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Influence functions (IFs) elucidate how training data changes model behavior. However, the increasing size and non-convexity in large-scale models make IFs inaccurate. We suspect that the fragility comes from the first-order approximation…

Machine Learning · Computer Science 2024-05-07 Hyeonsu Lyu , Jonggyu Jang , Sehyun Ryu , Hyun Jong Yang

How does the training data affect a model's behavior? This is the question we seek to answer with data attribution. The leading practical approaches to data attribution are based on influence functions (IF). IFs utilize a first-order Taylor…

Machine Learning · Computer Science 2025-09-11 Ittai Rubinstein , Samuel B. Hopkins

The Influence Function (IF) is a widely used technique for assessing the impact of individual training samples on model predictions. However, existing IF methods often fail to provide reliable influence estimates in deep neural networks,…

Machine Learning · Computer Science 2025-12-02 Xichen Ye , Yifan Wu , Weizhong Zhang , Cheng Jin , Yifan Chen

Influence functions approximate the "influences" of training data-points for test predictions and have a wide variety of applications. Despite the popularity, their computational cost does not scale well with model and training data size.…

Machine Learning · Computer Science 2021-09-13 Han Guo , Nazneen Fatema Rajani , Peter Hase , Mohit Bansal , Caiming Xiong

How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data,…

Machine Learning · Statistics 2021-01-01 Pang Wei Koh , Percy Liang

Diffusion models have led to significant advancements in generative modelling. Yet their widespread adoption poses challenges regarding data attribution and interpretability. In this paper, we aim to help address such challenges in…

Machine Learning · Computer Science 2025-05-27 Bruno Mlodozeniec , Runa Eschenhagen , Juhan Bae , Alexander Immer , David Krueger , Richard Turner

Influence functions (IF) have been seen as a technique for explaining model predictions through the lens of the training data. Their utility is assumed to be in identifying training examples "responsible" for a prediction so that, for…

Machine Learning · Computer Science 2023-05-29 Andrea Schioppa , Katja Filippova , Ivan Titov , Polina Zablotskaia

Influence functions offer a principled way to trace model predictions back to training data, but their use in deep learning is hampered by the need to invert a large, ill-conditioned Hessian matrix. Approximations such as Generalised…

Machine Learning · Computer Science 2026-02-17 Steve Hong , Runa Eschenhagen , Bruno Mlodozeniec , Richard Turner

Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…

Methodology · Statistics 2019-10-29 Aaron Fisher , Edward H. Kennedy

Influence functions serve as crucial tools for assessing sample influence in model interpretation, subset training set selection, noisy label detection, and more. By employing the first-order Taylor extension, influence functions can…

Machine Learning · Computer Science 2026-03-27 Ziao Yang , Han Yue , Jian Chen , Hongfu Liu

Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current…

Machine Learning · Computer Science 2024-06-21 Myeongseob Ko , Feiyang Kang , Weiyan Shi , Ming Jin , Zhou Yu , Ruoxi Jia

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…

Machine Learning · Computer Science 2026-04-06 Subhodip Panda , Dhruv Tarsadiya , Shashwat Sourav , Prathosh A. P , Sai Praneeth Karimireddy

Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However,…

Machine Learning · Computer Science 2025-08-21 Haoru Tan , Sitong Wu , Xiuzhe Wu , Wang Wang , Bo Zhao , Zeke Xie , Gui-Song Xia , Xiaojuan Qi

Influence functions (IFs) are a powerful tool for detecting anomalous examples in large scale datasets. However, they are unstable when applied to deep networks. In this paper, we provide an explanation for the instability of IFs and…

Computation and Language · Computer Science 2023-05-03 Thang Nguyen-Duc , Hoang Thanh-Tung , Quan Hung Tran , Dang Huu-Tien , Hieu Ngoc Nguyen , Anh T. V. Dau , Nghi D. Q. Bui

With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test…

Machine Learning · Computer Science 2020-07-08 Samyadeep Basu , Xuchen You , Soheil Feizi

Influence functions approximate the effect of training samples in test-time predictions and have a wide variety of applications in machine learning interpretability and uncertainty estimation. A commonly-used (first-order) influence…

Machine Learning · Computer Science 2021-02-12 Samyadeep Basu , Philip Pope , Soheil Feizi

Influence functions estimate the effect of removing a training point on a model without the need to retrain. They are based on a first-order Taylor approximation that is guaranteed to be accurate for sufficiently small changes to the model,…

Machine Learning · Computer Science 2019-11-22 Pang Wei Koh , Kai-Siang Ang , Hubert H. K. Teo , Percy Liang

Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing…

Machine Learning · Computer Science 2025-06-27 Xinyu Zhou , Simin Fan , Martin Jaggi

Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an…

Machine Learning · Computer Science 2026-03-03 Philipp Alexander Kreer , Wilson Wu , Maxwell Adam , Zach Furman , Jesse Hoogland

Parameter estimation in empirical fields is usually undertaken using parametric models, and such models readily facilitate statistical inference. Unfortunately, they are unlikely to be sufficiently flexible to be able to adequately model…

Machine Learning · Computer Science 2022-06-13 Matthew J. Vowels , Sina Akbari , Necati Cihan Camgoz , Richard Bowden
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