κ-stereographic model
A mathematical model that describes constant-curvature spaces with a single curvature parameter κ: κ>0 for spherical, κ=0 for Euclidean, and κ<0 for hyperbolic. It allows the type of geometric space to be adjusted continuously during training.
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The Event2Vec library provides several non-commutative or geometrized alternative spaces: hyperbolic space (Möbius addition), the κ-stereographic model, spherical space (SO(n) rotations), and the Heisenberg group.
The κ-stereographic model (Bachmann et al., 2020) uses a single curvature parameter κ to uniformly describe constant-curvature spaces: κ > 0 is spherical, κ = 0 is Euclidean, and κ < 0 is hyperbolic, and it can be continuously adjusted during training.
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The Event2Vec library provides several non-commutative or geometrized alternative spaces: hyperbolic space (Möbius addition), the κ-stereographic model, spherical space (SO(n) rotations), and the Heisenberg group.
50%UnverifiedThe κ-stereographic model (Bachmann et al., 2020) uses a single curvature parameter κ to uniformly describe constant-curvature spaces: κ > 0 is spherical, κ = 0 is Euclidean, and κ < 0 is hyperbolic, and it can be continuously adjusted during training.
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