GALACTIC: Global and Local Counterfactuals for Time-Series Classification

Time-series classifiers inform decisions from clinical diagnosis to industrial monitoring, yet the usual explanations, saliency over timesteps and discriminative subsequences, indicate what supported a prediction rather than what would change it. Counterfactual explanations address this, but existing methods for time-series classifiers describe individual predictions and leave open how recurring temporal changes connect classes across a population. Summarizing many local counterfactuals is the natural route to a population-level answer, and we show why it falls short: an objective asking only for the smallest change to one series drives that change toward the decision boundary, leaving no margin for similar series, and selecting among such changes cannot add a margin the objective never asked for. We introduce GALACTIC, the first unified local-to-global counterfactual framework for differentiable multiclass time-series classifiers. At the local level, GALACTIC-L asks each counterfactual to be as small as possible while crossing the decision boundary by a margin shared across the structural subgroup of its series. At the global level, GALACTIC-G selects rather than generates: it accepts the perturbations of any local generator and keeps a small reusable set for each directed class transition. It expresses coverage, sparsity, and perturbation magnitude in one unit, bits, under a Minimum Description Length criterion, so no weights between them are set, and greedy selection carries the $(1-1/e)$ guarantee under stated conditions. Across ten UCR datasets, eight local generators, and six adapted global methods, the perturbations of GALACTIC-L cover on average more of each class transition, at a shorter description length, than those of any competing generator.