# Fine-Tuning is Subgraph Search: A New Lens on Learning Dynamics

arXiv: https://arxiv.org/abs/2502.06106 · HTML: https://mlsanity.com/paper/2502.06106/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Gender Bias in Coreference Resolution: Evaluation and Debiasing Methods](https://mlsanity.com/paper/1804.06876/) (2018)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [AI Alignment: A Comprehensive Survey](https://mlsanity.com/paper/2310.19852/) (2023)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)

## Built on by (most cited first, 3 of 3)

- [Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Models](https://mlsanity.com/paper/2601.14004/) (2026)
- [Constructive Circuit Amplification: Improving Math Reasoning in LLMs via Targeted Sub-Network Updates](https://mlsanity.com/paper/2512.16914/) (2025)
- [Beyond Transfer Accuracy: Mechanism-Guided Controlled Adaptation for Low-Resource Languages](https://mlsanity.com/paper/2601.08146/) (2026)

## Abstract (arXiv)

The study of mechanistic interpretability aims to reverse-engineer a model to explain its behaviors. While recent studies have focused on the static mechanism of a certain behavior, the learning dynamics inside a model remain to be explored. In this work, we develop a fine-tuning method for analyzing the mechanism behind learning. Inspired by the concept of intrinsic dimension, we view a model as a computational graph with redundancy for a specific task, and treat the fine-tuning process as a search for and optimization of a subgraph within this graph. Based on this hypothesis, we propose circuit-tuning, an algorithm that iteratively builds the subgraph for a specific task and updates the relevant parameters in a heuristic way. We first validate our hypothesis through a carefully designed experiment and provide a detailed analysis of the learning dynamics during fine-tuning. Subsequently, we conduct experiments on more complex tasks, demonstrating that circuit-tuning could strike a balance between the performance on the target task and the general capabilities. Our work offers a new analytical method for the dynamics of fine-tuning, provides new findings on the mechanisms behind the training process, and inspires the design of superior algorithms for the training of neural networks.