Hint-before-Solving Prompting: Guiding LLMs to Effectively Utilize Encoded Knowledge (2402.14310v1)

Abstract: LLMs have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical reasoning processes. To mitigate this problem, we introduced Hint-before-Solving Prompting (HSP), which guides the model to generate hints (e.g., specific knowledge or key ideas) for solving the problem and then generate solutions containing intermediate reasoning steps. Since HSP is orthogonal to prompting methods (e.g., Chain-of-Thought (CoT)), we applied HSP to CoT, Least-to-Most, Plan-and-Solve, and Standard promptings. The results of extensive experiments on 6 reasoning benchmarks and 4 open-source LLMs demonstrate that HSP can effectively improve the accuracy of reasoning tasks: (1) By applying high-quality hint-enhanced HSP to CoT prompting, Llama2-70B-Chat shows an improvement of 9.7. (2) Beyond exploring training-free LLM capabilities, we built the HSPMATH dataset based on HSP and fine-tuned Llemma-7B, reaching 64.3 accuracy, surpassing GPT-3.5 and WizardMath-13B. We make our code and dataset publicly available at \url{https://github.com/jinlanfu/HSP}.

• The paper presents the Hint-before-Solving Prompting framework, which instructs LLMs to generate hints prior to solving to enhance reasoning accuracy.
• It empirically demonstrates a 9.7% relative accuracy boost in CoT settings and significant improvement through fine-tuning on the HSPMATH dataset.
• The study highlights that the method’s efficiency scales with model capacity and hint quality, enabling modular integration of external cues for better performance.

Hint-before-Solving Prompting: Enhancing LLM Knowledge Utilization

The paper "Hint-before-Solving Prompting: Guiding LLMs to Effectively Utilize Encoded Knowledge" (2402.14310) presents a comprehensive paper on explicitly guiding LLMs to leverage their internalized knowledge during reasoning tasks. The authors introduce Hint-before-Solving Prompting (HSP), a framework whereby LLMs are first instructed to generate or consider task-specific hints prior to producing solutions. This mechanism is explored in conjunction with established reasoning prompt paradigms such as Chain-of-Thought (CoT), Least-to-Most (LtM), Plan-and-Solve (PS), and standard direct-answer prompting.

Methodological Overview

HSP is formulated as an orthogonal extension to existing prompting methods: after presenting a query, the model–rather than generating a direct answer or reasoning sequence immediately–is prompted to first output a contextually relevant hint. The hint is intended to focus the model’s attention on key knowledge, strategies, or decompositional cues pertinent to problem-solving. In the experimental formulation, HSP is instantiated either as a one-stage approach (where hints and solutions are combined in a single generation) or a two-stage variant (HSP2), in which the model outputs the hint and solution sequentially.

Empirical evaluation encompasses six diverse reasoning benchmarks (mathematical and commonsense) and multiple open-source LLMs spanning parameter scales from 7B to 70B, as well as a mixture-of-experts model (Mixtral-8x7B-Instruct). A notable contribution is the introduction of the HSPMATH dataset containing 75,000 hint-enhanced samples for fine-tuning.

Key Findings and Numerical Results

The core empirical claims are supported by extensive ablation and comparative studies:

• HSP consistently improves accuracy in standard and CoT prompting frameworks. For instance, pairing high-quality, externally-generated hints with CoT on Llama2-70B-Chat yields a 9.7% relative accuracy boost across reasoning tasks.
• Supervised fine-tuning on hint-augmented datasets produces nontrivial improvements over both baseline and established closed-source models. Llemma-7B fine-tuned on HSPMATH achieves an accuracy of 64.3% on GSM8K, outperforming GPT-3.5 (57.1%) and WizardMath-13B (63.9%) under equivalent settings.
• Effectiveness scales with model capacity: Larger models (13B, 70B) benefit more from HSP than smaller ones, indicating a synergy between model size and the ability to self-generate salient hints.
• On challenging tasks (e.g. MATH dataset), HSP’s utility is modulated by LLM competence. For sufficiently capable models (Mixtral-56B), HSP improves performance even in the self-consistency regime, particularly for complex question types or difficulty levels. Lower-capacity models struggle to generate useful hints without external intervention.
• Hint quality is a critical factor. Incorporating externally generated hints from a more capable model (GPT-4) leads to further improvements. This effect is most pronounced for weaker LLMs, narrowing the performance gap with stronger models.
• Solutions generated after hinting are generally more concise and focused, especially in mathematical domains, suggesting more efficient internal reasoning.

Contradictory and Nuanced Observations

Although HSP is beneficial for standard and CoT promptings, its integration with planning- or decomposition-centric methods like Plan-and-Solve and Least-to-Most produces inconsistent or marginal improvements. The authors attribute this to the interaction between externally provided hints and the internal planning mechanism, which sometimes leads to misaligned or redundant reasoning steps.

On the most demanding tasks, such as advanced mathematical problem solving, not all LLMs are able to autonomously generate effective hints—highlighting a competence threshold for HSP’s self-directed variant. Nevertheless, when access to high-quality, externally sourced hints is available, even smaller models realize substantial gains.

Practical and Theoretical Implications

This work introduces a fundamentally modular approach to enhancing LLM reasoning by operationalizing the intermediate use of hints. While prior work has pursued external retrieval or post-hoc verification, the HSP paradigm demonstrates that structured, contextually-attuned scaffolding at the prompt level can substantially bridge the reasoning performance gap, with minimal modification to architecture or training regime. The release of HSPMATH provides a new resource for benchmarking fine-tuning strategies in mathematical reasoning.

From a methodological standpoint, two implications are salient:

• Prompt-level modularization: By separating hint generation from reasoning, HSP facilitates the integration of external knowledge sources and the potential for pipeline architectures (e.g., specialist hint generators feeding into LLM solvers), enabling new multi-agent or composite reasoning systems.
• Adaptive scaling: Given the observed model-size dependency, HSP can be selectively deployed for tasks and models where reasoning generalization is not yet robust. For more capable LLMs, HSP can be used to expose weaknesses in internal knowledge representation, guiding targeted fine-tuning.

Future Directions

Several avenues arise from this paper:

• External hint generation at scale: Automating high-quality hint provision (perhaps via more advanced LLMs or retrieval-augmented modules) could further democratize robust reasoning, especially for lightweight models or resource-constrained deployments.
• Integration with planning/graph-based reasoning paradigms: Adapting HSP to interleave with more structured problem decompositions may address the observed integration inefficiencies, especially for multi-step algorithmic or scientific reasoning.
• Adaptive prompting: Dynamically invoking hint generation only for queries triggering indicators of model uncertainty or multi-hop requirements could optimize resource utilization and latency in production systems.

Conclusion

Hint-before-Solving Prompting substantiates the claim that explicit intermediate supervision—via contextually focused hints—facilitates more precise and efficient reasoning in LLMs. The method’s compatibility with standard prompting, demonstrable empirical gains, and straightforward integration make it a promising tool for both research and practical deployments in knowledge-intensive domains. Its efficacy is closely tied to both model capacity and hint quality, underscoring the interplay between prompt engineering and model architecture in the ongoing advancement of general-purpose LLMs.