Abstract
Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.
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Large language models can often generate plausible mathematical reasoning traces, but reliably identifying the correct solution among multiple candidates remains a key challenge. Existing test-time reasoning pipelines typically rely on text-based verifiers that re-read each generated solution, making verification an expensive component of inference. Prior work has shown, however, that LLMs often encode correctness-related signals in their internal representations, including awareness of when their own answers are likely to be wrong. Building on this observation, we introduce HSRM, a lightweight hidden-state reward model that verifies candidate solutions by directly reading the generator's internal representations rather than re-processing its text. HSRM extracts hidden states from a frozen generator at reasoning-step boundaries and uses a small Transformer encoder to rank candidates. It is trained from self-generated trajectories with outcome labels, requiring neither human-written process supervision nor a large pretrained verifier. Across four mathematical reasoning benchmarks, HSRM matches or outperforms a 55M-parameter text-only energy verifier in 15 of 16 generator--dataset settings while using only about 2M parameters, providing an efficient alternative to text-only verification by reusing representations already computed during generation.
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Process reward models (PRMs) provide dense step-level guidance for search-based reasoning, enabling inference-time compute to be allocated toward promising partial solutions. However, recent evidence suggests that PRM-guided search can over-optimize imperfect process rewards, pruning viable trajectories while expanding spurious ones. In this work, we theoretically show that directly leveraging PRM score is vulnerable to verifier noise through an extreme-value effect: non-viable prefixes become more likely to receive spuriously high scores as reasoning depth increase. Therefore, we formulate the PRM-guided search as a robust optimization problem over plausible reward perturbations, termed maximin PRM-guided search, leading to a training-free robust process supervision method that preserves promising alternatives when step-level scores are noisy. Maximin PRM-guided search mitigates this failure mode by reducing sensitivity to over-optimized PRM outliers. Without fine-tuning or online adaptation, maximin search consistently improves the PRM-guided search by 17-35% on average, outperforming outcome- and step-level baselines in 14 out of 16 settings. Our source code is available at https://github.com/tjoo512/maximin-search.
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