Do covariates explain why these groups differ? The choice of reference group can reverse conclusions in the Oaxaca-Blinder decomposition

The demand for Explainable AI (XAI) has triggered an explosion of methods, producing a landscape so fragmented that we now rely on surveys of surveys. Yet, fundamental challenges persist: conflicting metrics, failed sanity checks, and unresolved debates over robustness and fairness. The only consensus on how to achieve explainability is a lack of one. This has led many to point to the absence of a ground truth for defining ``the'' correct explanation as the main culprit. This position paper posits that the persistent discord in XAI arises not from an absent ground truth but from a ground truth that exists, albeit as an elusive and challenging target: the causal model that governs the relevant system. By reframing XAI queries about data, models, or decisions as causal inquiries, we prove the necessity and sufficiency of causal models for XAI. We contend that without this causal grounding, XAI remains unmoored. Ultimately, we encourage the community to converge around advanced concept and causal discovery to escape this entrenched uncertainty.

Explainable machine learning (XML) pipelines applied to composite mental health outcomes can produce apparently-robust, cross-population-stable risk hierarchies that are largely artefacts of how the outcome was constructed. We demonstrate this using an ElasticNet pipeline applied to 886 medical students at the University of Lausanne (primary cohort, 2022), validated across 2,580 longitudinal observations at three time points and 701 non-medical students from eight faculties; all three datasets share identical instruments. The pipeline produces a hierarchy in which trait anxiety and health satisfaction dominate wherever the outcome is measured, with Kendall $τ= 1.0$ for the top-two positions across all five evaluation sets and consistent transfer performance ($R^2$: 0.41-0.49). Two residualization experiments, which isolate shared variance between correlated variables via regression, reveal the mechanism: when trait anxiety (STAI-T) is residualized against the co-included depression subscale (CES-D, $r = 0.72$), model $R^2$ drops from 0.41 to 0.16 and STAI-T falls from rank 1 to rank 6; when burnout subscales are residualized against CES-D, $R^2$ collapses to 0.016. Prediction intervals average 35.4 units on a 0-100 scale (2.4 outcome standard deviations), independently ruling out individual-level deployment. The residualization protocol is the paper's transferable contribution: any XAI study combining correlated predictor and outcome constructs should apply this check before interpreting apparent stability as a finding.

Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = Γ . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for the full transformed experiment exactly when the conditional law of the raw observation given treatment, covariates and the quotient has a parameter-free version. Conditional Haar contamination on a compact group yields Blackwell equivalence as a special case; it is not imposed in the main model. We also separate independent site-specific product actions from shared diagonal actions and show why componentwise canonicalization can discard relative cross-site information. Under explicit metric and kernel regularity, an approximate-contamination theorem bounds quotient-law Wasserstein error and the induced perturbation of population maximum mean discrepancy. For finite-support multichannel lattice images, we construct a maximal invariant under integer translations and quarter turns, combine its characteristic Gaussian kernel with a complete paired-swap test, and retain the original simulations and RxRx1 HUVEC study. Under the sharp null, the quotient test rejected in 0.052 of simulation replicates; at unit effect strength its power was 0.992. The primary RxRx1 contrast had an enumerated paired-swap p-value of 0.0078.