Cosine Similarity Is Not Evidence: Measuring the Noise Floor of Interpretability Transfer Under Quantization

The paper argues that reporting scale‑invariant statistics such as cosine similarity without their noise floor is misleading when evaluating interpretability transfer from full‑precision to quantized neural networks. It derives a closed‑form expression for the expected cosine similarity based on a dimensionless parameter κ = n ho^2/d, measures the class separation ρ on real activations, and shows that a reported cosine of 0.996 between full‑precision and INT4 models cannot be interpreted as preservation without knowing the sample size n. The authors demonstrate that at INT4 the direction of the interpretability artifact rotates beyond the estimator’s own noise, while at INT8 no significant movement is detected, and they highlight that scale‑invariant metrics cannot distinguish between translation and attenuation of a transferred decision variable.