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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2601.17982 |
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| _version_ | 1866908788566523904 |
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| author | Mishra, Kshitij Lukas, Nils Lahlou, Salem |
| author_facet | Mishra, Kshitij Lukas, Nils Lahlou, Salem |
| contents | Small language models (SLMs) struggle with complex reasoning because exploration is expensive under tight compute budgets. We introduce Semantic Diversity-Exploration-Exploitation (SD-E$^2$), a reinforcement learning framework that makes exploration explicit by optimizing semantic diversity in generated reasoning trajectories. Using a frozen sentence-embedding model, SD-E$^2$ assigns a diversity reward that captures (i) the coverage of semantically distinct solution strategies and (ii) their average pairwise dissimilarity in embedding space, rather than surface-form novelty. This diversity reward is combined with outcome correctness and solution efficiency in a z-score-normalized multi-objective objective that stabilizes training. On GSM8K, SD-E$^2$ surpasses the base Qwen2.5-3B-Instruct and strong GRPO baselines (GRPO-CFL and GRPO-CFEE) by +27.4, +5.2, and +1.5 percentage points, respectively, while discovering on average 9.8 semantically distinct strategies per question. We further improve MedMCQA to 49.64% versus 38.37% for the base model and show gains on the harder AIME benchmark (1983-2025), reaching 13.28% versus 6.74% for the base. These results indicate that rewarding semantic novelty yields a more compute-efficient exploration-exploitation signal for training reasoning-capable SLMs. By introducing cognitive adaptation-adjusting the reasoning process structure rather than per-token computation-SD-E$^2$ offers a complementary path to efficiency gains in resource-constrained models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SD-E$^2$: Semantic Exploration for Reasoning Under Token Budgets Mishra, Kshitij Lukas, Nils Lahlou, Salem Computation and Language Artificial Intelligence Small language models (SLMs) struggle with complex reasoning because exploration is expensive under tight compute budgets. We introduce Semantic Diversity-Exploration-Exploitation (SD-E$^2$), a reinforcement learning framework that makes exploration explicit by optimizing semantic diversity in generated reasoning trajectories. Using a frozen sentence-embedding model, SD-E$^2$ assigns a diversity reward that captures (i) the coverage of semantically distinct solution strategies and (ii) their average pairwise dissimilarity in embedding space, rather than surface-form novelty. This diversity reward is combined with outcome correctness and solution efficiency in a z-score-normalized multi-objective objective that stabilizes training. On GSM8K, SD-E$^2$ surpasses the base Qwen2.5-3B-Instruct and strong GRPO baselines (GRPO-CFL and GRPO-CFEE) by +27.4, +5.2, and +1.5 percentage points, respectively, while discovering on average 9.8 semantically distinct strategies per question. We further improve MedMCQA to 49.64% versus 38.37% for the base model and show gains on the harder AIME benchmark (1983-2025), reaching 13.28% versus 6.74% for the base. These results indicate that rewarding semantic novelty yields a more compute-efficient exploration-exploitation signal for training reasoning-capable SLMs. By introducing cognitive adaptation-adjusting the reasoning process structure rather than per-token computation-SD-E$^2$ offers a complementary path to efficiency gains in resource-constrained models. |
| title | SD-E$^2$: Semantic Exploration for Reasoning Under Token Budgets |
| topic | Computation and Language Artificial Intelligence |
| url | https://arxiv.org/abs/2601.17982 |