# Scalable Multi-Stage Influence Function for Large Language Models via Eigenvalue-Corrected Kronecker-Factored Parameterization

arXiv: https://arxiv.org/abs/2505.05017 · HTML: https://mlsanity.com/paper/2505.05017/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [Input Similarity from the Neural Network Perspective](https://mlsanity.com/paper/2102.05262/) (2021)
- [Kronecker-Factored Approximate Curvature for Modern Neural Network Architectures](https://mlsanity.com/paper/2311.00636/) (2023)
- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [Towards Tracing Factual Knowledge in Language Models Back to the Training Data](https://mlsanity.com/paper/2205.11482/) (2022)
- [Multi-Stage Influence Function](https://mlsanity.com/paper/2007.09081/) (2020)

## Abstract (arXiv)

Pre-trained large language models (LLMs) are commonly fine-tuned to adapt to downstream tasks. Since the majority of knowledge is acquired during pre-training, attributing the predictions of fine-tuned LLMs to their pre-training data may provide valuable insights. Influence functions have been proposed as a means to explain model predictions based on training data. However, existing approaches fail to compute ``multi-stage'' influence and lack scalability to billion-scale LLMs. In this paper, we propose the multi-stage influence function to attribute the downstream predictions of fine-tuned LLMs to pre-training data under the full-parameter fine-tuning paradigm. To enhance the efficiency and practicality of our multi-stage influence function, we leverage Eigenvalue-corrected Kronecker-Factored (EK-FAC) parameterization for efficient approximation. Empirical results validate the superior scalability of EK-FAC approximation and the effectiveness of our multi-stage influence function. Additionally, case studies on a real-world LLM, dolly-v2-3b, demonstrate its interpretive power, with exemplars illustrating insights provided by multi-stage influence estimates. Our code is public at https://github.com/colored-dye/multi_stage_influence_function.