Exploring Efficiency Frontiers of Thinking Budget in Medical Reasoning: Scaling Laws between Computational Resources and Reasoning Quality

This study presents the first comprehensive evaluation of thinking budget mechanisms in medical reasoning tasks, revealing fundamental scaling laws between computational resources and reasoning quality. We systematically evaluated two major model families, Qwen3 (1.7B to 235B parameters) and DeepSeek-R1 (1.5B to 70B parameters), across 15 medical datasets spanning diverse specialties and difficulty levels. Through controlled experiments with thinking budgets ranging from zero to unlimited tokens, we establish logarithmic scaling relationships where accuracy improvements follow a predictable pattern with both thinking budget and model size. Our findings identify three distinct efficiency regimes: high-efficiency (0 to 256 tokens) suitable for real-time applications, balanced (256 to 512 tokens) offering optimal cost-performance tradeoffs for routine clinical support, and high-accuracy (above 512 tokens) justified only for critical diagnostic tasks. Notably, smaller models demonstrate disproportionately larger benefits from extended thinking, with 15 to 20% improvements compared to 5 to 10% for larger models, suggesting a complementary relationship where thinking budget provides greater relative benefits for capacity-constrained models. Domain-specific patterns emerge clearly, with neurology and gastroenterology requiring significantly deeper reasoning processes than cardiovascular or respiratory medicine. The consistency between Qwen3 native thinking budget API and our proposed truncation method for DeepSeek-R1 validates the generalizability of thinking budget concepts across architectures. These results establish thinking budget control as a critical mechanism for optimizing medical AI systems, enabling dynamic resource allocation aligned with clinical needs while maintaining the transparency essential for healthcare deployment.