Reasoning Large Language Model Errors Arise from Hallucinating Critical Problem Features

Large language models have recently made great strides in reasoning task performance through chain-of-thought (CoT) strategies trained via reinforcement learning; however, these "reasoning large language models" (RLLMs) remain imperfect reasoners, and understanding the frequencies and causes of their failure modes is important for both users and developers. We test o1-mini, o3-mini, DeepSeek-R1, Claude 3.7 Sonnet, Gemini 2.5 Pro Preview, and Grok 3 Mini Beta on graph coloring as a variable-complexity constraint-satisfaction logic problem, and find evidence from both error rate comparisons and CoT/explanation text analysis that RLLMs are prone to hallucinate edges not specified in the prompt's description of the graph. This phenomenon persists across multiple problem complexity levels and semantic frames, and it appears to account for a significant fraction of the incorrect answers from every tested model, and the vast majority of them for some models. Our results indicate that RLLMs may possess broader issues with misrepresentation of problem specifics, and we offer suggestions for design choices to mitigate this weakness.

Evaluating the Systematic Reasoning Abilities of Large Language Models through Graph Coloring

Contemporary large language models are powerful problem-solving tools, but they exhibit weaknesses in their reasoning abilities which ongoing research seeks to mitigate. We investigate graph coloring as a means of evaluating an LLM's capacities for systematic step-by-step reasoning and possibility space exploration, as well as effects of semantic problem framing. We test Claude 3.5 Sonnet, Llama 3.1 405B, Gemini 1.5 Pro, GPT-4o, o1-mini, and DeepSeek-R1 on a dataset of $k$-coloring problems with $2 \leq k \leq 4$ and vertex count $4 \leq n \leq 8$, using partial algorithmic solvers to further categorize problems by difficulty. In addition to substantial but varying framing effects, we find that all models except o1-mini and R1 exhibit $>60\%$ error rates on difficult problem types in all frames ($>15\%$ for o1-mini and $>10\%$ for R1), and no model achieves perfect accuracy even in the simple domain of 2-coloring 4-vertex graphs. Our results highlight both the considerable recent progress in LLM systematic reasoning and the limits of its reliability, especially in relation to increasing computational costs. We expect that more complex graph coloring problems, and procedural generation of arbitrary-complexity reasoning problems more broadly, offer further untapped potential for LLM benchmarking.