Probability Simplex
The geometric representation of probability distributions, defined as the set of vectors that are non-negative and whose components sum to one. Its non-negativity constraint and unit-mass constraint provide a structural prior when used in embedding learning.
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.
The contribution of this paper is to point out that the modality gap is essentially the result of a geometric choice: the sphere allows modalities to separate without penalty, while the non-negativity constraint of the simplex rules out this degenerate solution.
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%UnverifiedThe contribution of this paper is to point out that the modality gap is essentially the result of a geometric choice: the sphere allows modalities to separate without penalty, while the non-negativity constraint of the simplex rules out this degenerate solution.
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