Abstract.A key challenge to transferring knowledge between species is that different species have fundamentally different genetic architectures. Initial computational approaches to transfer knowledge across species have relied on measures of heredity such as genetic homology, but these approaches suffer from limitations. First, only a small subset of genes have homologs, limiting the amount of knowledge that can be transferred, and second, genes change or repurpose functions, complicating the transfer of knowledge. Many approaches address this problem by expanding the notion of homology by leveraging high-throughput genomic and proteomic measurements, such as through network alignment.In this work, we take a new approach to transferring knowledge across species by expanding the notion of homology through explicit measures of functional similarity between proteins in different species. Specifically, our kernel-based method, Handl (Homology Assessment across Networks using Diffusion and Landmarks), integrates sequence and network structure to create a functional embedding in which proteins from different species are embedded in the same vector space. We show that inner products in this space and the vectors themselves capture functional similarity across species, and are useful for a variety of functional tasks. We perform the first whole-genome method for predicting phenologs, generating many that were previously identified, but also predicting new phenologs supported from the biological literature. We also demonstrate the Handl embedding captures pairwise gene function, in that gene pairs with synthetic lethal interactions are significantly separated in Handl space, and the direction of separation is conserved across species. Software for the Handl algorithm is available at http://bit.ly/lrgr-handl.