Beyond the Frontier: Stochastic Backtracking for Efficient Test-Time Scaling

Test-time scaling improves language-model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce $\textbf{stochastic backtracking over a persistent pool}$ of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. $\textbf{Subpool Selection}$ strengthens greedy PRM-guided search by applying Top-$N$ selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. $\textbf{Power Backtrack Sequential Monte Carlo}$ extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy–token trade-off in test-time scaling.