Reinforced Efficient Reasoning via Semantically Diverse Exploration — part 1/3

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# Reinforced Efficient Reasoning via Semantically Diverse Exploration

###### Abstract

Reinforcement learning with verifiable rewards (RLVR) has proven effective in enhancing the reasoning of large language models (LLMs). Monte Carlo Tree Search (MCTS)-based extensions improve upon vanilla RLVR (e.g., GRPO) by providing tree-based reasoning rollouts that enable fine-grained and segment-level credit assignment. However, existing methods still suffer from limited exploration diversity and inefficient reasoning. To address the above challenges, we propose r einforced efficient reas o ning via s emantically diverse e xplorations, i.e., ROSE , for LLMs. To encourage more diverse reasoning exploration, our method incorporates a semantic-entropy-based branching strategy and an ε \varepsilon -exploration mechanism. The former operates on already sampled reasoning rollouts to capture semantic uncertainty and select branching points with high semantic divergence to generate new successive reasoning paths, whereas the latter stochastically initiates reasoning rollouts from the root, preventing the search process from becoming overly local. To improve efficiency, we design a length-aware segment-level advantage estimator that rewards concise and correct reasoning while penalizing unnecessarily long reasoning chains. Extensive experiments on various mathematical reasoning benchmarks with Qwen and Llama models validate the effectiveness and efficiency of ROSE. Codes are available at https://github.com/ZiqiZhao1/ROSE-rl .

## 1 Introduction

Reinforcement learning with verifiable rewards (RLVR) has recently been proposed to enhance the reasoning of large language models (LLMs) in verifiable settings, including mathematical reasoning and code generation Guo et al. (2025) ; Shao et al. (2024) ; Liu et al. (2025) ; Yu et al. (2025) . Typical RLVR algorithms, such as GRPO Guo et al. (2025) ; Shao et al. (2024) and its variants Yu et al. (2025) ; Liu et al. (2025) , estimate the advantage of an entire rollout response based on the verified reward and uniformly propagate this advantage to all tokens within the response.

While the uniform credit assignment is simple yet effective, it constrains the learning potential of the model and conflicts with human intuition. For example, a reasoning chain that produces an incorrect response may still contain certain correct steps. Moreover, recent studies have indicated that this training paradigm may lead to “overthinking”, in which models are engaged in redundant reasoning Chen et al. (2024) ; Dai et al. (2025) ; Nie et al. (2026) . To further improve model performance, a more effective credit assignment approach is to employ Monte Carlo Tree Search (MCTS) Kocsis and Szepesvári (2006) during response rollout sampling. Unlike vanilla GRPO, which generates a group of independent responses for a given problem, MCTS enables the model to produce responses in a tree-based structure, as illustrated in Figure 1(a) , allowing segment-level credit assignment by computing value differences between parent and child nodes.

Despite the progress achieved by MCTS-based RLVR algorithms Li et al. (2025) ; Yang et al. (2025b) ; Zheng et al. (2025b) ; Dong et al. (2025) , limited exploration diversity and inefficient reasoning still exist. Specifically, most existing work uses generation entropy as the criterion for MCTS branching Zheng et al. (2025b) ; Dong et al. (2025) . These methods first identify the position with the highest generation entropy. Then, tokens preceding this position are kept fixed, and successive tokens are regenerated. Although generation entropy measures a policy’s uncertainty over token selection in the current action space, this metric does not generalize well to the semantic space. Figure 1(b) shows a case study of generation entropy-based branching. The tokens can in response 1 and need in response 2 correspond to the positions of highest entropy in two separate generations, yet their semantic meanings are largely the same, and the subsequent reasoning in both responses is identical (highlighted in blue). Furthermore, although response 2 and response 3 follow different reasoning paths after branching, they are semantically similar, and their subsequent reasoning remains consistent with other responses (highlighted in green). This indicates that current methods fail to generate semantically diverse rollouts. Additionally, existing MCTS-based methods do not address the overthinking problem effectively, and current approaches for efficient reasoning either incur performance degradation or offer trivial performance gains Dai et al. (2025) ; Arora and Zanette (2025) . How to achieve both improved performance and efficient reasoning based on MCTS remains an open question.

To address the aforementioned challenges, we propose r einforced efficient reas o ning via s emantically diverse e xplorations, i.e., ROSE , for LLMs. To address the first challenge, we introduce a semantic-entropy-based branching strategy together with an ε \varepsilon -exploration mechanism. The semantic entropy metric, defined over differences in token semantics, identifies positions along a reasoning path where the model exhibits high uncertainty in the semantic space, thereby guiding the exploration toward more diverse reasoning paths. In addition, to prevent the search process from becoming overly local, the ε \varepsilon -exploration mechanism stochastically regenerates the reasoning rollout from scratch. Together, these methods promote more diverse and effective exploration. To address the second challenge, we integrate credit assignment with the length of the reasoning chain. Leveraging the tree structure, we estimate values for each node and assign credit at the segment level. For different correct reasoning chains originating from the same node, longer chains with deeper depth are penalized to encourage more efficient reasoning. These components make fuller use of MCTS samples, aiming to enhance the model’s reasoning ability through more diverse and efficient exploration. In summary, our contributions are: • We introduce a semantic-entropy guided MCTS-based rollout strategy together with an ϵ \epsilon -exploration mechanism, which enables more diverse exploration compared with existing approaches.

• We propose a segment-level advantage estimation method that incorporates reasoning length, enabling stronger performance while producing more efficient reasoning.

• Extensive experiments on a wide range of mathematical reasoning tasks (AIME2025, AIME2024, AMC2023, MATH500), using both Qwen and Llama models, validate the effectiveness and efficiency of our approach.

## 2 Related Work

### 2.1 Reinforcement Learning for LLMs

Reinforcement learning has been widely adopted to align LLMs with human preferences through reinforcement learning from human feedback (RLHF) Lee et al. (2024) ; Ouyang et al. (2022) . More recently, reinforcement learning with verifiable rewards (RLVR) has emerged as an effective approach for enhancing the reasoning ability of LLMs Guo et al. (2025) ; Shao et al. (2024) ; Dai et al. (2025) ; Hao et al. (2025) ; Zhou et al. (2026) ; Wu et al. (2026) ; Xie et al. (2025) ; Wu et al. (2025b) ; An et al. (2025) . By using rule-based binary (0/1) rewards to simplify reward design, GRPO Guo et al. (2025) ; Shao et al. (2024) removes the need for training an extra critic model compared with vanilla PPO Schulman et al. (2017) , leading to a substantial reduction in RL training overhead. Recent studies, including DAPO Yu et al. (2025) , Dr.GRPO Liu et al. (2025) , VAPO Yue et al. (2025) , GSPO Zheng et al. (2025a) , and CPG Chu et al. (2025) , have explored improving the GRPO loss function to further enhance its reasoning capability. In contrast to these approaches, our work focuses on improving the rollout process to enable more diverse exploration and credit assignment, without modifying the loss function. As a result, the proposed method is in principle compatible with a wide range of GRPO-based algorithms.

### 2.2 MCTS for LLM Reasoning

Monte Carlo Tree Search (MCTS) Kocsis and Szepesvári (2006) ; Świechowski et al. (2023) offers a principled framework for exploring structured decision spaces, making it a natural candidate for performing credit assignment based on the intermediate reasoning steps. Recent studies have explored MCTS-based sampling in RL training, showing progress on mathematical reasoning tasks Li et al. (2025) ; Yang et al. (2025b) ; Zheng et al. (2025b) as well as other complex problems Ji et al. (2025) ; Dong et al. (2025) .

A key challenge in applying MCTS lies in deciding where to branch, as this choice fundamentally determines the exploration trajectory and the quality of the reasoning. Prior approaches rely on random branching Ji et al. (2025) , generation-entropy-based branching Dong et al. (2025) ; Zheng et al. (2025b) , branching based on fixed-length segments Li et al. (2025) , or performing branching during decoding via beam search Yang et al. (2025b) . However, all these strategies fall short in promoting sufficient diverse exploration. Meanwhile, existing methods do not explicitly account for the impact of reasoning length during advantage estimation, which can lead to overthinking during model inference. In contrast, our approach enhances exploration diversity and enables more efficient reasoning, leading to improved performance on complex reasoning tasks.

## 3 Method

This section details ROSE. We first introduce how to achieve effective and diverse exploration in Section 3.1 . Section 3.2 then describes how tree-based exploration is leveraged to perform advantage estimation and encourage efficient reasoning. Finally, Section 3.3 presents the overall learning objective. Figure 2 illustrates an overview of ROSE.

### 3.1 Semantic-Entropy Guided Exploration

Given a question q q , vanilla GRPO performs rollouts by sampling a group of independent responses { 𝐨 i } i = 1 G \{\mathbf{o}_{i}\}_{i=1}^{G} . In contrast, MCTS-based methods introduce tree-structured rollouts, allowing different responses to share common prefix tokens. The key to tree-based rollout is identifying appropriate branching positions, which encourages the model to perform more effective exploration. A common practice is to use generation entropy to determine branching positions Dong et al. (2025) ; Zheng et al. (2025b) . Generation entropy provides a principled measure of the uncertainty of a policy π θ \pi_{\theta} , i.e., the LLM, over its action space, i.e., the vocabulary 𝒱 \mathcal{V} . Given a question q q and a generated response 𝐨 i \mathbf{o}_{i} , the generation entropy of the policy at position k k is defined as: ℋ k = − ∑ v ∈ 𝒱 p θ ( v | q , 𝐨 i , < k ) log p θ ( v | q , 𝐨 i , < k ) \mathcal{H}_{k}=-\sum_{v\in\mathcal{V}}p_{\theta}(v|q,\mathbf{o}_{i,<k})\log p_{\theta}(v|q,\mathbf{o}_{i,<k}) (1) where p θ ​ ( v | q , 𝐨 i , < k ) p_{\theta}(v|q,\mathbf{o}_{i,<k}) represents the probability distribution over the vocabulary 𝒱 \mathcal{V} at position k k . Such entropy has been widely used in traditional RL Haarnoja et al. (2018) ; Wang et al. (2022) , where different actions often exhibit significant differences, such as movement directions in a game environment Bellemare et al. (2013) . However, this assumption does not always hold in language generation. Consider the two words can and need in Figure 1(b) . When the LLM is uncertain about which one to select, the generation entropy may be high. From a semantic perspective, however, this choice is actually well-determined, as both words serve the same functional role of indicating modal intent. As a result, the responses branched from this position may exhibit extremely high similarity, and in some cases even follow identical subsequent trajectories, thereby limiting the potential for more diverse exploration.

Based on this observation, we design an additional metric to evaluate the semantic divergence among the current candidate tokens. Specifically, given a question q q and a generated response 𝐨 i \mathbf{o}_{i} , at position k k , we first select the top-20 tokens from 𝒱 \mathcal{V} with the highest probabilities to form the set 𝒱 k \mathcal{V}_{k} for efficiency. Then, for each token v i ∈ 𝒱 k v_{i}\in\mathcal{V}_{k} , its corresponding embedding 𝐞 v i \mathbf{e}_{v_{i}} is obtained from the LLM. We then compute semantic divergence as the sum of pairwise similarities between all tokens in 𝒱 k \mathcal{V}_{k} , weighted by their probabilities:

S D k = − ∑ v i , v j ∈ 𝒱 k p θ ( v i | q , 𝐨 i , < k ) p θ ( v j | q , 𝐨 i , < k ) ⋅ cos ⟨ 𝐞 v i , 𝐞 v j ⟩ SD_{k}=\displaystyle-\sum_{v_{i},v_{j}\in\mathcal{V}_{k}}p_{\theta}(v_{i}|q,\mathbf{o}_{i,<k})p_{\theta}(v_{j}|q,\mathbf{o}_{i,<k})\cdot\cos\langle\mathbf{e}_{v_{i}},\mathbf{e}_{v_{j}}\rangle

where cos ⁡ ⟨ 𝐞 v i , 𝐞 v j ⟩ \cos\langle\mathbf{e}_{v_{i}},\mathbf{e}_{v_{j}}\rangle represents the cosine similarity between the embeddings of tokens v i v_{i} and v j v_{j} . The key idea of semantic divergence is that when the high-probability tokens exhibit large semantic differences, the current position becomes an ideal branching point, leading to more distinct subsequent reasoning paths.

Finally, we define semantic entropy as the product of generation entropy and semantic divergence, and use it as the branching indicator: S ​ E k = S ​ D k ⋅ ℋ k SE_{k}=SD_{k}\cdot\mathcal{H}_{k} (3) This combined measure captures both probabilistic uncertainty and semantic dispersion, allowing ROSE to more accurately identify positions where alternative continuations are more likely to lead to genuinely diverse reasoning paths.

The rollout process based on branching metrics is summarized as follows. Given a question q q , a complete response is first generated. For each position in the generated response, the proposed branching metric is computed, and the position with the highest value is selected. Then a new response is regenerated at this position, keeping the preceding part of the response unchanged. The corresponding metric of the newly generated sequence is computed, and the selection is then performed on all existing rollout responses. The whole process is repeated until the number of generated responses reaches the predefined parameter G G .

In addition, inspired by the ε \varepsilon -greedy Sutton et al. (1998) strategy in reinforcement learning, we propose an ε \varepsilon -exploration mechanism. Specifically, before generating each response, there is an ε \varepsilon probability of generating the response from scratch, i.e., rolling out an independent response; otherwise, the rollout follows the proposed semantic-entropy-based branching strategy. This mechanism prevents the search from becoming overly focused on local regions and further balances the depth and breadth of exploration. After completing the rollout process for a given query, we can obtain a tree structure, an example of which is shown on the left side of Figure 2 . During rollout, we apply dynamic sampling Yu et al. (2025) to remove groups whose responses receive identical rewards, improving efficiency. The proposed methods offer an effective exploration-exploitation tradeoff to better search the reasoning paths for LLMs.

### 3.2 Advantage Estimation

Based on the tree-structured exploration, we perform segment-level credit assignment through (1) node value assignment, (2) segment advantage estimation and (3) length-aware calibration.