  Hyperbolic geometry is gaining traction in machine learning for its
effectiveness at capturing hierarchical structures in real-world data.
Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial
advantages and consistently deliver state-of-the-art results across diverse
applications. However, hyperbolic classifiers often grapple with computational
challenges. Methods reliant on Riemannian optimization frequently exhibit
sluggishness, stemming from the increased computational demands of operations
on Riemannian manifolds. In response to these challenges, we present hyperDT, a
novel extension of decision tree algorithms into hyperbolic space. Crucially,
hyperDT eliminates the need for computationally intensive Riemannian
optimization, numerically unstable exponential and logarithmic maps, or
pairwise comparisons between points by leveraging inner products to adapt
Euclidean decision tree algorithms to hyperbolic space. Our approach is
conceptually straightforward and maintains constant-time decision complexity
while mitigating the scalability issues inherent in high-dimensional Euclidean
spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest
model. Extensive benchmarking across diverse datasets underscores the superior
performance of these models, providing a swift, precise, accurate, and
user-friendly toolkit for hyperbolic data analysis.
