<ul><li>The hyperbolic space is capable of embedding trees with arbitrarily small distortion, making it suitable for representing hierarchical datasets.</li><li>However, training hyperbolic learning models can lead to numerical instability and NaN problems due to the exponential growth property of the hyperbolic space.</li><li>A study compares two popular models, the Poincaré ball and the Lorentz model, and finds that the Lorentz model has superior numerical stability and optimization performance.</li><li>Additionally, an Euclidean parametrization of the hyperbolic space is proposed to alleviate numerical limitations, which also improves the performance of hyperbolic SVM.</li></ul>

The Numerical Stability of Hyperbolic Representation Learning

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