Determine the functional form of interpolation responses

Determine whether the behavioral response to source-target K/V interpolation at layers 9--20 is linear, thresholded, or otherwise nonlinear beyond the two tested interpolation strengths.

Background

The interpolation experiment blends source and target K/V representations in layers 9--20 at only two strengths, alpha equal to 0.25 and 0.50. Both the V-space gap and target-marker density increase monotonically across these tested values.

The observed two-point trend establishes graded behavior over the tested range but is insufficient to identify the underlying response function or distinguish linear from thresholded or other nonlinear behavior.

References

The response is monotonic over the two tested strengths; whether it is linear, thresholded, or otherwise nonlinear is unresolved.

— K/V-Cache Interventions Dissociate Representation Alignment from Persona Expression in Decoder-Only Language Models  (2609.11020 - Sun et al., 10 Sep 2026) in Section 5.5, K/V cosine analysis