The paper by J. J. Hopfield and D. W. Tank explores the computational capabilities of highly interconnected networks of nonlinear analog neurons in solving optimization problems. These networks can rapidly compute a collective solution to problems based on analog input information, often subject to constraints. The authors discuss the general principles of constructing such networks to solve specific problems and present computer simulations of a network designed to solve the Traveling-Salesman Problem (TSP). The network's effectiveness is demonstrated by computing good solutions within a few neural time constants, highlighting the importance of both the nonlinear analog response of neurons and their large connectivity. The paper suggests that dedicated networks of biological or microelectronic neurons could provide computational capabilities for a wide class of combinatorial problems, contributing to the efficiency of biological information processing. The authors also emphasize the parallel processing and collective analog mode of biological systems, which enhance computational power and speed, making them suitable for real-time sensory information processing.The paper by J. J. Hopfield and D. W. Tank explores the computational capabilities of highly interconnected networks of nonlinear analog neurons in solving optimization problems. These networks can rapidly compute a collective solution to problems based on analog input information, often subject to constraints. The authors discuss the general principles of constructing such networks to solve specific problems and present computer simulations of a network designed to solve the Traveling-Salesman Problem (TSP). The network's effectiveness is demonstrated by computing good solutions within a few neural time constants, highlighting the importance of both the nonlinear analog response of neurons and their large connectivity. The paper suggests that dedicated networks of biological or microelectronic neurons could provide computational capabilities for a wide class of combinatorial problems, contributing to the efficiency of biological information processing. The authors also emphasize the parallel processing and collective analog mode of biological systems, which enhance computational power and speed, making them suitable for real-time sensory information processing.