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Hyperbolic networks have shown prominent improvements over their Euclideancounterparts in several areas involving hierarchical datasets in variousdomains such as computer vision, graph analysis, and natural languageprocessing. However, their adoption in practice remains restricted due to (i)non-scalability on accelerated deep learning hardware, (ii) vanishing gradientsdue to the closure of hyperbolic space, and (iii) information loss due tofrequent mapping between local tangent space and fully hyperbolic space. Totackle these issues, we propose the approximation of hyperbolic operators usingTaylor series expansions, which allows us to reformulate the computationallyexpensive tangent and cosine hyperbolic functions into their polynomialequivariants which are more efficient. This allows us to retain the benefits ofpreserving the hierarchical anatomy of the hyperbolic space, while maintainingthe scalability over current accelerated deep learning infrastructure. Thepolynomial formulation also enables us to utilize the advancements in Euclideannetworks such as gradient clipping and ReLU activation to avoid vanishinggradients and remove errors due to frequent switching between tangent space andhyperbolic space. Our empirical evaluation on standard benchmarks in the domainof graph analysis and computer vision shows that our polynomial formulation isas scalable as Euclidean architectures, both in terms of memory and timecomplexity, while providing results as effective as hyperbolic models.Moreover, our formulation also shows a considerable improvement over itsbaselines due to our solution to vanishing gradients and information loss.

Towards Scalable Hyperbolic Neural Networks using Taylor Series Approximations