The paper by J. J. Hopfield explores a model of a large network of "neurons" with graded responses (sigmoid input-output relations) and compares it to the earlier stochastic model based on McCulloch–Pitts neurons. The deterministic system exhibits collective properties that closely match those of the stochastic model, including content-addressable memory (CAM) and other emergent collective behaviors. The presence of these properties in the graded response model supports the idea that such collective properties are relevant in biological systems. The paper demonstrates that the important properties of the original model remain intact when the simplifications of two-state neurons and stochastic algorithms are eliminated. The continuous, deterministic model is shown to have the same flow properties as the stochastic model, with stable states corresponding to each other in a simple manner. The paper also discusses the relationship between the stable states of the two models, showing that for steep response curves, there is a 1:1 correspondence between the memories of the two models. For less steep responses, the continuous-response model can have fewer stable states but still corresponds to specific stable states of the stochastic model. The analysis suggests that real circuits of operational amplifiers, capacitors, and resistors should function as CAMs, reconstructing the stable states designed into the synaptic interconnections. The paper concludes by discussing the inclusion of action potentials in the model and the implications for the behavior of the system.The paper by J. J. Hopfield explores a model of a large network of "neurons" with graded responses (sigmoid input-output relations) and compares it to the earlier stochastic model based on McCulloch–Pitts neurons. The deterministic system exhibits collective properties that closely match those of the stochastic model, including content-addressable memory (CAM) and other emergent collective behaviors. The presence of these properties in the graded response model supports the idea that such collective properties are relevant in biological systems. The paper demonstrates that the important properties of the original model remain intact when the simplifications of two-state neurons and stochastic algorithms are eliminated. The continuous, deterministic model is shown to have the same flow properties as the stochastic model, with stable states corresponding to each other in a simple manner. The paper also discusses the relationship between the stable states of the two models, showing that for steep response curves, there is a 1:1 correspondence between the memories of the two models. For less steep responses, the continuous-response model can have fewer stable states but still corresponds to specific stable states of the stochastic model. The analysis suggests that real circuits of operational amplifiers, capacitors, and resistors should function as CAMs, reconstructing the stable states designed into the synaptic interconnections. The paper concludes by discussing the inclusion of action potentials in the model and the implications for the behavior of the system.