# An Information Theoretic Evaluation Metric For Strong Unlearning

arXiv: https://arxiv.org/abs/2405.17878 · HTML: https://mlsanity.com/paper/2405.17878/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 28 May 2024.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)

## Built on by (most cited first, 11 of 11)

- [Are We Truly Forgetting? A Critical Re-examination of Machine Unlearning Evaluation Protocols](https://mlsanity.com/paper/2503.06991/) (2025)
- [Towards Reliable Forgetting: A Survey on Machine Unlearning Verification](https://mlsanity.com/paper/2506.15115/) (2025)
- [Erase at the Core: Representation Unlearning for Machine Unlearning](https://mlsanity.com/paper/2602.05375/) (2026)
- [DUSK: Do Not Unlearn Shared Knowledge](https://mlsanity.com/paper/2505.15209/) (2025)
- [Unlearning Comparator: A Visual Analytics System for Comparative Evaluation of Machine Unlearning Methods](https://mlsanity.com/paper/2508.12730/) (2025)
- [An Illusion of Unlearning? Assessing Machine Unlearning Through Internal Representations](https://mlsanity.com/paper/2604.08271/) (2026)
- [Auditing Language Model Unlearning via Information Decomposition](https://mlsanity.com/paper/2601.15111/) (2026)
- [Efficient Machine Unlearning by Model Splitting and Core Sample Selection](https://mlsanity.com/paper/2505.07026/) (2025)
- [Do Vision Models Truly Forget? New Findings from Representation-Level Certification of Visual Unlearning in Vertical Federated Learning](https://mlsanity.com/paper/2605.20282/) (2026)
- [Erased, but Not Gone: Output Forgetting Is Not True Forgetting](https://mlsanity.com/paper/2606.25001/) (2026)
- [MemLeak: Diagnosing Information Leaks in Multimodal Agent Memory](https://mlsanity.com/paper/2606.29788/) (2026)

## Abstract (arXiv)

Machine unlearning (MU) aims to remove the influence of specific data from trained models, addressing privacy concerns and ensuring compliance with regulations such as the ``right to be forgotten.'' Evaluating strong unlearning, where the unlearned model is indistinguishable from one retrained without the forgetting data, remains a significant challenge in deep neural networks (DNNs). Common black-box metrics, such as variants of membership inference attacks and accuracy comparisons, primarily assess model outputs but often fail to capture residual information in intermediate layers. To bridge this gap, we introduce the Information Difference Index (IDI), a novel white-box metric inspired by information theory. IDI quantifies retained information in intermediate features by measuring mutual information between those features and the labels to be forgotten, offering a more comprehensive assessment of unlearning efficacy. Our experiments demonstrate that IDI effectively measures the degree of unlearning across various datasets and architectures, providing a reliable tool for evaluating strong unlearning in DNNs.