In our case, we have only one object class ("insect") so the

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These components enhance the model's ability to extract

Decision trees have gained popularity as interpretable surrogate models for learning-based control policies.

In recent years, explaining decisions made by complex machine learning models has become essential in high-stakes domains such as energy systems, healthcare, finance, and autonomous systems. However, the reliability of these explanations, namely, whether they remain stable and consistent under realistic, non-adversarial changes, remains largely unmeasured. Widely used methods such as SHAP and Integrated Gradients (IG) are well-motivated by axiomatic notions of attribution, yet their explanations can vary substantially even under system-level conditions, including small input perturbations, correlated representations, and minor model updates. Such variability undermines explanation reliability, as reliable explanations should remain consistent across equivalent input representations and small, performance-preserving model changes. We introduce the Explanation Reliability Index (ERI), a family of metrics that quantifies explanation stability under four reliability axioms: robustness to small input perturbations, consistency under feature redundancy, smoothness across model evolution, and resilience to mild distributional shifts. For each axiom, we derive formal guarantees, including Lipschitz-type bounds and temporal stability results. We further propose ERI-T, a dedicated measure of temporal reliability for sequential models, and introduce ERI-Bench, a benchmark designed to systematically stress-test explanation reliability across synthetic and real-world datasets. Experimental results reveal widespread reliability failures in popular explanation methods, showing that explanations can be unstable under realistic deployment conditions. By exposing and quantifying these instabilities, ERI enables principled assessment of explanation reliability and supports more trustworthy explainable AI (XAI) systems.

Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by lin-earizing the DNN and applying Laplace inference to the resulting model. Importantly, the linear model is also used for prediction. We argue this linearization in the posterior may degrade fidelity to the true Laplace approximation. To alleviate this problem, without increasing significantly the computational cost, we propose the Quadratic Laplace Approximation (QLA). QLA approximates each second order factor in the approximate Laplace log-posterior using a rank-one factor obtained via efficient power iterations. QLA is expected to yield a posterior precision closer to that of the full Laplace without forming the full Hessian, which is typically intractable. For prediction, QLA also uses the linearized model.