Beyond traditional emission-line diagnostics: using autoencoders to uncover active galactic nuclei in DESI spectra

The growing volume of spectroscopic data in modern surveys motivates data-driven approaches that complement traditional emission-line diagnostics for active galactic nuclei (AGN) identification. We present a machine learning framework that exploits the full optical spectrum using unsupervised representation learning within a semi-supervised classification scheme. We use the SPENDER autoencoder to compress DESI galaxy spectra into a low-dimensional latent space and classify sources through a k-d tree nearest-neighbor search. The model is trained on 50,222 DESI Main Survey spectra from the Guadalupe dataset and released as part of Data Release 1 (DR1), restricted to z <= 0.5. We validate the performance using labels derived from FastSpecFit's emission line measurements defining seven galaxy classes: AGN, broad-line (BL), composite, star-forming, passive, retired, and Other. The method achieves high accuracies for AGN (0.952) and broad-line AGN (0.965), reliably identifying these sources even in low signal-to-noise spectra and recovering AGN missed by standard single-diagnostic methods. Our classification metrics are benchmarked against traditional diagnostics, and we show they represent lower limits of the model's true performance. We also find that the learned latent space correlates with key galaxy properties such as stellar mass and star-formation rate, demonstrating that it captures physically meaningful information. These results show that unsupervised spectral representation learning, implemented within a semi-supervised classification framework, provides a scalable and effective approach for constructing more complete AGN catalogues for current and future spectroscopic surveys.