Fig. 2. An example PNN, implemented experimentally using broadband optical SHG.

a, Input data are encoded into the spectrum of a laser pulse (Methods, Supplementary Section 2). To control transformations implemented by the broadband SHG process, a portion of the pulse’s spectrum is used as trainable parameters (orange). The physical computation result is obtained from the spectrum of a blue (about 390 nm) pulse generated within a χ⁽²⁾ medium. b, To construct a deep PNN, the outputs of the SHG transformations are used as inputs to subsequent SHG transformations, with independent trainable parameters. c, d, After training the SHG-PNN (see main text, Fig. 3), it classifies test vowels with 93% accuracy. c, The confusion matrix for the PNN on the test set. d, Representative examples of final-layer output spectra, which show the SHG-PNN’s prediction.