Determine the optimal SLERP interpolation weight

Determine the optimal interpolation weight along the spherical geodesic between the old-model query embedding and the SVD-aligned new-model query embedding for a given deployment distribution, so that the interpolation weight can be selected without relying on support-set or target-distribution estimation.

Background

The proposed backward-compatible retrieval method interpolates between an old-model query embedding and an SVD-aligned new-model query embedding using SLERP. Its performance depends on selecting an interpolation weight along the geodesic arc. In the experiments, the weight is either selected on the CC3M alignment support set or estimated using a labeled subset of the deployment distribution.

The paper explicitly states that the optimal value is not known in advance. Consequently, determining how to identify the optimal interpolation weight—particularly when no representative target-distribution data or labels are available—remains unresolved within the described method.

References

The optimal value is not known a priori and must be estimated from data, either from the deployment distribution or from a separate support set.

— Spherical Interpolation for Backward-Compatible Multimodal Representations  (2609.39836 - Ricci et al., 30 Sep 2026) in Appendix, Section “Limitations,” paragraph “Selection of the interpolation weight”