In-domain reconstruction and cycle reconstruction. This figure shows the residuals between the 5000 synthetic spectra in the test set and themselves after in-domain reconstruction and cycle reconstruction. These spectra cover most of the stellar parameter range. The blue part indicates the residuals after reconstruction of each spectrum in the wavelength range 4000–5500 Å. The colour depth is positively correlated with the number of spectra in this error. The red line in the figure indicates the average residuals, and the orange line indicates the average absolute residuals. The upper panel shows the in-domain reconstruction residuals as the relative residuals between 𝒳_{synth→synth} and the original spectra 𝒳_synth, and the lower panel shows the cycle reconstruction residuals as the relative residuals between the spectra 𝒳_{synth→obs→synth} and the original spectra 𝒳_synth. The residuals for both the in-domain and cycle reconstructions are very small and can be neglected, as can be seen in the figure.