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Energy of a neural network

Scalar function measuring the quality of a network configuration, whose minimization corresponds to solving the optimization problem. It combines synaptic weights and neuron states to guide convergence.

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Traveling salesman problem

Classic combinatorial optimization problem consisting of finding the shortest path visiting each city exactly once. Hopfield networks can encode this problem in their energy structure.

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Stable state

Configuration of the neural network where no further update is possible and energy is locally minimized. These states correspond to admissible solutions of the optimization problem being addressed.

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Cost function

Mathematical expression quantifying the quality of a potential solution to an optimization problem. In neural networks, it is directly linked to the system's energy function.

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Binary units

Neurons taking only values 0 or 1 (or -1/+1) in optimization networks. Their discrete state allows modeling combinatorial problems with binary decision variables.

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Weight matrix

Square structure containing connection strengths between all pairs of neurons in the network. It encodes the constraints and objectives of the optimization problem in the network topology.

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Network convergence

Process by which a neural network dynamically evolves toward a stable state minimizing its energy. The speed and guarantee of convergence depend on the network architecture and parameters.

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Neuronal bias

Constant term added to the weighted input of a neuron to adjust its activation threshold. In optimization networks, it represents individual constraints or decision preferences.

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State vector

Vector representation of the complete configuration of neural activations at a given instant. Each component corresponds to the binary state of a neuron in the network.

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