Circuit-Level Knowledge Distillation for Large Language Models

Existing knowledge distillation methods supervise only *what* a student outputs, leaving *how* it computes those outputs unconstrained, so students may match teacher behavior through entirely different internal mechanisms. We propose **Meta Circuit Distillation (MCD)**, which reframes distillation as the explicit transfer of reasoning circuits, the structured computational pathways uncovered by mechanistic interpretability. MCD represents each model's computation as a transcoder-based attribution graph and aligns teacher and student circuits via an optimal-transport pathway-matching loss that plugs into any standard distillation pipeline. We prove that minimizing this loss bounds the discrepancy in MLP-level computation between teacher and student. Across two model families, six distillation objectives, and three instruction-following benchmarks, MCD delivers consistent improvements that transfer to mathematical reasoning, with the largest gains under aggressive compression.