Unlike for DNA and RNA, accurate and high-throughput sequencing methods for proteins are lacking, hindering the utility of proteomics in applications where the sequences are unknown including variant calling, neoepitope identification, and metaproteomics. We introduce Spectralis, a de novo peptide sequencing method for tandem mass spectrometry. Spectralis leverages several innovations including a convolutional neural network layer connecting peaks in spectra spaced by amino acid masses, proposing fragment ion series classification as a pivotal task for de novo peptide sequencing, and a peptide-spectrum confidence score. On spectra for which database search provided a ground truth, Spectralis surpassed 40% sensitivity at 90% precision, nearly doubling state-of-the-art sensitivity. Application to unidentified spectra confirmed its superiority and showcased its applicability to variant calling. Altogether, these algorithmic innovations and the substantial sensitivity increase in the high-precision range constitute an important step toward broadly applicable peptide sequencing.