AI Explanations Collapse When Supply Networks Fracture, Spectral Study Warns

When South Africa’s chronic medicines distribution programme issued internally contradictory AI explanations during the COVID-19 lockdown of March to June 2020, procurement officers could not justify the system’s recommendations to regulators under Good Distribution Practice audit requirements, even though every standard performance metric looked normal. A new theoretical and computational study argues that the failure was not algorithmic but geometric: the supply network had lost a structural property that determines whether any permutation-based explainability method, including SHAP and LIME, can produce valid attributions at all. The paper, published in Frontiers in Artificial Intelligence by Ntebogang Dinah Moroke and Mapula Merriam Lebele of North-West University, introduces SpectralGuard, a framework designed to certify when AI explanations are theoretically valid before they are acted upon.

The mathematical heart of the framework is the Fiedler eigenvalue, denoted lambda-2, the second-smallest eigenvalue of the normalized hypergraph Laplacian. In spectral graph theory, this quantity measures a network’s algebraic connectivity: how readily information, or in this case procurement transactions and feature samples, can mix across the whole structure. The authors prove a theorem establishing that as lambda-2 approaches zero, the relaxation time of a random walk on the network, given by two divided by lambda-2, diverges. Because SHAP-style estimators draw background samples from the empirical distribution of supply-network transactions, a collapsing network traps those samples in isolated connected components. The result is a proof that lambda-2 tending to zero is a sufficient condition for permutation-based XAI failure: once connectivity collapses, no increase in sampling effort can recover valid attributions, because the estimator becomes inconsistent, with an irreducible error floor.

Crucially, the theorem is a sufficient condition, not a necessary one. Attribution methods can fail for other reasons, such as distribution shift or model misspecification, even when connectivity remains high. Conversely, certifying that lambda-2 exceeds a calibrated threshold only rules out connectivity-induced failure. The authors are explicit that their validity certificate therefore aggregates four spectral governance metrics rather than relying on the eigenvalue alone: a spectral gap metric, an explanation drift index, a topological stability index computed through persistent homology, and the fraction of hyperedges with negative Ollivier-Ricci curvature, a discrete geometric measure of local connectivity.

The choice of a hypergraph rather than a pairwise graph reflects the structure of pharmaceutical regulation. A supply contract in the South African chronic medicines programme binds at minimum a manufacturer, a cold-chain logistics operator and a dispensing cluster under a single regulatory obligation, forming a hyperedge of three or more parties. Projecting such contracts onto pairwise edges destroys the joint accountability structure and creates spurious independence assumptions, which the authors argue degrades both connectivity estimates and attribution quality. The framework is deliberately interdisciplinary, drawing on spectral hypergraph theory, the axiomatic foundations of additive attribution methods, and information processing theory, which predicts that explanations become unreliable when the network’s information propagation capacity falls below the demands of global feature attribution.

Empirically, the study is a calibrated simulation, and the authors are unusually emphatic about this limitation. The supply hypergraph itself is entirely synthetic, generated with parameters calibrated to the Central Chronic Medicines Dispensing and Distribution programme. What is real are the shock inputs: a cleaned panel of 3,227 business days spanning 2014 to 2026, combining Eskom daily load-shedding stage records and South African Reserve Bank ZAR/USD exchange rates. The composite shock index built from these two series correlates with the synthetic spectral gap at r = 0.975, but the authors caution that this near-unity correlation is a calibration consistency check, not an independent empirical discovery, since the shock index directly drives the simulated weight reductions. The substantive contribution at this level is that documented South African shock magnitudes are large enough to push the synthetic network into degraded governance regimes.

The framework’s constructive component is lambda-SHAP, a spectral shrinkage estimator that blends current SHAP attributions toward a validated fluid-regime prior, using the time-varying Fiedler eigenvalue as the shrinkage weight. Under normal connectivity the estimator reduces to standard SHAP; as lambda-2 falls, weight shifts toward historically validated attributions. This trades variance for a controlled, documented bias, and the authors flag the directional risk openly: in a genuine structural break where current feature importances differ qualitatively from the past, the estimator may suppress exactly the signals that matter, a false-safety risk mitigated by mandatory human review in the red regime and a prior recalibration protocol.

In an oracle experiment using a linear model with analytically known true Shapley values, lambda-SHAP reduced attribution mean squared error by 70.4 percent in the green regime to 89.2 percent in the red regime, with the advantage growing monotonically as connectivity declined. An ablation study identified the spectral gate as the decisive component: removing it collapsed performance to standard SHAP levels, while the probabilistic certificate layer contributed governance features rather than error reduction. On the real proxy panel, using exchange-rate volatility as an attribution surrogate, lambda-SHAP cut explanation drift index exceedances of the 0.30 regulatory threshold from 9.2 percent to 4.6 percent of red-regime days, and produced zero threshold exceedances during the COVID-19 episode compared with twelve for standard SHAP.

Detection performance also favoured the spectral approach. In Monte Carlo experiments with 500 replications, the topological stability index detected disruptions in a mean of 6.3 business days, versus 28.3 days for GNNExplainer and 38.4 days for a CUSUM change-point detector, with all comparisons statistically significant. The authors attribute part of this advantage to persistent homology detecting path loss before full connectivity loss registers in the spectral gap. An early-warning analysis of the synthetic series found the calibrated amber threshold alert preceded the red-threshold crossing by 19 business days, lead time the authors argue could allow patient re-routing before supply exhaustion, though they stress that quantifying the operational impact requires field data. Extreme value analysis added a further warning: once the network enters the arrested state, the tail of the spectral risk index follows a Generalized Pareto distribution with positive shape parameter, meaning disruption severity becomes structurally unbounded precisely when conventional bounded-tail risk models assume the opposite.

The governance output is a probabilistic validity certificate: a continuous score between zero and one, produced by ridge-regularized logistic regression over the four spectral metrics, with 95 percent bootstrap confidence intervals and SHA-256 tamper-evidence, readable by a procurement officer as a confidence percentage alongside a regime flag and a prescribed action. Within the synthetic setting the certificate was well calibrated, with a cross-validated log-loss of 0.0076, though the authors note that a near-perfect AUC of 1.0 reflects the deterministic coupling built into the simulation and will not transfer to noisy real data. A nine-step, costed deployment pathway, totalling R915,000, describes integration with the existing DHIS2 national health information infrastructure across South Africa’s nine provinces, with optional blockchain anchoring of certificate hashes on a permissioned ledger proposed for later phases.

The limitations are structural and clearly stated. No real pharmaceutical hypergraph was analysed, no field deployment has occurred, and disruptions were injected as parametric weight reductions that may not capture the correlated, non-monotone character of real crises. Field validation on actual procurement transaction data from the chronic medicines programme is planned for 2027 under the PLMIF-2 study, which will test whether the predicted regime-dependent attribution instability appears in a deployed model and whether the proxy-panel reduction estimates hold on real data. If it does, the authors argue the implication extends well beyond medicines: any AI-governed networked system with multi-party, hypergraph-like contracts, from energy dispatch to emergency logistics, faces the same geometric vulnerability, and the reliability of its explanations is bounded above by the algebraic connectivity of the network on which it operates.

Subject of Research: Spectral XAI validity certification for AI-governed pharmaceutical supply chains using the Fiedler eigenvalue

Article Title: SpectralGuard: a Spectrally grounded λ-SHAP framework for XAI validity certification in pharmaceutical supply chain networks

Article References: Moroke, N. D., & Lebele, M. M. (2026). SpectralGuard: a Spectrally grounded λ-SHAP framework for XAI validity certification in pharmaceutical supply chain networks. Frontiers in Artificial Intelligence, 9, Article 1884880. https://doi.org/10.3389/frai.2026.1884880

Image Credits: AI Generated

DOI: 10.3389/frai.2026.1884880

Keywords: explainable AI, SHAP, Fiedler eigenvalue, hypergraph Laplacian, pharmaceutical supply chain, spectral governance, South Africa, load-shedding, lambda-SHAP, validity certificate, AI regulation, network connectivity