DASH: Fast, Valid Counterfactuals For Deep Networks Via Batched Directional Search

Counterfactual explanations are most useful when they can be generated with low latency, remain close to the factual input, and satisfy input-domain, categorical, and actionability constraints. Achieving these objectives simultaneously is challenging for deep neural networks. Heuristic methods are often fast but may return invalid counterfactuals, whereas exact methods can certify global proximity but may not finish within practical time limits. We introduce DASH, a batched heuristic search method for finding close, valid, and actionable counterfactuals for deep neural networks under ${\ell }_1$, ${\ell }_2$, and ${\ell }_{\infty }$ objectives. DASH uses directional Lipschitz bounds and local affine models to generate anchors, then ranks and expands promising regions with batched network evaluations. We compare DASH against nine prior heuristic methods and time-limited exact mixed-integer baselines on four tabular datasets, with network depths from 2 to 32, and evaluate scalability on PBMC3k. Across 9,000 tabular query-norm cases, DASH returns a valid counterfactual within $5$ of the best heuristic-observed valid distance in $94.6$ of cases, with a median CPU search runtime of $0.061$ s. PGD-bisect, the baseline with the highest pooled within-$5\%$ coverage, meets this criterion in $41.1$ of cases, with a median runtime of $0.298$ s. These results show that the proposed search maintains high valid proximity across norms while keeping its search runtime practical.