Unit Sphere
The most commonly used constraint surface in embedding learning, on which all vectors have unit norm, cosine similarity is defined, and which exhibits a high degree of symmetry.
Timeline (last 90 days)
The paper proposes changing the embedding domain from the unit sphere to the probability simplex, forcing the two modalities to calibrate to the same coordinate system through non-negativity and unit-mass constraints.
When d=0 the two spheres coincide completely and the intersection volume is 4π/3; when d=2 the two spheres are tangent at only one point and the volume is 0.
All Facts (2)
The paper proposes changing the embedding domain from the unit sphere to the probability simplex, forcing the two modalities to calibrate to the same coordinate system through non-negativity and unit-mass constraints.
50%UnverifiedWhen d=0 the two spheres coincide completely and the intersection volume is 4π/3; when d=2 the two spheres are tangent at only one point and the volume is 0.
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