“Neural” computation of decisions in optimization problems

By John J. Hopfield, David W. Tank. 1985

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Citations in the corpus

Neural Combinatorial Optimization with Reinforcement Learning (2016, background): “One of the earliest proposals is the use of Hopfield networks (Hopfield & Tank, 1985) for the TSP.”
Up or Down? Adaptive Rounding for Post-Training Quantization (2020, methodology): “These methods optimize h ( V i,j ) = σ V i,j T with a version of gradient descent with respect to V i,j , and annealing the temperature T (Hopﬁeld & Tank, 1985; Smith et al.).”
A projection neural network and its application to constrained optimization problems (2002, background): “One promising approach to handle these optimization problems with high dimensions and dense structure is to employ artificial neural networks based on circuit implementation [11].”
From the neuron doctrine to neural networks (2015, background): “Attractors are another example of the emergent states of the activity of the network and could serve to implement associative memories, decision-making, or — more generally — solutions to optimization or other computational problems 99,100 .”
Attention, Learn to Solve Routing Problems! (2018, unknown): “The application of Neural Networks (NNs) for optimizing decisions in combinatorial optimization problems dates back to Hopﬁeld & Tank (1985), who applied a Hopﬁeld-network for solving small TSP instances.”
Computer-aided process planning – A critical review of recent developments and future trends (2011, methodology): “They combined a Hopﬁeld neural network (Hopﬁeld and Tank 1985) and GAs to solve the above problem.”
Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons (2011, background): “, [54] for the case of constraint satisfaction problems).”
Ising machines as hardware solvers of combinatorial optimization problems (2022, background): “The particular optimization problem they designed their system for was k -SAT, which is—like the Ising problem—an NP-complete decision problem with an NP-hard optimization version.”
Information Theory, Inference, and Learning Algorithms (2004, background): “Hopfield and Tank (1985) suggested that one might take an interesting constraint satisfaction problem and design the weights of a binary or continuous Hopfield network such that the settling process of the network would minimize the objective function of the problem.”