Current approaches to genomic sequence modeling often struggle to align the inductive biases of machine learning models with the evolutionarily-informed structure of biological systems. To this end, we formulate a novel application of hyperbolic CNNs that exploits this structure, enabling more expressive DNA sequence representations. Our strategy circumvents the need for explicit phylogenetic mapping while discerning key properties of sequences pertaining to core functional and regulatory behavior. Across 37 out of 42 genome interpretation benchmark datasets, our hyperbolic models outperform their Euclidean equivalents. Notably, our approach even surpasses state-of-the-art performance on seven GUE benchmark datasets, consistently outperforming many DNA language models while using orders of magnitude fewer parameters and avoiding pretraining. Our results include a novel set of benchmark datasets---the Transposable Elements Benchmark---which explores a major but understudied component of the genome with deep evolutionary significance. We further motivate our work by exploring how our hyperbolic models recognize genomic signal under various data-generating conditions and by constructing an empirical method for interpreting the hyperbolicity of dataset embeddings. Throughout these assessments, we find persistent evidence highlighting the potential of our hyperbolic framework as a robust paradigm for genome representation learning. Our code and benchmark datasets are available at https://github.com/rrkhan/HGE.

Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation respects manifold geometry while preserving the algorithmic properties that make decision trees effective. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. In benchmarks on a diverse suite of 57 classification, regression, and link prediction tasks, our product RFs ranked first on 29 tasks and came in the top 2 for 41. This highlights the value of product RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our method is available at https://github.com/pchlenski/manify.