Complex organic molecules (COMs) are found to be abundant in various astrophysical environments, particularly toward star-forming regions, where they are observed both toward protostellar envelopes as well as shocked regions. The emission spectrum, especially that of heavier COMs, might consist of up to hundreds of lines, where line blending hinders the analysis. However, identifying the molecular composition of the gas that leads to the observed millimeter spectra is the first step toward a quantitative analysis. We have developed a new method based on supervised machine learning to recognize spectroscopic features of the rotational spectrum of molecules in the 3 mm atmospheric transmission band for a list of species including COMs, with the aim of obtaining a detection probability. We used local thermodynamic equilibrium (LTE) modeling to build a large set of synthetic spectra of 20 molecular species, including COMs with a range of physical conditions typical for star-forming regions. We successfully designed and trained a convolutional neural network (CNN) that provides detection probabilities of individual species in the spectra. We demonstrate that the CNN model we developed has a robust performance to detect spectroscopic signatures from these species in synthetic spectra. We evaluated its ability to detect molecules according to the noise level, frequency coverage, and line-richness, as well as to test its performance for an incomplete frequency coverage with high detection probabilities for the tested parameter space, with no false predictions. Finally, we applied the CNN model to obtain predictions on observational data from the literature toward line-rich hot core-like sources, where the detection probabilities remain reasonable, with no false detections. We demonstrate the use of CNNs in facilitating the analysis of complex millimeter spectra both on synthetic spectra, along with the first tests performed on observational data. Further analyses on its explainability, as well as calibration using a larger observational dataset, will help improve the performance of our method for future applications.