Predicting whether a protein sequence possesses a biochemical property of interest is important for understanding and designing protein functionality. Modern protein sequence databases provide valuable training data for functional prediction, but they exhibit survivorship bias: natural selection favors variants that support organismal survival while eliminating many others before they can be observed, complicating classifier training. This setting motivates positive-unlabeled (PU) learning, which treats observed functional sequences as positive and unobserved sequences as unlabeled rather than nonfunctional. However, existing protein PU methods do not account for cross-sequence heterogeneity in evolutionary accessibility: sequences one nucleotide mutation away from a common variant arise far more readily than distant ones. We introduce PULSE: PU Learning with Surveillance and Evolution, a framework that trains a probabilistic classifier for a target protein function using an evolution-aware observation likelihood. When considering functionality of proteins with high genomic sequence coverage, PULSE combines a probabilistic classifier that estimates whether an amino acid sequence performs the target function with an evolutionary model that estimates the likelihood that its encoding nucleotide sequences emerge and are detected based on mutational accessibility, parental prevalence, and surveillance e!ciency. By coupling these two components, PULSE treats the absence of an evolutionarily accessible sequence as stronger evidence of non-functionality than the absence of one unlikely to arise. Tested on eleven tasks focusing on multiple Spike protein properties spanning five SARS-CoV-2 variants, PULSE ranks first or second on all of them, and achieves the best overall performance among all methods, including standard PU learning, one-class classification methods, and protein language models.

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