Small language models (SLMs) offer promising and efficient alternatives to large language models (LLMs). However, SLMs' limited capacity restricts their reasoning capabilities and makes them sensitive to prompt variations. To address these challenges, we propose a novel framework that enhances SLM reasoning capabilities through LLM generated blueprints. The blueprints provide structured, high-level reasoning guides that help SLMs systematically tackle related problems. Furthermore, our framework integrates a prompt template search mechanism to mitigate the SLMs' sensitivity to prompt variations. Our framework demonstrates improved SLM performance across various tasks, including math (GSM8K), coding (MBPP), and logic reasoning (BBH). Our approach improves the reasoning capabilities of SLMs without increasing model size or requiring additional training, offering a lightweight and deployment-friendly solution for on-device or resource-constrained environments.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning.To address this, we propose \textbf{Additional Logic Training (ALT)}, which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples.We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights.Then, based on these principles, we construct a synthetic corpus named \textbf{Formal} \ \textbf{Logic} \ \textbf{\textit{D}eduction} \ \textbf{\textit{D}iverse} (FLD _{\times2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors.Finally, we empirically show that ALT on FLD _{\times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B.Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.