Most microbes have the capacity to acquire genetic material from their environment. Recombination of foreign DNA yields genomes that are, at least in part, incongruent with the vertical history of their species. Dominant approaches for detecting these transfers are phylogenetic, requiring a painstaking series of analyses including alignment and tree reconstruction. But these methods do not scale. Here, we propose an unsupervised, alignment-free, and tree-free technique based on the sequential information bottleneck, an optimization procedure designed to extract some portion of relevant information from 1 random variable conditioned on another. In our case, this joint probability distribution tabulates occurrence counts of k-mers against their genomes of origin with the expectation that recombination will create a strong signal that unifies certain sets of co-occurring k-mers. We conceptualize the technique as a rate-distortion problem, measuring distortion in the relevance information as k-mers are compressed into clusters based on their co-occurrence in the source genomes. The result is fast, model-free, lossy compression of k-mers into learned groups of shared genome sequence, differentiating recombined elements from the vertically inherited core. We show that the technique yields a new recombination measure based purely on information, divorced from any biases and limitations inherent to alignment and phylogeny.