# Revisiting the Fragility of Influence Functions

arXiv: https://arxiv.org/abs/2303.12922 · HTML: https://mlsanity.com/paper/2303.12922/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [Three Mechanisms of Weight Decay Regularization](https://mlsanity.com/paper/1810.12281/) (2018)
- [On Second-Order Group Influence Functions for Black-Box Predictions](https://mlsanity.com/paper/1911.00418/) (2019)
- [Detecting Adversarial Samples Using Influence Functions and Nearest Neighbors](https://mlsanity.com/paper/1909.06872/) (2019)
- [On Model Stability as a Function of Random Seed](https://mlsanity.com/paper/1909.10447/) (2019)
- [Negative eigenvalues of the Hessian in deep neural networks](https://mlsanity.com/paper/1902.02366/) (2019)
- [Self-Compression in Bayesian Neural Networks](https://mlsanity.com/paper/2111.05950/) (2021)

## Built on by (most cited first, 20 of 20)

- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [A Bayesian Approach To Analysing Training Data Attribution In Deep Learning](https://mlsanity.com/paper/2305.19765/) (2023)
- [Better Training Data Attribution via Better Inverse Hessian-Vector Products](https://mlsanity.com/paper/2507.14740/) (2025)
- [Deeper Understanding of Black-box Predictions via Generalized Influence Functions](https://mlsanity.com/paper/2312.05586/) (2023)
- [Building Flexible, Scalable, and Machine Learning-ready Multimodal Oncology Datasets](https://mlsanity.com/paper/2310.01438/) (2023)
- [Towards User-Focused Research in Training Data Attribution for Human-Centered Explainable AI](https://mlsanity.com/paper/2409.16978/) (2024)
- [DMin: Scalable Training Data Influence Estimation for Diffusion Models](https://mlsanity.com/paper/2412.08637/) (2024)
- [Better Hessians Matter: Studying the Impact of Curvature Approximations in Influence Functions](https://mlsanity.com/paper/2509.23437/) (2025)
- [Influence-based Attributions can be Manipulated](https://mlsanity.com/paper/2409.05208/) (2024)
- [Aggregation Hides Out-of-Distribution Generalization Failures from Spurious Correlations](https://mlsanity.com/paper/2510.24884/) (2025)
- [AIDE: Antithetical, Intent-based, and Diverse Example-Based Explanations](https://mlsanity.com/paper/2407.16010/) (2024)
- [IMU: Influence-guided Machine Unlearning](https://mlsanity.com/paper/2508.01620/) (2025)
- [PARIS: Pruning Algorithm via the Representer theorem for Imbalanced Scenarios](https://mlsanity.com/paper/2512.06950/) (2025)
- [Training data attribution in diffusion models via mirrored unlearning and noise-consistent skew](https://mlsanity.com/paper/2605.17938/) (2026)
- [DRIFT: Data Selection for LLM Instruction Tuning via On-Policy Attribution](https://mlsanity.com/paper/2606.18307/) (2026)
- [Deployment of a Robust and Explainable Mortality Prediction Model: The COVID-19 Pandemic and Beyond](https://mlsanity.com/paper/2311.17133/) (2023)
- [Salutary Labeling with Zero Human Annotation](https://mlsanity.com/paper/2405.17627/) (2024)
- [What Is The Performance Ceiling of My Classifier? Utilizing Category-Wise Influence Functions for Pareto Frontier Analysis](https://mlsanity.com/paper/2510.03950/) (2025)
- [Adaptive Data Selection for Multi-Layer Perceptron Training: A Sub-linear Value-Driven Method](https://mlsanity.com/paper/2510.21286/) (2025)
- [Divide and Predict: An Architecture for Input Space Partitioning and Enhanced Accuracy](https://mlsanity.com/paper/2603.08649/) (2026)

## Abstract (arXiv)

In the last few years, many works have tried to explain the predictions of deep learning models. Few methods, however, have been proposed to verify the accuracy or faithfulness of these explanations. Recently, influence functions, which is a method that approximates the effect that leave-one-out training has on the loss function, has been shown to be fragile. The proposed reason for their fragility remains unclear. Although previous work suggests the use of regularization to increase robustness, this does not hold in all cases. In this work, we seek to investigate the experiments performed in the prior work in an effort to understand the underlying mechanisms of influence function fragility. First, we verify influence functions using procedures from the literature under conditions where the convexity assumptions of influence functions are met. Then, we relax these assumptions and study the effects of non-convexity by using deeper models and more complex datasets. Here, we analyze the key metrics and procedures that are used to validate influence functions. Our results indicate that the validation procedures may cause the observed fragility.