Natural Geometry of Robust Data Attribution: From Convex Models to Deep Networks

Data attribution methods identify which training examples are responsible for a model's predictions, but their sensitivity to distributional perturbations undermines practical reliability. We present a unified framework for certified robust attribution that extends from convex models to deep networks. For convex settings, we derive Wasserstein-Robust Influence Functions (W-RIF) with provable coverage guarantees. For deep networks, we demonstrate that Euclidean certification is rendered vacuous by spectral amplification -- a mechanism where the inherent ill-conditioning of deep representations inflates Lipschitz bounds by over $10{,}000\times$. This explains why standard TRAK scores, while accurate point estimates, are geometrically fragile: naive Euclidean robustness analysis yields 0\% certification. Our key contribution is the Natural Wasserstein metric, which measures perturbations in the geometry induced by the model's own feature covariance. This eliminates spectral amplification, reducing worst-case sensitivity by $76\times$ and stabilizing attribution estimates. On CIFAR-10 with ResNet-18, Natural W-TRAK certifies 68.7\% of ranking pairs compared to 0\% for Euclidean baselines -- to our knowledge, the first non-vacuous certified bounds for neural network attribution. Furthermore, we prove that the Self-Influence term arising from our analysis equals the Lipschitz constant governing attribution stability, providing theoretical grounding for leverage-based anomaly detection. Empirically, Self-Influence achieves 0.970 AUROC for label noise detection, identifying 94.1\% of corrupted labels by examining just the top 20\% of training data.

Algorithm-Relative Trajectory Valuation in Policy Gradient Control

We study how trajectory value depends on the learning algorithm in policy-gradient control. Using Trajectory Shapley in an uncertain LQR, we find a negative correlation between Persistence of Excitation (PE) and marginal value under vanilla REINFORCE ($r\approx-0.38$). We prove a variance-mediated mechanism: (i) for fixed energy, higher PE yields lower gradient variance; (ii) near saddles, higher variance increases escape probability, raising marginal contribution. When stabilized (state whitening or Fisher preconditioning), this variance channel is neutralized and information content dominates, flipping the correlation positive ($r\approx+0.29$). Hence, trajectory value is algorithm-relative. Experiments validate the mechanism and show decision-aligned scores (Leave-One-Out) complement Shapley for pruning, while Shapley identifies toxic subsets.

Constrained Optimal Planning to Minimize Battery Degradation of Autonomous Mobile Robots

This paper proposes an optimization framework that addresses both cycling degradation and calendar aging of batteries for autonomous mobile robot (AMR) to minimize battery degradation while ensuring task completion. A rectangle method of piecewise linear approximation is employed to linearize the bilinear optimization problem. We conduct a case study to validate the efficiency of the proposed framework in achieving an optimal path planning for AMRs while reducing battery aging.

Robust Optimal Task Planning to Maximize Battery Life

This paper proposes a control-oriented optimization platform for autonomous mobile robots (AMRs), focusing on extending battery life while ensuring task completion. The requirement of fast AMR task planning while maintaining minimum battery state of charge, thus maximizing the battery life, renders a bilinear optimization problem. McCormick envelop technique is proposed to linearize the bilinear term. A novel planning algorithm with relaxed constraints is also developed to handle parameter uncertainties robustly with high efficiency ensured. Simulation results are provided to demonstrate the utility of the proposed methods in reducing battery degradation while satisfying task completion requirements.

Flashpoints Signal Hidden Inherent Instabilities in Land-Use Planning

Land-use decision-making processes have a long history of producing globally pervasive systemic equity and sustainability concerns. Quantitative, optimization-based planning approaches, e.g. Multi-Objective Land Allocation (MOLA), seemingly open the possibility to improve objectivity and transparency by explicitly evaluating planning priorities by the type, amount, and location of land uses. Here, we show that optimization-based planning approaches with generic planning criteria generate a series of unstable "flashpoints" whereby tiny changes in planning priorities produce large-scale changes in the amount of land use by type. We give quantitative arguments that the flashpoints we uncover in MOLA models are examples of a more general family of instabilities that occur whenever planning accounts for factors that coordinate use on- and between-sites, regardless of whether these planning factors are formulated explicitly or implicitly. We show that instabilities lead to regions of ambiguity in land-use type that we term "gray areas". By directly mapping gray areas between flashpoints, we show that quantitative methods retain utility by reducing combinatorially large spaces of possible land-use patterns to a small, characteristic set that can engage stakeholders to arrive at more efficient and just outcomes.