Step Guided Reasoning: Improving Mathematical Reasoning using Guidance Generation and Step Reasoning (2410.19817v2)

Abstract: Mathematical reasoning has been challenging for LLMs. However, the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. Despite this progress, current approaches either necessitate extensive inference datasets for training or depend on few-shot methods that frequently compromise computational accuracy. To address these bottlenecks in mathematical reasoning, we propose a novel method called Step Guidied Reasoning, which is more stable and generalizable than few-shot methods and does not involve further fine-tuning of the model. In this approach, LLMs reflect on small reasoning steps, similar to how humans deliberate and focus attention on what to do next. By incorporating this reflective process into the inference stage, LLMs can effectively guide their reasoning from one step to the next. Through extensive experiments, we demonstrate the significant effect of Step Guidied Reasoning in augmenting mathematical performance in state-of-the-art LLMs. Qwen2-72B-Instruct outperforms its math-specific counterpart, Qwen2.5-72B-Math-Instruct, on MMLU- STEM with a score of 90.9%, compared to 87.3%. The average scores of Qwen2-7B-Instruct and Qwen2-72B-Instruct increase from 27.1% to 36.3% and from 36.5% to 47.4% on the mathematics domain, respectively.

• The paper introduces Step Guided Reasoning, a method that improves LLM mathematical problem-solving through iterative, reflective guidance.
• It leverages self-generated step guidance to boost accuracy—showing up to a 91.7% relative gain on benchmarks like AMC23.
• Experimental results demonstrate SGR’s adaptability across varied step lengths, indicating potential for cost-effective, scalable AI in education.

An Overview of Step Guided Reasoning for Mathematical Reasoning Enhancement

Lang Cao, Chao Peng, and Yitong Li's work proposes a novel procedure, Step Guided Reasoning (SGR), to address persistent challenges in mathematical reasoning for LLMs. Despite the considerable strides made with the Chain-of-Thought (CoT) reasoning strategies, limitations remain, especially in dealing with complex and competition-level mathematical problems. The proposed method introduces a reflective mechanism that guides LLMs through reasoning steps more akin to human problem-solving processes.

Key Methodological Contributions

The essence of the SGR approach lies in its ability to improve the inference process without requiring further model fine-tuning. This contrasts with existing methods that often mandate extensive training datasets or compromise accuracy to enhance performance. The proposed model adopts a multi-step reflective reasoning process, prompting self-questioning for the next steps and employing previous context effectively.

When triggered by a mathematical problem, the model generates a 'step guidance' that involves determining the relevant knowledge needed for that step and self-answering these reflections. Subsequently, these guided reflections are utilized to develop the answer iteratively. The cyclic process of guidance generation and step reasoning continues until a problem solution is achieved or a predefined iteration ceiling is reached.

Experimental Outcomes

The efficacy of the SGR method is evident in substantial improvements across challenging benchmarks like the AMC23 and AIME24 datasets, where it significantly enhances problem-solving accuracy. Notably, in the AMC23 dataset, the accuracy improved from 30% to 57.5%, representing a remarkable 91.7% relative gain. Similarly, in sampled level 5 problems of the MATH dataset, accuracy improved by 55.8%.

Table 1 in the paper provides a comparative analysis of the SGR against the CoT methodology under different settings. SGR consistently outperforms CoT across all examined datasets, underlining its potential to enhance reasoning without additional model learning processes. The SGR method also showed adaptability in handling various step lengths, as evidenced by experiments that adjusted step lengths from 100 to 600, with optimal performance noted at a step length of 300.

Graphical Presentation and Illustrative Use-Cases

The paper elucidates its methodology graphically, showcasing how SGR orchestrates guidance and reasoning generation phases. Figure 1 provides a visual schema of this step-wise generation, reinforcing the theoretical framework with a practical demonstration. A prominent case paper (Figure 2) exemplifies SGR's prowess in systematically identifying and answering intermediate reasoning questions where previous CoT techniques would falter. This practical illustration further emphasizes SGR's potential in real-applications, reinforcing its robustness and reliability in varied problem-solving scenarios.

Theoretical and Practical Implications

Theoretically, SGR enhances the cognitive modularity in LLM reasoning, imparting a structured reflective capacity that aligns closely with human problem-solving. This has broader implications for the development of AI models that require minimal training for enhanced accuracy in niche domains such as competitive mathematics.

From a practical perspective, without the constraint of needing massive, high-quality datasets for finetuning, this methodology could significantly reduce infrastructure and training costs, facilitating more expansive and accessible AI deployment in educational technologies and beyond.

Speculation on Future Developments

The focus on integrating a guided reasoning process opens new avenues for AI research in cognitive emulation. Future lines of inquiry may explore adaptive step length strategies within SGR or broader, cross-domain applications requiring similar stepwise reasoning. Furthermore, coupling SGR with other inference techniques might yield promising hybrid approaches, further elevating the reasoning capabilities of LLMs.

Overall, the SGR framework contributes notably to advancing LLMs' mathematical reasoning capabilities, marking a step forward in the strategic manipulation of logical task decomposition and internal reflection. This paper offers a foundation upon which further enhancements and applications in reasoning AI systems can be innovatively developed.