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Rethinking LLM Unlearning Objectives: A Gradient Perspective and Go Beyond
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Proposes the gradient effect (G-effect), a gradient-dot-product diagnostic for LLM unlearning objectives, uses it to analyze GA, NPO, PO, RMU and regularizers, and introduces WGA, TNPO and WTNPO as improved objectives evaluated on TOFU.
Problem
LLM unlearning objectives (GA, NPO, PO, RMU) each have distinct properties, and no unified framework exists to compare them or explain their trade-offs between removing targeted data and retaining non-targeted performance.
Approach
Quantify the effect of an unlearning objective on removal and retention as the dot product between gradients of the risk metric and the unlearning loss (the G-effect), decomposed across instances, steps and layers; use this to diagnose excessive unlearning in GA and motivate confidence-weighted variants (WGA, token-wise NPO).
Key results
- On TOFU with KL regularization, WGA and WTNPO achieve the best trade-offs; e.g., Phi-1.5 at 1% forget set: WGA ES-exact unlearn 0.0344 vs GA 0.0530 with retain 0.3629 vs GA 0.1103.
- GA removes targeted data most strongly but sharply degrades retained performance (e.g., Phi-1.5 5% retain ES-exact 0.0000).
- PO is least attractive, with limited removal and possible relearning; NPO and RMU balance removal and retention better than GA.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace GA with confidence-weighted GA | GA · TOFU 5%, Phi-1.5 | FQ: -11.4040 -> -1.3076 | Helped |
| replace GA with confidence-weighted GA | GA · TOFU 5%, Llama-2-7B | FQ: -12.4230 -> -16.3271 | Hurt |
| use token-wise NPO weighting instead of sequence-level NPO weighting | NPO · TOFU 5%, Phi-1.5 | FQ: -7.7503 -> -2.1867 | Helped |
| use token-wise NPO weighting instead of sequence-level NPO weighting | NPO · TOFU 5%, Llama-2-7B | MU: 0.5285 -> 0.6348 | Helped |
| add further weighting to token-wise NPO | TNPO · TOFU 5%, Phi-1.5 | MU: 0.4673 -> 0.5084 | Helped |
| add further weighting to token-wise NPO | TNPO · TOFU 5%, Llama-2-7B | FQ: -32.1330 -> -21.4429 | Helped |
| use PO instead of NPO | NPO · TOFU 5%, Phi-1.5 | FQ: -7.7503 -> -26.5061 | Hurt |
| use PO instead of NPO | NPO · TOFU 5%, Llama-2-7B | FQ: -9.9550 -> -28.8476 | Hurt |
| increase the NPO inverse temperature beta (ablation) | NPO · TOFU 5% G-effect analysis | G-effect magnitude | Helped |
| set WGA confidence-weighting alpha to 0 instead of using confidence weighting (ablation) | WGA · TOFU 5% G-effect analysis | unlearning G-effect | Hurt |
| perturb middle-layer representations instead of deep-layer representations (ablation) | RMU · TOFU 5% G-effect analysis | G-effect stability | Helped |
| vary the RMU scaling parameter c (ablation) | RMU · TOFU 5% G-effect analysis | G-effect stability | Mixed |
Surprising findings
- PO may inadvertently facilitate knowledge relearning and is only effective for early updates.
- Token-wise application of NPO weighting is notably more effective than sequence-level NPO.
Limitations
- G-effect computation requires gradients and Hessian approximations, making full computation costly.
- NLL used as risk metric may not be optimal for characterizing knowledge parameterization.
- Regularization is still needed for retention; the proposed objectives retain negative retaining G-effect overall.
Experimental setup
Datasets: TOFU
Benchmarks: TOFU
Metrics: ES-exact ES-perturb forget quality (FQ) model utility (MU)
Baselines: GA NPO PO RMU WGA
Builds on: gradient ascent negative preference optimization representation misdirection for unlearning unlearning with control influence functions
Closest papers by meaning
- Towards Effective Evaluations and Comparisons for LLM Unlearning Methods (ICLR 2025 · similarity 0.94)
- OpenUnlearning: Accelerating LLM Unlearning via Unified Benchmarking of Methods and Metrics (NeurIPS 2025 · similarity 0.93)
- GRU: Mitigating the Trade-off between Unlearning and Retention for LLMs (ICML 2025 · similarity 0.93)
- WAGLE: Strategic Weight Attribution for Effective and Modular Unlearning in Large Language Models (NeurIPS 2024 · similarity 0.92)
- Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning (NeurIPS 2025 · similarity 0.92)
- Catastrophic Failure of LLM Unlearning via Quantization (ICLR 2025 · similarity 0.92)
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