# Auditing Language Model Unlearning via Information Decomposition

arXiv: https://arxiv.org/abs/2601.15111 · HTML: https://mlsanity.com/paper/2601.15111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [On the Necessity of Auditable Algorithmic Definitions for Machine Unlearning](https://mlsanity.com/paper/2110.11891/) (2021)
- [Can Sensitive Information Be Deleted From LLMs? Objectives for Defending Against Extraction Attacks](https://mlsanity.com/paper/2309.17410/) (2023)
- [An Adversarial Perspective on Machine Unlearning for AI Safety](https://mlsanity.com/paper/2409.18025/) (2024)
- [Large Language Model Unlearning via Embedding-Corrupted Prompts](https://mlsanity.com/paper/2406.07933/) (2024)
- [Min-K%++: Improved Baseline for Detecting Pre-Training Data from Large Language Models](https://mlsanity.com/paper/2404.02936/) (2024)
- [Reversing the Forget-Retain Objectives: An Efficient LLM Unlearning Framework from Logit Difference](https://mlsanity.com/paper/2406.08607/) (2024)
- [Position: LLM Unlearning Benchmarks are Weak Measures of Progress](https://mlsanity.com/paper/2410.02879/) (2024)
- [UNDIAL: Self-Distillation with Adjusted Logits for Robust Unlearning in Large Language Models](https://mlsanity.com/paper/2402.10052/) (2024)
- [What does the Knowledge Neuron Thesis Have to do with Knowledge?](https://mlsanity.com/paper/2405.02421/) (2024)
- [WAGLE: Strategic Weight Attribution for Effective and Modular Unlearning in Large Language Models](https://mlsanity.com/paper/2410.17509/) (2024)
- [Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data](https://mlsanity.com/paper/2307.10515/) (2023)
- [DiffusionPID: Interpreting Diffusion via Partial Information Decomposition](https://mlsanity.com/paper/2406.05191/) (2024)
- [Bits and Pieces: Understanding Information Decomposition from Part-whole Relationships and Formal Logic](https://mlsanity.com/paper/2008.09535/) (2020)
- [Differentially Private Steering for Large Language Model Alignment](https://mlsanity.com/paper/2501.18532/) (2025)
- [Analyzing Memorization in Large Language Models through the Lens of Model Attribution](https://mlsanity.com/paper/2501.05078/) (2025)
- [Quantifying Knowledge Distillation Using Partial Information Decomposition](https://mlsanity.com/paper/2411.07483/) (2024)
- [Understanding Probe Behaviors through Variational Bounds of Mutual Information](https://mlsanity.com/paper/2312.10019/) (2023)

## Built on by (most cited first, 3 of 3)

- [Position: The Term "Machine Unlearning" Is Overused in LLMs](https://mlsanity.com/paper/2606.27379/) (2026)
- [Null-Space Constrained Low-Rank Adaptation for Response-Specified Large Language Model Unlearning](https://mlsanity.com/paper/2606.10989/) (2026)
- [Fair on the Surface? Benchmarking Hidden-Output Fairness Gaps in LLM Recommenders](https://mlsanity.com/paper/2608.08284/) (2026)

## Abstract (arXiv)

We expose a critical limitation in current approaches to machine unlearning in language models: despite the apparent success of unlearning algorithms, information about the forgotten data remains linearly decodable from internal representations. To systematically assess this discrepancy, we introduce an interpretable, information-theoretic framework for auditing unlearning using Partial Information Decomposition (PID). By comparing model representations before and after unlearning, we decompose the mutual information with the forgotten data into distinct components, formalizing the notions of unlearned and residual knowledge. Our analysis reveals that redundant information, shared across both models, constitutes residual knowledge that persists post-unlearning and correlates with susceptibility to known adversarial reconstruction attacks. Leveraging these insights, we propose a representation-based risk score that can guide abstention on sensitive inputs at inference time, providing a practical mechanism to mitigate privacy leakage. Our work introduces a principled, representation-level audit for unlearning, offering theoretical insight and actionable tools for safer deployment of language models.