KACE: Knowledge-Adaptive Context Engineering for Mathematical Reasoning
Summary
Knowledge-Adaptive Context Engineering (KACE) addresses the context bloat limitation in large language models performing mathematical reasoning by separating knowledge storage from usage. Unlike existing methods that conflate these aspects, KACE organizes learned guidance through difficulty- and domain-based stratification. Offline, a self-reflective learning loop constructs an "epistemic tree," a knowledge base of typed cards categorized by problem difficulty and epistemic domain, based on failure origins. During evaluation, a tiered self-consistency mechanism dynamically classifies problems as easy, medium, or hard using per-tier agreement gates. Easy problems are solved directly, while harder problems retrieve relevant branches from the epistemic tree. This approach achieves 62.2% accuracy on AIME 2025, representing a 10.4-point absolute gain over fixed Best-of-5 self-consistency and a 5.6-point gain over Tiered + GEPA, both at comparable solver-call budgets. KACE also shows consistent gains on MATH-HARD and OlymMATH, classifying problem difficulty with 78% pairwise concordance.
Key takeaway
For Machine Learning Engineers developing LLMs for mathematical reasoning, if you are struggling with context bloat and performance ceilings, KACE provides a robust solution. By separating knowledge storage from usage and dynamically retrieving difficulty- and domain-specific guidance, your models can achieve substantial accuracy gains, such as the 10.4-point increase observed on AIME 2025. You should explore implementing a tiered self-consistency and epistemic tree approach to enhance your model's problem-solving capabilities.
Key insights
KACE improves mathematical reasoning in LLMs by adaptively retrieving knowledge from a difficulty- and domain-stratified epistemic tree.
Principles
- Separate knowledge storage from usage.
- Stratify knowledge by difficulty and domain.
- Use self-reflection to build knowledge bases.
Method
KACE uses an offline self-reflective loop to build an epistemic tree of typed cards. At evaluation, tiered self-consistency classifies problem difficulty to retrieve matching knowledge branches.
In practice
- Implement tiered self-consistency for problem classification.
- Organize learned context into domain-specific trees.
- Distill training traces into failure-based knowledge cards.
Topics
- Context Engineering
- Mathematical Reasoning
- Large Language Models
- Knowledge Bases
- Self-Consistency
- Epistemic Tree
Best for: AI Engineer, Research Scientist, AI Scientist, Machine Learning Engineer, NLP Engineer
Related on AIssential
Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.