Spherical Noising
A variant of the diffusion process defined on the unit sphere that performs noising by interpolating toward a mask-biased endpoint along spherical geodesics, keeping the vector norm fixed at 1. This eliminates norm decay and reduces token comparison to purely directional angular comparison.
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LLaCO adopts a spherical noising process, formalized as geodesic interpolation toward a mask-biased endpoint, thereby eliminating norm decay and preserving accurate token competition.
In the spherical noising process, all intermediate states remain on the unit sphere and the vector norm is always 1, thereby bypassing the spurious transcendence problem of Euclidean distance.
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LLaCO adopts a spherical noising process, formalized as geodesic interpolation toward a mask-biased endpoint, thereby eliminating norm decay and preserving accurate token competition.
50%UnverifiedIn the spherical noising process, all intermediate states remain on the unit sphere and the vector norm is always 1, thereby bypassing the spurious transcendence problem of Euclidean distance.
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