Fact-checking real-world claims, particularly numerical claims, is inherently complex that require multistep reasoning and numerical reasoning for verifying diverse aspects of the claim. Although large language models (LLMs) including reasoning models have made tremendous advances, they still fall short on fact-checking real-world claims that require a combination of compositional and numerical reasoning. They are unable to understand nuance of numerical aspects, and are also susceptible to the reasoning drift issue, where the model is unable to contextualize diverse information resulting in misinterpretation and backtracking of reasoning process. In this work, we systematically explore scaling test-time compute (TTS) for LLMs on the task of fact-checking complex numerical claims, which entails eliciting multiple reasoning paths from an LLM. We train a verifier model (VERIFIERFC) to navigate this space of possible reasoning paths and select one that could lead to the correct verdict. We observe that TTS helps mitigate the reasoning drift issue, leading to significant performance gains for fact-checking numerical claims. To improve compute efficiency in TTS, we introduce an adaptive mechanism that performs TTS selectively based on the perceived complexity of the claim. This approach achieves 1.8x higher efficiency than standard TTS, while delivering a notable 18.8% performance improvement over single-shot claim verification methods. Our code and data can be found atthis https URL
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