# f-INE: A Hypothesis Testing Framework for Estimating Influence under Training Randomness

arXiv: https://arxiv.org/abs/2510.10510 · HTML: https://mlsanity.com/paper/2510.10510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [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)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [What makes ImageNet good for transfer learning?](https://mlsanity.com/paper/1608.08614/) (2016)
- [Backdooring Instruction-Tuned Large Language Models with Virtual Prompt Injection](https://mlsanity.com/paper/2307.16888/) (2023)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [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)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Privacy Auditing with One (1) Training Run](https://mlsanity.com/paper/2305.08846/) (2023)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [Auditing Black-box Models for Indirect Influence](https://mlsanity.com/paper/1602.07043/) (2016)
- [Revisiting Methods for Finding Influential Examples](https://mlsanity.com/paper/2111.04683/) (2021)
- [Efficient computation and analysis of distributional Shapley values](https://mlsanity.com/paper/2007.01357/) (2020)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)

## Abstract (arXiv)

Influence estimation methods promise to explain and debug machine learning by estimating the impact of individual samples on the final model. Yet, existing methods collapse under training randomness: the same example may appear critical in one run and irrelevant in the next. Such instability undermines their use in data curation or cleanup since it is unclear if we indeed deleted/kept the correct datapoints. To overcome this, we introduce *f-influence* -- a new influence estimation framework grounded in hypothesis testing that explicitly accounts for training randomness, and establish desirable properties that make it suitable for reliable influence estimation. We also design a highly efficient algorithm **f**-**IN**fluence **E**stimation (**f-INE**) that computes f-influence **in a single training run**. Finally, we scale up f-INE to estimate influence of instruction tuning data on Llama-3.1-8B and show it can reliably detect poisoned samples that steer model opinions, demonstrating its utility for data cleanup and attributing model behavior.