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DISC: Dynamic Decomposition Improves LLM Inference Scaling (SSI-FM)

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Inference scaling methods often rely on decomposing problems into steps, followed by sampling and selecting the best next steps. However, these steps and their sizes are typically fixed or depend on domain knowledge. We propose dynamic decomposition, a method that adaptively and automatically breaks down solution and reasoning traces into manageable steps during inference. By allocating compute more effectively, particularly by subdividing challenging steps and sampling them more frequently, dynamic decomposition significantly enhances inference efficiency. Experiments on benchmarks such as APPS, MATH, and LiveCodeBench demonstrate that dynamic decomposition outperforms static approaches, including token-level, sentence-level, and single-step decompositions. These findings highlight the potential of dynamic decomposition to improve a wide range of inference scaling techniques.

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DISC: Dynamic Decomposition Improves LLM Inference Scaling (DL4C)

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Inference scaling methods often rely on decomposing problems into steps, followed by sampling and selecting the best next steps. However, these steps and their sizes are typically fixed or depend on domain knowledge. We propose dynamic decomposition, a method that adaptively and automatically breaks down solution and reasoning traces into manageable steps during inference. By allocating compute more effectively—particularly by subdividing challenging steps and sampling them more frequently—dynamic decomposition significantly enhances inference efficiency. Experiments on benchmarks such as APPS, MATH, and LiveCodeBench demonstrate that dynamic decomposition outperforms static approaches, including token-level, sentence-level, and single-step decompositions. These findings highlight the potential of dynamic decomposition to improve a wide range of inference scaling techniques.

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SFS: Smarter Code Space Search improves LLM Inference Scaling

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We frame code generation as a black-box optimization problem within the code space and demonstrate how optimization-inspired techniques can enhance inference scaling. Based on this perspective, we propose SCATTERED FOREST SEARCH (SFS), a novel approach that improves solution diversity and better exploits feedback during evolutionary search. Our theoretical analysis illustrates how these methods help avoid local optima during optimization, leading to more efficient exploration. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance gains. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our approach scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

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