Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing
Authors: Yutong Yin, Mingyu Jin, Jin Pan, Changyi Yang, Zijie Xia, Dhruv Pai, Shuming Hu, Zhen Zhang, +7 more
Organizations: 1Northwestern University · 2Rutgers University · University of Wisconsin–Madison · 5LMSYS Org · 4Carnegie Mellon University · 6Tilde Research · University of California, Santa Barbara · University of Toronto · University of British Columbia · University of California, San Diego
Abstract
Test-time scaling improves language-model reasoning, but existing approaches often face a difficult trade-off: long chain-of-thought sampling remains single-threaded, while sentence- or solution-level search can be computationally expensive and hard to train end-to-end. We introduce Local Branch Routing (LBR), a token-level test-time scaling framework that expands a small local lookahead tree, forwards all sampled branches through the language model, and uses a lightweight router to select the depth-1 subtree to commit. By routing over the hidden states of candidate local futures, LBR allows each token decision to use evidence beyond the root next-token distribution while avoiding full solution-level search. The resulting prune-shift-grow decoding process preserves discrete branch identities and defines a tractable tree-trajectory likelihood: newly grown nodes are counted when first sampled, and router decisions are assigned explicit probabilities. This enables end-to-end reinforcement learning with verifiable rewards, jointly optimizing the base model and router under the same likelihood-ratio principle as discrete-token RLVR. On synthetic hierarchical-planning tasks, LBR shows that post-candidate hidden states provide useful routing evidence. On mathematical reasoning benchmarks, LBR improves both Pass@1 and Pass@32 over discrete chain-of-thought, vanilla discrete-token RLVR, and RL-compatible soft-token branching baselines. These results suggest that lightweight local branching offers an efficient, trainable, and discrete form of language-model 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 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. 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. 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.
Large Reasoning Models (LRMs) improve performance by allocating additional inference-time compute to generate extended chain-of-thought reasoning. However, recent studies reveal that sequential test-time scaling often yields diminishing or even negative returns, as longer traces exhibit increased uncertainty, error compounding, and drift from the original problem. We propose ThinkRetrieve, a test-time scaling framework that augments the reasoning traces of LRMs with dynamically retrieved solved examples at each reasoning step. Given an external corpus of problems paired with step-by-step solutions, ThinkRetrieve retrieves relevant exemplars at each intermediate step and injects them directly into the thinking trace, providing the model with guidance on how to reason rather than merely what facts are relevant. Experiments across five reasoning models (1.5B--8B parameters) on GSM-8K, MATH-500, AIME 2025, and SciQ demonstrate that ThinkRetrieve consistently improves accuracy over standard test-time scaling, with relative gains of up to 60% on AIME 2025.
Scaling inference-time computation has emerged as a reliable method to improve the performance of large language models on complex reasoning and programming tasks. However, standard approaches such as independent sampling and sequential multi-turn refinement operate without token-level credit assignment, resulting in computational inefficiency, since valid reasoning prefixes are frequently discarded. In this work, we introduce Test-Time Scaling via Error Localization (TTEL), an inference-time algorithm that utilizes fixed or environment feedback to perform token-level error localization. By comparing conditional probabilities under informed feedback against a null-context baseline, TTEL isolates the step at which an error occurred. The algorithm then truncates the trajectory and branches a new generation, maximally reusing the valid prefix. Extensive evaluations demonstrate that TTEL establishes strictly dominating Pareto frontiers across sequential reasoning domains, measured by pass-at-k vs. generated-token cost. With Qwen3-8B on LiveCodeBench, TTEL attains a pass@64 of 71.0% while generating approximately half as many tokens as independent sampling (360.4k vs. 735.0k). Generalizing to math benchmarks AIME-2025 and HMMT-2025, TTEL cleanly outperforms competing test-time baselines across both Qwen3-8B and Qwen3-4B-Thinking-2507.