Relative value of learned vs. random quaternion rotations in IsoQuant

Determine the relative performance of learned normalized unit-quaternion parameters versus random fixed unit-quaternion parameters for the blockwise SO(4) rotations used by IsoQuant in stage-1 online vector quantization for KV-cache compression.

Background

IsoQuant implements blockwise SO(4) rotations via pairs of unit quaternions to decorrelate features prior to scalar quantization. The paper describes both learned quaternion parameters and random fixed quaternion parameters sampled from appropriate distributions as practical options for the transform.

Although the paper validates stage-1 reconstruction error and kernel latency, it does not establish whether learning the quaternion parameters yields consistently better performance than using random rotations, leaving the comparative benefit of learning versus randomization unresolved.