# Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models

arXiv: https://arxiv.org/abs/2506.05314 · HTML: https://mlsanity.com/paper/2506.05314/

## Key facts

- Cited by 10 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 54 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## 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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [BioBERT: a pre-trained biomedical language representation model for biomedical text mining](https://mlsanity.com/paper/1901.08746/) (2019)
- [SciBERT: A Pretrained Language Model for Scientific Text](https://mlsanity.com/paper/1903.10676/) (2019)
- [CodeBERT: A Pre-Trained Model for Programming and Natural Languages](https://mlsanity.com/paper/2002.08155/) (2020)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [ClinicalBERT: Modeling Clinical Notes and Predicting Hospital Readmission](https://mlsanity.com/paper/1904.05342/) (2019)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (2023)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models](https://mlsanity.com/paper/2205.10770/) (2022)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Can Sensitive Information Be Deleted From LLMs? Objectives for Defending Against Extraction Attacks](https://mlsanity.com/paper/2309.17410/) (2023)
- [TLDR: Extreme Summarization of Scientific Documents](https://mlsanity.com/paper/2004.15011/) (2020)
- [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)
- [Unlearning or Obfuscating? Jogging the Memory of Unlearned LLMs via Benign Relearning](https://mlsanity.com/paper/2406.13356/) (2024)
- [Safe Policies for Reinforcement Learning via Primal-Dual Methods](https://mlsanity.com/paper/1911.09101/) (2019)
- [LLM Unlearning via Loss Adjustment with Only Forget Data](https://mlsanity.com/paper/2410.11143/) (2024)
- [Rethinking LLM Unlearning Objectives: A Gradient Perspective and Go Beyond](https://mlsanity.com/paper/2502.19301/) (2025)
- [A Closer Look at Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2410.08109/) (2024)
- [UNDIAL: Self-Distillation with Adjusted Logits for Robust Unlearning in Large Language Models](https://mlsanity.com/paper/2402.10052/) (2024)
- [Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate](https://mlsanity.com/paper/2410.22086/) (2024)

## Built on by (most cited first, 10 of 10)

- [OpenUnlearning: Accelerating LLM Unlearning via Unified Benchmarking of Methods and Metrics](https://mlsanity.com/paper/2506.12618/) (2025)
- [Maximizing Local Entropy Where It Matters: Prefix-Aware Localized LLM Unlearning](https://mlsanity.com/paper/2601.03190/) (2026)
- [Contrastive Representation Shaping for LLM Unlearning](https://mlsanity.com/paper/2601.22028/) (2026)
- [Forget to Know, Remember to Use: Context-Aware Unlearning for Large Language Models](https://mlsanity.com/paper/2510.17620/) (2025)
- [Position: The Term "Machine Unlearning" Is Overused in LLMs](https://mlsanity.com/paper/2606.27379/) (2026)
- [Inference-Time Machine Unlearning via Gated Activation Redirection](https://mlsanity.com/paper/2605.12765/) (2026)
- [Fast Unlearning at Scale via Margin Self-Correction](https://mlsanity.com/paper/2606.02920/) (2026)
- [SAGE: Retain-Aware Post-Hoc Sanitization of Final Unlearning Vector](https://mlsanity.com/paper/2606.18309/) (2026)
- [Beyond Average Safety: Chance-Constrained LLM Fine-tuning](https://mlsanity.com/paper/2609.29960/) (2026)
- [LLM Persona Unlearning](https://mlsanity.com/paper/2609.39882/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) deployed in real-world settings increasingly face the need to unlearn sensitive, outdated, or proprietary information. Existing unlearning methods typically formulate forgetting and retention as a regularized trade-off, combining both objectives into a single scalarized loss. This often leads to unstable optimization and degraded performance on retained data, especially under aggressive forgetting. We propose a new formulation of LLM unlearning as a constrained optimization problem: forgetting is enforced via a novel logit-margin flattening loss that explicitly drives the output distribution toward uniformity on a designated forget set, while retention is preserved through a hard constraint on a separate retain set. Compared to entropy-based objectives, our loss is softmax-free, numerically stable, and maintains non-vanishing gradients, enabling more efficient and robust optimization. We solve the constrained problem using a scalable primal-dual algorithm that exposes the trade-off between forgetting and retention through the dynamics of the dual variable, all without any extra computational overhead. Evaluations on the TOFU and MUSE benchmarks across diverse LLM architectures demonstrate that our approach consistently matches or exceeds state-of-the-art baselines, effectively removing targeted information while preserving downstream utility.