Stabilizing black-box algorithms through task-oriented randomization

Algorithmic stability refers to the property of an algorithm being insensitive to perturbations of the input data, where the type of perturbation may vary depending on the setting. In this work, we develop a general framework to quantify the extent to which any ensembling strategy defined via averaging can yield stability guarantees for any type of data perturbation. Our main theoretical result is a guarantee on the stability of this ensembled algorithm, given in terms of the norm of a certain covariance operator that describes the ensembling process. We show how our general framework yields interpretable and intuitive insights in several examples of perturbations of practical interest, and provides much sharper guarantees than those obtained from privacy considerations.

Looped Transformers, which repeatedly apply a shared transformer block, are an architecturally natural fit for variable-length algorithmic tasks. Although they can exhibit strong length generalization beyond the length of training sequences, this behavior is brittle, yielding high out-of-distribution (OOD) variance, even across well-performing in-distribution solutions. We trace this variance to the spurious correlation in simple algorithmic tasks between sequence length and number of loops. Introducing stochasticity into the number of loops during training sharply reduces OOD variance and stabilizes predictions across inference-time loop counts. To improve upon heuristic randomization schemes, we further analyze RL-Halting as a learned stochastic schedule and find that it generally improves the accuracy-stability trade-off. Across binary addition, Dyck-1, Unique Set, and Copy, learned stochastic stopping often improves this trade-off but can also stabilize a suboptimal computation. Our work suggests that "when to stop" should be treated as a training-time design choice, not merely an inference-time computation-allocation rule.

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging guarantees stability for any bounded-outcome regression algorithm. We introduce a new cross-fitting procedure, adaptive cross-bagging, which simultaneously eliminates seed dependence from both nuisance estimation and sample splitting in debiased machine learning. Numerical experiments confirm that the method achieves the targeted level of stability whereas alternatives do not. Our method incurs a small computational penalty relative to standard practice whereas alternative methods incur large penalties.