Mathematics of neural networks in machine learning: Difference between revisions

Revision as of 09:24, 28 May 2023

Revision as of 10:02, 28 May 2023

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The network corresponds to a function <math>y = f_N(w, x)</math> which, given a weight <math>w</math>, maps an input <math>x</math> to an output <math>y</math>.

In [[supervised learning]], a sequence of ''[[Training set|training examples]]'' <math>(x_1,y_1), \dots, (x_p, y_p)</math> produces a sequence of weights <math>w_0, w_1, \dots, w_p</math> starting from some initial weight <math>w_0</math>, usually chosen at random.

These weights are computed in turn: first compute <math>w_i</math> using only <math>(x_i, y_i, w_{i-1})</math> for <math>i = 1, \dots, p</math>. The output of the algorithm is then <math>w_p</math>, giving a new function <math>x \mapsto f_N(w_p, x)</math>. The computation is the same in each step, hence only the case <math>i = 1</math> is described.