Title: KACE: Knowledge-Adaptive Context Engineering for Mathematical Reasoning

Abstract:

While context engineering offers a method to enhance large language models without requiring weight updates, mathematical reasoning tasks reveal a significant bottleneck: the accumulation of feedback within an expanding prompt leads to context bloat, thereby restricting the volume of learned guidance that can be effectively utilized. Current approaches frequently fail to distinguish between storage (knowledge acquired across multiple sessions) and usage (information included for specific problems), resulting in an inherent limitation on prompt size. To address this, we propose Knowledge-Adaptive Context Engineering (KACE), a framework that decouples storage from usage by organizing information according to domain and difficulty levels.

During the offline phase, a self-reflective learning loop condenses training traces into an epistemic tree, which serves as a knowledge base composed of typed cards. These cards are categorized by their originating problem’s difficulty and epistemic domain. At the evaluation stage, a tiered self-consistency mechanism with per-tier agreement gates dynamically categorizes each problem into easy, medium, or hard tiers. Easy problems bypass the retrieval of cards entirely, whereas more challenging problems access only the relevant branch of the epistemic tree. This hierarchical approach not only matches or outperforms Best-of-N methods but does so with similar computational costs, while achieving a 78 percent pairwise concordance in difficulty classification.

The primary empirical contribution of this work is the development and application of a knowledge base stratified by difficulty and domain, facilitated by tiered self-consistency. On the AIME 2025 benchmark, KACE secured a 62.2 percent accuracy rate. This represents an absolute improvement of 10.4 points over fixed Best-of-5 self-consistency, given a comparable budget of solver calls, and a 5.6-point advantage over the leading learned-context baseline, Tiered + GEPA. Additionally, the method demonstrates consistent performance improvements on the MATH-HARD dataset and the verifiable subset of OlymMATH.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC