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Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models
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Casts LLM unlearning as an epsilon-constrained problem (retain loss as hard constraint) and solves it with a warm-started primal-dual method using a softmax-free logit-margin flattening forget loss, evaluated on TOFU and MUSE.
Problem
LLM unlearning typically combines forget and retain objectives into a single scalarized loss, causing unstable optimization and utility degradation on retained data, especially under aggressive forgetting.
Approach
Reformulate unlearning as minimizing a forget loss subject to a retain-loss constraint solved by primal-dual updates (single warm-started dual step per iteration), paired with a logit-margin flattening loss that drives logits toward constancy on the forget set without softmax or entropy computation.
Key results
- On TOFU forget10 with Llama 3.2 3B, PDU reaches forget success 0.914 and model utility 0.680 versus 0.676/0.514 for the best baseline NPO on forget success and NPO's utility respectively.
- On TOFU forget10 with Llama 3.1 8B, PDU attains aggregated success 0.880 vs 0.864 for RMU (best baseline).
- On MUSE-Books Llama 2 7B, PDU achieves forget ROUGE 0.001 but retain ROUGE drops to 0.413, lower than RMU's 0.626 and aggregated success 0.638 is below RMU's 0.733.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PDU instead of retraining | Llama 3.2 1B · TOFU Forget10/Retain90 | Aggregated Success: 0.775 -> 0.770 | Hurt |
| Use PDU instead of retraining | Llama 3.2 3B · TOFU Forget10/Retain90 | Aggregated Success: 0.806 -> 0.848 | Helped |
| Use PDU instead of RMU | Llama 3.1 8B · TOFU Forget10/Retain90 | Aggregated Success: 0.864 -> 0.880 | Helped |
| Use PDU instead of retraining | Gemma 7B · TOFU Forget10/Retain90 | Aggregated Success: 0.788 -> 0.792 | Helped |
| Use PDU instead of RMU | Llama 2 7B · MUSE Books | Aggregated Success: 0.733 -> 0.638 | Hurt |
| Use PDU instead of SimNPO | Llama 2 13B · MUSE Books | Aggregated Success: 0.755 -> 0.752 | Hurt |
| Use PDU instead of GradDiff | Llama 2 7B · MUSE News | Aggregated Success: 0.595 -> 0.555 | Hurt |
| Use PDU instead of GradDiff | Llama 2 13B · MUSE News | Aggregated Success: 0.638 -> 0.593 | Hurt |
Surprising findings
- GradDiff yields zero forget success on 7B/8B models while the LLM judge gives full forget score, because the model abstains from generating text, exposing a limitation of the judge-based forgetting metric.
- PDU shows reduced generation fluency (LLM-judged fluency around 7.3-8.0 vs ~9.5 for the target), attributed to the strong uniformity induced by logit flattening.
Limitations
- The constraint threshold epsilon is model- and data-dependent and sensitive; tight or loose values hurt unlearning or utility.
- Limited hyperparameter tuning due to resource constraints; the method shows reduced fluency and mixed results on some MUSE settings.
Experimental setup
Datasets: TOFU MUSE-News MUSE-Books
Benchmarks: TOFU MUSE
Metrics: model utility forget success retain ROUGE forget ROUGE LLM-judged forget/retain scores fluency relevance aggregated harmonic-mean success
Baselines: target model retrained model GradDiff DPO NPO SimNPO RMU
Builds on: gradient ascent unlearning NPO SimNPO RMU dual ascent
Closest papers by meaning
- SHRED: Retain-Set-Free Unlearning via Self-Distillation with Logit Demotion (NeurIPS 2026 · similarity 0.93)
- A Closer Look at Machine Unlearning for Large Language Models (ICLR 2025 · similarity 0.92)
- Reversing the Forget-Retain Objectives: An Efficient LLM Unlearning Framework from Logit Difference (NeurIPS 2024 · similarity 0.92)
- LLM Unlearning via Loss Adjustment with Only Forget Data (ICLR 2025 · similarity 0.92)
- RULE: Reinforcement UnLEarning Achieves Forget-retain Pareto Optimality (NeurIPS 2025 · similarity 0.91)
- Large Language Model Unlearning via Embedding-Corrupted Prompts (NeurIPS 2024 · similarity 0.91)
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