KACE: Knowledge-Adaptive Context Engineering for Mathematical Reasoning

Researchers introduce KACE, a novel context engineering method that improves large language models' mathematical reasoning by separating knowledge storage from usage through difficulty and domain-based organization. The approach achieves 62.2% accuracy on AIME 2025, significantly outperforming existing self-consistency methods while maintaining comparable computational efficiency.

KACE represents a meaningful advancement in prompt engineering for mathematical problem-solving by addressing a fundamental inefficiency in how language models learn from feedback. Traditional context engineering accumulates guidance in a single growing prompt, creating bloat that reduces effectiveness—a constraint that limits how much learned information can be practically applied. The researchers' key insight is treating storage and usage as separate concerns, allowing a knowledge base to be built offline while retrieval during inference adapts dynamically to problem difficulty.

The technical approach employs a self-reflective learning loop that distills training traces into an epistemic tree, a structured knowledge base organized by problem difficulty and domain. This hierarchical organization enables tiered self-consistency at evaluation time, where each problem is classified as easy, medium, or hard through agreement-gated mechanisms. Easy problems bypass costly retrieval entirely, while harder problems access only relevant knowledge branches, reducing both prompt size and computational overhead.

The empirical results demonstrate substantial practical value. On AIME 2025, KACE achieves a 10.4-point absolute improvement over Best-of-5 self-consistency with comparable solver calls, and a 5.6-point gain over the previous strongest learned-context baseline. The 78% pairwise concordance in difficulty classification suggests the method reliably identifies problem complexity, enabling efficient knowledge routing.

For AI researchers and practitioners, KACE demonstrates that intelligent retrieval strategies can extract more value from limited context windows—a critical constraint as models tackle more complex reasoning tasks. The separation of storage from usage creates a generalizable framework applicable beyond mathematics, potentially improving performance in law, coding, and science domains where structured knowledge organization could enhance reasoning.

• →KACE separates knowledge storage from usage through difficulty- and domain-based organization, solving context bloat limitations in prompt engineering.
• →The method achieves 62.2% accuracy on AIME 2025, a 10.4-point improvement over Best-of-5 self-consistency at comparable computational cost.
• →Tiered self-consistency dynamically classifies problem difficulty with 78% pairwise concordance, enabling efficient knowledge retrieval.
• →Easy problems bypass knowledge retrieval entirely while harder problems access only matching knowledge branches, reducing prompt size overhead.
• →The epistemic tree framework creates a generalizable architecture applicable across mathematical reasoning, coding, law, and scientific domains.