When Standard MI Tools Break: Chain Property Failures and Probe-Delta Dissociation in Hybrid Physics-ML Architectures

We document two failure modes of standard mechanistic interpretability tools in hybrid physics-ML architectures, using a gravitational lens classifier as a controlled testbed. (1) Chain property: interchange interventions yield structurally identical logit deltas at every classification head hook in all three models tested, making head-level routing/collapse verdicts structurally uninformative. The triggering condition—deterministic eval-mode sequential subgraphs—is identified precisely, instantiating Mueller et al. (2024)'s theoretical non-transitivity result. (2) Probe-delta dissociation: at the Poisson layer, D4LensPINN and a non-equivariant control show 3.6× different causal sensitivity (bootstrap 95% CIs non-overlapping: 0.402 vs. 1.429), yet near-identical group-element probe accuracy (0.485 vs. 0.479). Equivariance reshapes causal sensitivity without reshaping representational content. Spectral analysis identifies the mechanism: the Poisson 1/k² operator empirically collapses 59.5% mid-frequency orbit variance at D4's κ̂ to near-zero (VanillaLensPINN: identical operator, δH09=1.43). These findings apply to any architecture with deterministic physics operators or eval-mode fixed normalizations.