Divergent-Convergent Thinking in Large Language Models for Creative Problem Generation

Abstract: LLMs have significant potential for generating educational questions and problems, enabling educators to create large-scale learning materials. However, LLMs are fundamentally limited by the ``Artificial Hivemind'' effect, where they generate similar responses within the same model and produce homogeneous outputs across different models. As a consequence, students may be exposed to overly similar and repetitive LLM-generated problems, which harms diversity of thought. Drawing inspiration from Wallas's theory of creativity and Guilford's framework of divergent-convergent thinking, we propose CreativeDC, a two-phase prompting method that explicitly scaffolds the LLM's reasoning into distinct phases. By decoupling creative exploration from constraint satisfaction, our method enables LLMs to explore a broader space of ideas before committing to a final problem. We evaluate CreativeDC for creative problem generation using a comprehensive set of metrics that capture diversity, novelty, and utility. The results show that CreativeDC achieves significantly higher diversity and novelty compared to baselines while maintaining high utility. Moreover, scaling analysis shows that CreativeDC generates a larger effective number of distinct problems as more are sampled, increasing at a faster rate than baseline methods.

• The paper presents CreativeDC, a two-phase mechanism that decouples divergent ideation from convergent constraint satisfaction to enhance creative problem generation.
• It employs persona simulation and iterative selection, achieving up to 72% higher semantic diversity over baseline methods without compromising solution utility.
• The study utilizes lexical and semantic metrics to quantify diversity and novelty, demonstrating the method’s promise for automated educational and creative content generation.

Divergent-Convergent Thinking in LLMs for Creative Problem Generation

Introduction and Motivation

LLMs have achieved proficiency in automatic problem generation for educational applications but are subject to an "Artificial Hivemind" effect, marked by intramodel repetition and intermodel homogeneity. This effect leads to the generation of highly similar, low-diversity problems, even as the underlying models increase in scale and capability. Prior work has established that methods such as naive decoding temperature increases, persona simulation, or contextualized prompting only marginally mitigate this limitation and often fail to fundamentally alter the solution space explored by LLMs [hivemind, DBLP:conf/iclr/LuSHM0HEJCD025].

This paper introduces CreativeDC, a two-phase prompting mechanism for LLM-based creative problem generation. CreativeDC operationalizes Wallas’s theory of staged creativity and Guilford’s framework for divergent–convergent cognitive modes, decoupling unconstrained ideation (divergent thinking) from the phase of constraint satisfaction (convergent thinking). The method thus scaffolds reasoning trajectories in a manner consistent with established human creativity theories, enabling exploration of a broader semantic manifold prior to commitment to a constraint-compliant solution.

Figure 1: CreativeDC employs a two-phase reasoning process—divergent ideation followed by convergent constraint satisfaction—to scaffold creative programming problem generation.

Methodology

CreativeDC decomposes prompt-driven problem generation into distinct divergent and convergent thinking stages. In the divergent phase, the LLM is instructed to enumerate unconventional, thematically relevant entities or situations, eschewing all task constraints. Prompts explicitly reinforce the generation of unorthodox, out-of-distribution ideas (e.g., “list down wildly different and underexplored scenarios relevant to the theme”), thereby suppressing the drive for immediate constraint satisfaction.

In the convergent phase, the model is tasked with selecting a single idea and transforming it into a fully specified problem that meets explicit requirements (e.g., target programming concepts). This step is iterative—the model is instructed to resample from the divergent list if a given idea cannot be reconciled with structural constraints (such as requiring only Python lists).

Persona simulation further augments CreativeDC by inserting a sampled persona description from the Persona Hub dataset into the prompt, leveraging prior results indicating increased output diversity via persona role-play [DBLP:journals/corr/abs-2406-20094].

Evaluation Framework

The effectiveness of CreativeDC is assessed in the domain of programming problem generation along three axes:

• Diversity: Lexical diversity is computed as the ratio of unique $n$-grams to all $n$-grams across a sample, while semantic diversity is the mean pairwise embedding cosine distance within a set of $K$ generated problems.
• Novelty: Lexical novelty measures out-of-corpus $n$-gram rate with a strong in-domain reference set, while semantic novelty uses the average minimal semantic distance to any reference problem.
• Utility: Utility measures aggregated binary indicators for solution validity (test suite correctness), contextual relevance, and comprehensibility.

The primary LLM is Qwen3-235B-A22B-Instruct-2507 [DBLP:journals/corr/abs-2505-09388], semantic metrics employ Qwen3-Embedding-0.6B [DBLP:journals/corr/abs-2506-05176], and utility is standardized using Gemini 2.5 Flash-Lite as an LLM-as-a-judge [DBLP:journals/corr/abs-2507-06261]. CreativeDC and baselines (Base, Chain-of-Thought) are compared on 20 contexts (4 themes $\times$ 5 program concepts) with $K=100$ generations each.

Experimental Results

CreativeDC yields statistically significant improvements in both diversity and novelty relative to all baselines. In the setting without persona simulation, CreativeDC achieves +16.7% higher semantic diversity and +63.5% higher semantic novelty versus the Chain-of-Thought baseline (all $p<0.001$, Mann-Whitney U test). With persona simulation, these advantages are slightly moderated but remain substantial (+8.5% diversity, +32.9% novelty over COT).

Figure 2: Kernel density estimates for per-problem semantic diversity and novelty; CreativeDC shows both higher means and lower variance, indicating reliable creativity improvements.

Notably, CreativeDC induces no statistically significant utility degradation compared to the baselines. This establishes that explicit divergent-convergent scaffolding enhances creative breadth without compromising correctness or contextual adequacy.

Scaling analysis with the Vendi Score [DBLP:journals/tmlr/FriedmanD23] demonstrates that CreativeDC generates a larger effective number of semantically distinct problems as $K$ increases (24.0% higher than COT at $K=10$; 72.0% higher at $K=100$).

Figure 3: Effective number of distinct generated problems (Vendi score) as a function of sample size $K$; CreativeDC advances more rapidly to higher diversity.

Contextual analysis shows that creativity and utility trade off: mundane themes (e.g., "Cooking") yield high utility but limited diversity, while open-ended themes (e.g., "Superheroes") facilitate greater unconstrained creative expressiveness.

Figure 4: Per-context performance breakdown showing that creativity is maximized in open-ended themes and simple programming concepts.

Theoretical and Practical Implications

CreativeDC provides an operational demonstration that explicitly structuring LLM prompting according to psychological models of creativity significantly enhances output originality and effective diversity, supporting the hypothesis that LLM output homogeneity is partially due to premature constraint convergence in standard prompts. As a method, it is modular, requires no model fine-tuning, and can be composed with other generative diversity-inducing interventions (e.g., persona role-play, multi-LLM debate frameworks).

This approach suggests that future LLM evaluation and deployment in creative, open-ended tasks should incorporate explicit cognitive process scaffolding at inference time. The results also highlight limitations of purely surface-driven diversity enhancements—such as temperature sampling—which fail to access novel solution regions without explicit ideation phases [lu2024discussion].

Potential extensions include application to broader creative domains (narrative, poetic, design generation), evaluation with direct human creativity ratings, and adaptation for multistage or multiagent collaborative creativity settings [wen2025explorationvsfixationscaffolding]. There is also scope for model-agnostic adoption, with likely positive transfer to other architectures and scales.

Conclusion

CreativeDC establishes that divergent-convergent scaffolding at the prompt level robustly elevates the creative capacity of LLMs for problem generation, as quantified by both semantic and lexical novelty/diversity metrics, without reduction in deterministic utility. The findings have immediate relevance for the design of automated educational content pipelines and broader creative generation tasks, and motivate further investigation of inference-time reasoning process control to counteract the inherent "hivemind" effect of current LLMs.

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