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📄 Research Article

Cognitive Agent Compilation for Explicit Problem Solver Modeling

◐ medium · 2026-05-11intelligent-tutoring, llm, adaptive-learning, personalized-learning, pedagogical-llm-training, adaptive-learning-systems, rag, ai-tutoring

Core Idea

Cognitive Agent Compilation (CAC) is a framework that uses a strong teacher LLM to compile problem-solving knowledge into an explicit, inspectable target agent. Unlike end-to-end LLM tutoring approaches, CAC separates the agent into three components:

1. Knowledge representation — explicit, structured representation of domain knowledge (skills, misconceptions, strategies)

2. Problem-solving policy — how the agent applies knowledge to solve problems

3. Verification and update rules — mechanisms for checking correctness and updating the knowledge state

The goal is bounded-knowledge AI for education: agents that know what they know, can explain their reasoning in terms of explicit skills, and can be inspected and edited by educators.

Motivation

LLMs are widely used for tutoring, feedback generation, and content creation, but their broad pretraining makes them hard to constrain. Key problems:

  • Inability to "not know": LLMs struggle to simulate a state of not knowing, making them poor proxies for student learners. Evidence suggests Chain-of-Thought and reasoning models operate fundamentally differently from human cognition.
  • Expert blind spot: Even human experts struggle to teach effectively without pedagogical training. LLMs, having absorbed vast unconstrained information, face an amplified version of this problem.
  • Inspectability gap: Educators need to know what a system assumes the learner knows; learners benefit when the system can justify actions in terms of explicit skills, misconceptions, and strategies. Opaque LLMs can't provide this.

    • Architecture

    CAC draws inspiration from cognitive architectures (ACT-R, SOAR) and compiles LLM knowledge into explicit, inspectable agents. The three separable components enable:

  • Inspectability: Educators can examine the knowledge representation and problem-solving policy directly
  • Editability: Knowledge states can be corrected or refined without retraining
  • Bounded reasoning: The agent operates within explicit knowledge boundaries rather than leveraging unbounded pretraining

    • A proof of concept was implemented using Small Language Models (SLMs), surfacing key design trade-offs between explicit control and scalable generalization.

    Connection to Existing Work

    CAC connects to several threads in AI education research:

  • Knowledge Tracing IRT: CAC makes knowledge tracing explicit and inspectable, complementing interpretable approaches like IRT-based knowledge tracing
  • Neural Symbolic Knowledge Tracing: Shares the goal of combining explicit (symbolic) knowledge representation with neural approaches for interpretable learner modeling
  • Agentic Workflows Education: CAC is a specific agentic architecture for education, separated into knowledge, policy, and verification components
  • Adaptive Learning: CAC enables adaptive behavior grounded in explicit, editable learner models
  • LLM Student Modeling Memory: CAC addresses the learner modeling challenge from the knowledge representation angle, complementing memory-based approaches
  • Pedagogical LLM Training: CAC offers an alternative to training pipelines — compile rather than train for pedagogical alignment
  • Personalized Learning: Explicit learner models in CAC enable personalization that is inspectable and editable by educators
  • Prober AI Inquiry Writing: Both approach bounded-knowledge tutoring from different angles — CAC via compilation, Prober via inverted questioning

    • Open Questions

  • Scalability vs. control trade-off: The proof of concept surfaces tension between explicit, editable representations and the scalability of end-to-end LLM approaches
  • Compilation fidelity: How faithfully can a teacher LLM compile its knowledge into a bounded agent?
  • Domain breadth: The initial implementation is domain-specific — can CAC generalize across subjects?
  • Bounded rationality in practice: Does bounded-knowledge AI actually improve educational outcomes compared to unbounded LLM tutors?

    • Connected Concepts

  • Adaptive Learning
  • Pedagogical LLM Training
  • Personalized Learning

    • Connected Articles

  • Knowledge Tracing IRT
  • Neural Symbolic Knowledge Tracing
  • Agentic Workflows Education
  • LLM Student Modeling Memory
  • Prober AI Inquiry Writing

    • Citation

    Moon, H., Rosé, C., & Stamper, J. (2026). Cognitive Agent Compilation for Explicit Problem Solver Modeling. arXiv:2605.07040. Accepted to AIED 2026 Blue Sky.