# Circuit Distillation

arXiv: https://arxiv.org/abs/2509.25002 · HTML: https://mlsanity.com/paper/2509.25002/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Evaluating Large Language Models in Theory of Mind Tasks](https://mlsanity.com/paper/2302.02083/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Clever Hans or Neural Theory of Mind? Stress Testing Social Reasoning in Large Language Models](https://mlsanity.com/paper/2305.14763/) (2023)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [How do Language Models Bind Entities in Context?](https://mlsanity.com/paper/2310.17191/) (2023)
- [MMToM-QA: Multimodal Theory of Mind Question Answering](https://mlsanity.com/paper/2401.08743/) (2024)
- [Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks](https://mlsanity.com/paper/2305.14201/) (2023)
- [OpenToM: A Comprehensive Benchmark for Evaluating Theory-of-Mind Reasoning Capabilities of Large Language Models](https://mlsanity.com/paper/2402.06044/) (2024)
- [NegotiationToM: A Benchmark for Stress-testing Machine Theory of Mind on Negotiation Surrounding](https://mlsanity.com/paper/2404.13627/) (2024)
- [Entity Tracking in Language Models](https://mlsanity.com/paper/2305.02363/) (2023)
- [Language Models use Lookbacks to Track Beliefs](https://mlsanity.com/paper/2505.14685/) (2025)
- [Language Models Represent Beliefs of Self and Others](https://mlsanity.com/paper/2402.18496/) (2024)
- [Hypothesis Testing the Circuit Hypothesis in LLMs](https://mlsanity.com/paper/2410.13032/) (2024)
- [Investigating Mysteries of CoT-Augmented Distillation](https://mlsanity.com/paper/2406.14511/) (2024)
- [Self-Knowledge Distillation for Learning Ambiguity](https://mlsanity.com/paper/2406.09719/) (2024)

## Abstract (arXiv)

Model distillation typically focuses on behavioral mimicry, where a student model is trained to replicate a teacher's output while treating its internal computations as a black box. In this work we propose an alternative approach: Distilling the underlying computational mechanisms implemented by a teacher model. Specifically, we propose circuit distillation, which introduces an objective to align internal representations between analogous circuit components in teacher and student models. We propose a method to match ``functionally correspondent'' circuit components and introduce a loss reflecting similarities between the representations that these induce. We evaluate circuit distillation on entity tracking and theory of mind (ToM) tasks using models from the Llama3 family. Our results demonstrate that circuit distillation outperforms standard distillation, successfully transferring algorithmic capabilities by adjusting only a small, targeted subset of student model parameters. This work establishes the feasibility of transferring mechanisms, which may in turn allow for efficient distillation of targeted teacher capabilities via interpretable and controllable internal student mechanisms.