arXiv:2604.01325v1 Announce Type: new Abstract: The fundamental problem of causal inference - that the counterfactual outcome for any individual is never observed - has shaped the entire methodology of the field. Every existing approach substitutes assumptions for missing data: ignorability, parallel trends, exclusion restrictions. None produces the counterfactual itself. This paper proposes the Digital Twin Counterfactual Framework (DTCF): rather than estimating the counterfactual statistically, we simulate it using a digital twin and subject the simulation to a hierarchical validation regime. We formalize the digital twin simulator as a stochastic mapping within the potential outcomes framework and introduce a hierarchy of twin fidelity assumptions - from marginal fidelity through joint fidelity to structural fidelity - each unlocking a progressively richer class of estimands. The central contribution is threefold. First, a five-level validation architecture converts the unfalsifiable claim that the simulator produces correct counterfactuals into falsifiable tests against observable data. Second, a formal decomposition separates causal quantities into those that are marginally validated (ATE, CATE, QTE - testable through observable-arm comparison) and those that are copula-dependent (the ITE distribution, probability of benefit/harm, variance of treatment effects - permanently reliant on the unobservable within-individual dependence structure). Third, bounding, sensitivity, and uncertainty quantification tools make the copula dependence explicit. The DTCF does not resolve the fundamental problem of causal inference. What it provides is a framework in which marginal causal claims become increasingly testable, joint causal claims become explicitly assumption-indexed, and the gap between the two is formally characterized.

arXiv:2604.01339v1 Announce Type: cross Abstract: Vision transformers (ViT) rely on attention mechanism to weigh input features, and therefore attention scores have naturally been considered as explanations for its decision-making process. However, attention scores are almost always non-zero, resulting in noisy and diffused attention maps and limiting interpretability. Can we quantify uncertainty measures of attention scores and obtain regularized attention scores? To this end, we consider attention scores of ViT in a statistical framework where independent noise would lead to insignificant yet non-zero scores. Leveraging statistical learning techniques, we introduce the bootstrapping for attention scores which generates a baseline distribution of attention scores by resampling input features. Such a bootstrap distribution is then used to estimate significances and posterior probabilities of attention scores. In natural and medical images, the proposed \emph{Attention Regularization} approach demonstrates a straightforward removal of spurious attention arising from noise, drastically improving shrinkage and sparsity. Quantitative evaluations are conducted using both simulation and real-world datasets. Our study highlights bootstrapping as a practical regularization tool when using attention scores as explanations for ViT. Code available: https://github.com/ncchung/AttentionRegularization