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The paper proposes a way to route math problems through a tiered self-consistency schedule and to show each tier only the learned prompt "cards" relevant to its difficulty and domain. Its reported gains over Best-of-5 and prior context-engineering baselines (ACE, GEPA) are modest and come from benchmark results on MATH-HARD, AIME 2025, and OlymMATH-EN. Readers should note that these are single-benchmark comparisons, and the component ablations are the more transferable part: they suggest that partitioning learned knowledge can matter as much as how much inference compute is spent.
KACE: Knowledge-Adaptive Context Engineering for Mathematical Reasoning
arXiv:2606.00532v2 Announce Type: replace Abstract: Context-engineering methods improve a frozen language model by learning text from execution feedback and placing it in the prompt. When one learned prompt carries everything that was learned, irrelevant lessons compete with relevant ones, and the system can keep only what fits in that prompt. We present Knowledge-Adaptive Context Engineering (KACE), which decides per problem both how much inference to spend and which learned knowledge to show. A fixed tiered self-consistency schedule (2, 3, then 5 samples behind agreement gates) lets easy problems exit after two agreeing samples, and the tier at which a problem exits serves as its difficulty label. Offline, a teacher-guided learner distills failed training traces into short typed cards kept in a store partitioned by difficulty tier and domain, and each escalated tier reads only the cards of its (tier, domain) cell. On MATH-HARD, KACE reaches 77.3% against 72.7% for Best-of-5 self-consistency with fewer solver calls, and it scores above tiered ACE (70.0%) and tiered GEPA (72.0%). It also achieves the highest accuracy on AIME 2025 (61.1% against 53.3% for Best-of-5 and 57.8% for tiered GEPA) and on OlymMATH-EN (48.1%). A component analysis shows that the store adds 4.0 points on MATH-HARD and 3.7 on OlymMATH-EN over the tiered schedule alone, and that the (tier, domain) reading rule outperforms every alternative rule for choosing cards from the same store.
Abstract:Context-engineering methods improve a frozen language model by learning text from execution feedback and placing it in the prompt. When one learned prompt carries everything that was learned, irrelevant lessons compete with relevant ones, and the system can keep only what fits in that prompt. We present Knowledge-Adaptive Context Engineering (KACE), which decides per problem both how much inference to spend and which learned knowledge to show. A fixed tiered self-consistency schedule (2, 3, then 5 samples behind agreement gates) lets easy problems exit after two agreeing samples, and the tier at which a problem exits serves as its difficulty label. Offline, a teacher-guided learner distills failed training traces into short typed cards kept in a store partitioned by difficulty tier and domain, and each escalated tier reads only the cards of its (tier, domain) cell. On MATH-HARD, KACE reaches 77.3% against 72.7% for Best-of-5 self-consistency with fewer solver calls, and it scores above tiered ACE (70.0%) and tiered GEPA (72.0%). It also achieves the highest accuracy on AIME 2025 (61.1% against 53.3% for Best-of-5 and 57.8% for tiered GEPA) and on OlymMATH-EN (48.1%). A component analysis shows that the store adds 4.0 points on MATH-HARD and 3.7 on OlymMATH-EN over the tiered schedule alone, and that the (tier, domain) reading rule outperforms every alternative rule for choosing cards from the same store.
Artificial Intelligence (cs.AI)
arXiv:2606.00532 [cs.AI]
(or arXiv:2606.00532v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.00532 Focus to learn more arXiv-issued DOI via DataCite
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