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Matrice dei pesi
The weight matrix is the table of numbers a neural network layer uses to transform an input vector into an output vector through matrix multiplication. It is the mathematical object where the "knowledge" learned by the model during training is actually stored: every number in the matrix is a parameter that gets adjusted step by step.
Multiplying an input vector by a weight matrix produces a new vector whose components are weighted linear combinations of the original components. By stacking multiple layers, each with its own weight matrix and an intermediate non-linear activation function, the network can learn increasingly complex transformations. The size of a weight matrix determines how many parameters that layer contributes to the model's total.
It is the element that makes a trained model different from a randomly initialized one: before training the matrices contain random values, after training they contain the values that minimize error on the observed data. Techniques such as quantization reduce the numerical precision with which these values are stored to save memory, while efficient adaptation techniques modify only small portions of some matrices instead of retraining them entirely.
The term derives from linear algebra, where a matrix is a rectangular table of numbers used to represent linear transformations between vector spaces; the use of the term "weights" for learned parameters reflects the idea that each number weighs, that is, modulates, the influence of an input on the final result.
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