Recent advancements in large language models (LLMs) have shown remarkable potential in various complex tasks requiring multi-step reasoning methods like tree search to explore diverse reasoning paths. However, existing methods often suffer from computational inefficiency and redundancy. First, they overlook the diversity of task difficulties, leading to unnecessarily extensive searches even for easy tasks. Second, they neglect the semantics of reasoning paths, resulting in redundant exploration of semantically identical paths. To address these limitations, we propose Semantic Exploration with Adaptive Gating (SEAG), a computationally efficient method. SEAG employs an adaptive gating mechanism that dynamically decides whether to conduct a tree search, based on the confidence level of answers from a preceding simple reasoning method. Furthermore, its tree-based exploration consolidates semantically identical reasoning steps, reducing redundant explorations while maintaining or even improving accuracy. Our extensive experiments demonstrate that SEAG significantly improves accuracy by 4.3% on average while requiring only 31% of computational costs compared to existing tree search-based methods on complex reasoning benchmarks including GSM8K and ARC with diverse language models such as Llama2, Llama3, and Mistral. Our code is available at https://github.com/ml-postech/SEAG-semantic-exploration-with-adaptive-gating.

Large language models (LLMs) have shown impressive performance by generating reasoning paths before final answers, but learning such a reasoning path requires costly human supervision. To address this issue, recent studies have explored self-training methods that improve reasoning capabilities using pseudo-labels generated by the LLMs themselves. Among these, confidence-based self-training fine-tunes LLMs to prefer reasoning paths with high-confidence answers, where confidence is estimated via majority voting. However, such methods exclusively focus on the quality of the final answer and may ignore the quality of the reasoning paths, as even an incorrect reasoning path leads to a correct answer by chance. Instead, we advocate the use of reasoning-level confidence to identify high-quality reasoning paths for self-training, supported by our empirical observations. We then propose a new self-training method, **CORE-PO**, that fine-tunes LLMs to prefer high-**CO**nfidence **RE**asoning paths through **P**olicy **O**ptimization. Our experiments show that CORE-PO improves the accuracy of outputs on four in-distribution and two out-of-distribution benchmarks, compared to existing self-training methods.

Scaling test-time computation, generating and analyzing multiple or sequential outputs for a single input, has become a promising strategy for improving the reliability and quality of large language models (LLMs), as evidenced by advances in uncertainty quantification and multi-step reasoning. A key shared component is semantic clustering, which groups outputs that differ in form but convey the same meaning. Semantic clustering enables estimation of the distribution over the semantics of outputs and helps avoid redundant exploration of reasoning paths. However, existing approaches typically rely on external models, which introduce substantial computational overhead and often fail to capture context-aware semantics. We propose Latent Semantic Clustering (LSC), a lightweight and context-sensitive method that leverages the generator LLM’s internal hidden states for clustering, eliminating the need for external models. Our extensive experiment across various LLMs and datasets shows that LSC significantly improves the computational efficiency of test-time scaling while maintaining or exceeding the performance of existing methods.