When Representation Effects Depend on the Measurement Condition

Representation analysis frequently treats an observed quantity as an intrinsic property of the representation being analyzed, despite the fact that it is generated by a particular measurement procedure. We make this dependency explicit by writing $R=\mathcal{M}(F;C)$, where $F$ denotes the representation being measured and $C$ denotes the measurement condition. This leads to a concrete invariance question: with $F$ held constant, does the measured size of a representational contrast stay the same as $C$ varies? To examine this empirically, we design a controlled protocol that keeps the representation fed into the measurement instrument bitwise identical while changing only the measurement condition. For vision representations, we find that two trained conditions yield very similar pairwise structure, yet they can assign markedly different magnitudes to identical representational contrasts. Therefore, matching relational structure does not guarantee that magnitudes transfer across conditions. Operating-point normalization accounts for a substantial portion of the observed scale gap, but does not eliminate it, and simpler probe families show the same qualitative behavior. Relative ordering and spatial concordance are far more stable than absolute magnitude, although they are not strictly invariant and may become effectively unmeasurable under a degenerate measurement condition. These findings support a measurement-conditioned view of representation analysis: a measured representational quantity should be attributed to $F$ alone only when invariance across the relevant measurement conditions is demonstrated; otherwise, the condition should remain part of the claim's scope, $X(F;C)$.