-quality solutions, and for solving a broad class of optimization problems. The extensions include a new technique called attention-shifting, the introduction of high-order connections in the network, and relaxation of the unit hypercube restriction