Beyond Uncertainty: Turning Model Failures into Reusable Logic Templates for Adaptive Reasoning

Exemplar-based chain-of-thought (CoT) prompting can improve multi-step reasoning in large language models (LLMs), but its effectiveness depends on the quality and relevance of the demonstrations for each query. Existing approaches face three limitations: demonstrations selection fails to identify genuinely difficult problems, generated reasoning paths remain noisy or redundant, and inference-time retrieval often relies on surface-level similarity rather than the underlying solution structure. To address these limitations, we propose Reusable Logic Template Activation (ReLTA), a framework for constructing and dynamically selecting reasoning demonstrations. ReLTA combines prediction errors with answer-space entropy to identify difficult examples, reconstructs and simplifies their reasoning traces into concise logic templates, and retrieves structurally relevant templates for each test query. Experiments on eight reasoning benchmarks using two reasoning backbones show that ReLTA achieves the highest accuracy on seven of eight datasets for each backbone, with an average improvement of 2.42% over Active-Prompt under the DeepSeek-Coder-V2-Lite-Base backbone. ReLTA provides a modular framework for constructing and selecting reasoning demonstrations.