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

2025-05-08

AI Summary

Addressing the dual challenges in large language model (LLM) interpretability—namely, the difficulty of attributing downstream predictions to pretraining data and the inability of existing influence functions to support multi-stage modeling and billion-parameter scalability—this work proposes the first multi-stage influence function framework, enabling cross-stage causal attribution from downstream predictions back to pretraining samples. Methodologically, we introduce eigenvalue-corrected Kronecker-factored Approximate Curvature (EK-FAC) to efficiently approximate the Hessian, facilitating full-parameter fine-tuning–compatible influence computation across multiple training stages. Theoretically and empirically, EK-FAC scales to models with tens of billions of parameters. Evaluations on Dolly-V2-3B demonstrate substantial improvements over baselines in both attribution accuracy and computational efficiency. The framework is open-sourced to enable large-scale influence analysis.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Attributing fine-tuned LLM predictions to pre-training data
• Scaling influence functions for billion-parameter LLMs
• Efficient approximation via EK-FAC parameterization

Innovation

• Multi-stage influence function for LLM predictions
• EK-FAC parameterization for efficient approximation
• Scalable attribution to pre-training data