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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.
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.
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.
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.
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.
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.
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.
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.
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.