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Determining the repertoire of a microbe's molecular functions is a central question in microbial biology. Modern techniques achieve this goal by comparing microbial genetic material against reference databases of functionally annotated genes/proteins or known taxonomic markers such as 16S rRNA. Here, we describe a novel approach to exploring bacterial functional repertoires without reference databases. Our Fusion scheme establishes functional relationships between bacteria and assigns organisms to Fusion-taxa that differ from otherwise defined taxonomic clades. Three key findings of our work stand out. First, bacterial functional comparisons outperform marker genes in assigning taxonomic clades. Fusion profiles are also better for this task than other functional annotation schemes. Second, Fusion-taxa are robust to addition of novel organisms and are, arguably, able to capture the environment-driven bacterial diversity. Finally, our alignment-free nucleic acid-based Siamese Neural Network model, created using Fusion functions, enables finding shared functionality of very distant, possibly structurally different, microbial homologs. Our work can thus help annotate functional repertoires of bacterial organisms and further guide our understanding of microbial communities.