Towards Mitigating Excessive Forgetting in LLM Unlearning via Entanglement-Guidance with Proxy Constraint

TL;DR

This paper introduces EGUP, a novel unlearning framework for large language models that uses entanglement guidance and proxy constraints to effectively forget specific data while preserving utility.

Contribution

EGUP is a new framework that adaptively guides unlearning in LLMs using entanglement and proxy constraints, reducing over-unlearning and utility loss.

Findings

EGUP improves the unlearning-utility trade-off on TOFU and MUSE benchmarks.

EGUP achieves near-retraining performance with better scalability and robustness.

EGUP is compatible with existing gradient-based unlearning methods.

Abstract

Large language models (LLMs) are trained on massive datasets that may include private or copyrighted content. Due to growing privacy and ownership concerns, data owners may request the removal of their data from trained models. Machine unlearning provides a practical solution by removing the influence of specific data without full retraining. However, most existing methods still suffer from over-unlearning due to the lack of a principled mechanism to regulate the forgetting boundary, leading to unnecessary utility degradation and heightened privacy and robustness risks. In this work, we propose EGUP (Entanglement-Guided Unlearning with Proxy Constraint), a novel framework that leverages entanglement and proxy constraint to guide the unlearning process while mitigating over-unlearning. Within each iteration, EGUP employs inter-sample entanglement to adaptively reweight the unlearning strength, assigning greater unlearning efforts to forget samples that are semantically closer to retained knowledge. Across iterations, EGUP leverages intra-sample entanglement to track the representation shift of each forget sample and dynamically adjust its unlearning effort. In addition, we incorporate a proxy constraint that approximates the model's expected outputs after unlearning, forming a reference boundary that softly regularizes the unlearning process. EGUP is compatible with existing gradient-based objectives and serves as a plug-and-play enhancement. We evaluate EGUP on the TOFU and MUSE benchmarks, demonstrating consistent improvements in the unlearning-utility trade-off across multiple LLMs. Moreover, EGUP achieves performance close to the retrained model while remaining scalable and robust.

Tables

Table 1. Table 1 . Results on TOFU benchmarks with different forgetting ratios (1%, 5%, and 10%). Each method is evaluated using four metrics: F.Q., M.U., and R-L represent forget quality, model utility and ROUGE-L respectively.

Method	TOFU-1%				TOFU-5%				TOFU-10%
	Forget Perf.		Retain Perf.		Forget Perf.		Retain Perf.		Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L	M.U. $\uparrow$	R-L	F.Q. $\uparrow$	R-L	M.U. $\uparrow$	R-L	F.Q. $\uparrow$	R-L	M.U. $\uparrow$	R-L
	Phi-1.5
GA	0.9900	0.2914	0.4151	0.4722	2.38e-6	0.3955	0.4075	0.3944	8.02e-5	0.3557	0.3878	0.3716
NPO	0.9188	0.2696	0.4126	0.4570	6.73e-6	0.4051	0.4203	0.4105	1.22e-8	0.3196	0.4197	0.3423
GD	0.9188	0.3193	0.4564	0.5456	1.39e-6	0.3480	0.4047	0.4160	1.40e-6	0.3738	0.4032	0.4033
NPO+GD	0.9188	0.2783	0.4375	0.5072	0.0878	0.3518	0.4158	0.3942	2.56e-5	0.4211	0.4200	0.4438
EGUP(GA)	0.9999	0.3260	0.4282	0.4764	1.12e-5	0.4094	0.4261	0.4064	2.36e-4	0.3399	0.4106	0.3505
EGUP(NPO)	0.9900	0.2946	0.4266	0.4723	1.12e-5	0.3962	0.4327	0.4082	5.52e-5	0.3847	0.4417	0.3983
EGUP(GD)	0.9900	0.2884	0.4567	0.5186	1.12e-5	0.3621	0.4391	0.4351	5.52e-5	0.3356	0.4363	0.3925
EGUP(NPO+GD)	0.9900	0.3366	0.4610	0.5558	0.7934	0.3474	0.4259	0.4147	0.3958	0.3601	0.4209	0.4211
Retrain LLM	1	0.4176	0.4845	0.6737	1	0.4202	0.4772	0.6740	1	0.4251	0.4917	0.7706
	LLaMA2-7B
GA	0.4046	0.4183	0.5590	0.7553	1.12e-5	0.4418	0.4921	0.4726	2.89e-11	0.0577	0	0.0756
NPO	0.7659	0.2905	0.5568	0.7187	2.61e-7	0.3885	0.5107	0.4625	2.55e-9	0.5009	0.4987	0.5082
GD	0.2657	0.2298	0.5255	0.4506	1.87e-9	0.0355	0.6106	0.7600	0.0017	0.2481	0.5281	0.3440
NPO+GD	0.7659	0.3793	0.6243	0.7737	7.54e-5	0.4559	0.5905	0.5681	5.02e-10	0.4490	0.5608	0.4815
EGUP(GA)	0.9188	0.3719	0.5660	0.7762	1.12e-5	0.4808	0.5106	0.5112	1.16e-5	0.0018	0	0.0040
EGUP(NPO)	0.9900	0.3605	0.5648	0.7543	1.12e-5	0.4504	0.5119	0.4912	2.17e-7	0.4987	0.5178	0.5176
EGUP(GD)	0.7659	0.3391	0.5325	0.6814	2.96e-5	0.0000	0.6244	0.5694	0.0043	0.0761	0.6189	0.6659
EGUP(NPO+GD)	0.9188	0.2417	0.6454	0.8059	0.9647	0.3022	0.6202	0.7926	0.3417	0.2735	0.6315	0.7266
Retrain LLM	1	0.3934	0.6305	0.9956	1	0.3930	0.6245	0.9810	1	0.3980	0.6218	0.9820

Table 2. Table 2 . Evaluation of unlearning performance on the MUSE benchmark. EGUP effectively reduces both C1 and C3 , demonstrating improved control over memorization and privacy leakage.

Method	C1. No Verbatim Mem.	C2. No Knowledge Mem.	C3. No Privacy Leak	C4. Utility Preserv.
	VerbMem $\downarrow$	KnowMem on ${𝒟}_{\text{forget}}$ $\downarrow$	PrivLeak $\in [-5\%,5\%]$	KnowMem on ${𝒟}_{\text{retain}}$ $\uparrow$
NEWS
Target $f_{\text{target}}$	58.4	63.9	-99.8	55.2
Retrain $f_{\text{retrain}}$	20.8	33.1	0.0	55.0
GA	0.0	0.0	24.7904	0.0
EGUP(GA)	15.5275 $\uparrow$	26.3561 $\uparrow$	-21.7735 $\downarrow$	35.4112 $\uparrow$
GD	0.0256	24.9395	108.5289	22.3922
EGUP(GD)	0.0000 $\downarrow$	0.0000 $\downarrow$	29.2539 $\downarrow$	0.0000 $\downarrow$
NPO	51.0327	61.4428	-99.8114	52.4327
EGUP(NPO)	42.5759 $\downarrow$	63.4412 $\uparrow$	-99.7275 $\downarrow$	52.0777 $\downarrow$
NPO+GD	16.3903	37.1143	-97.7578	37.4993
EGUP(NPO+GD)	5.6201 $\downarrow$	35.8123 $\downarrow$	83.2492 $\downarrow$	46.4921 $\uparrow$
BOOKS
Target $f_{\text{target}}$	99.8	59.4	-57.5	66.9
Retrain $f_{\text{retrain}}$	14.3	28.9	0.0	74.5
GA	89.2175	37.7380	-58.5759	56.7514
EGUP(GA)	84.3180 $\downarrow$	35.1689 $\downarrow$	-54.8234 $\downarrow$	55.8213 $\downarrow$
GD	15.5676	11.6565	20.4317	19.0662
EGUP(GD)	0.0000 $\downarrow$	0.0000 $\downarrow$	-24.8842 $\uparrow$	13.0053 $\downarrow$
NPO	16.1017	8.5882	31.0981	13.7530
EGUP(NPO)	13.9234 $\downarrow$	12.8425 $\uparrow$	-29.0881 $\downarrow$	16.7468 $\uparrow$
NPO+GD	26.6586	26.4127	-53.4026	43.8690
EGUP(NPO+GD)	7.8129 $\downarrow$	17.7289 $\downarrow$	-35.5122 $\downarrow$	38.8175 $\downarrow$

Table 3. Table 3 . Unlearning epochs for each unlearning method on MUSE.

Unlearning Method	News	Books
GA	epoch 1	epoch 1
EGUP(GA)	epoch 1	epoch 1
GD	epoch 7	epoch 1
EGUP(GD)	epoch 7	epoch 1
NPO	epoch 1	epoch 1
EGUP(NPO)	epoch 1	epoch 1
NPO+GD	epoch 10	epoch 1
EGUP(NPO+GD)	epoch 10	epoch 1

Table 4. Table 4 . PHI Results on TOFU-1% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.4176	0.4845	0.6737
GA	0.9900	0.2914	0.4151	0.4722
EGUP_w/o(GA)	0.9900	0.2914	0.4151	0.4722
EGU(GA)	0.9999	0.3260	0.4223	0.4843
EGUP(GA)	0.9999	0.3260	0.4223	0.4843
NPO	0.9188	0.2696	0.4126	0.4570
EGUP_w/o(NPO)	0.9188	0.2696	0.4126	0.4570
EGU(NPO)	0.9900	0.3016	0.4133	0.4762
EGUP(NPO)	0.9900	0.3016	0.4133	0.4762
GD	0.9188	0.3193	0.4564	0.5456
EGUP_w/o(GD)	0.9188	0.3193	0.4564	0.5456
EGU(GD)	0.9900	0.3594	0.4502	0.5564
EGUP(GD)	0.9900	0.3594	0.4502	0.5564
NPO+GD	0.9188	0.2783	0.4375	0.5072
EGUP_w/o(NPO+GD)	0.9188	0.2783	0.4375	0.5072
EGU(NPO+GD)	0.9900	0.3366	0.4610	0.5558
EGUP(NPO+GD)	0.9900	0.3366	0.4610	0.5558

Table 5. Table 5 . PHI Results on TOFU-5% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.4202	0.4772	0.6740
GA	2.38e-6	0.3955	0.4075	0.3944
EGUP_w/o(GA)	1.39e-6	0.4086	0.4255	0.4030
EGU(GA)	1.12e-5	0.4083	0.4156	0.3989
EGUP(GA)	1.12e-5	0.4094	0.4261	0.4064
NPO	6.73e-6	0.4051	0.4203	0.4105
EGUP_w/o(NPO)	1.12e-5	0.3962	0.4323	0.4042
EGU(NPO)	6.73e-6	0.4039	0.4187	0.4035
EGUP(NPO)	4.02e-6	0.4027	0.4234	0.4070
GD	1.39e-6	0.3480	0.4047	0.4160
EGUP_w/o(GD)	6.73e-6	0.3487	0.4373	0.4288
EGU(GD)	2.38e-6	0.3919	0.4344	0.4534
EGUP(GD)	1.83e-5	0.3520	0.4327	0.4181
NPO+GD	0.0878	0.3518	0.4158	0.3942
EGUP_w/o(NPO+GD)	0.0061	0.3993	0.4323	0.4211
EGU(NPO+GD)	0.6284	0.3426	0.4105	0.4199
EGUP(NPO+GD)	0.7934	0.3474	0.4259	0.4147

Table 6. Table 6 . PHI Results on TOFU-10% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.4251	0.4917	0.7706
GA	8.02e-5	0.3557	0.3878	0.3716
EGUP_w/o(GA)	3.77e-5	0.3685	0.4296	0.3805
EGU(GA)	1.16e-4	0.3373	0.4056	0.3440
EGUP(GA)	2.36e-4	0.3399	0.4106	0.3505
NPO	1.22e-8	0.3196	0.4197	0.3423
EGUP_w/o(NPO)	5.44e-8	0.3123	0.4214	0.3133
EGU(NPO)	3.77e-5	0.3581	0.4299	0.3834
EGUP(NPO)	3.77e-5	0.3718	0.4366	0.3892
GD	1.40e-6	0.3738	0.4032	0.4033
EGUP_w/o(GD)	7.69e-6	0.3431	0.4219	0.3876
EGU(GD)	2.17e-6	0.3582	0.4412	0.4053
EGUP(GD)	5.52e-5	0.3356	0.4363	0.3925
NPO+GD	2.56e-5	0.4211	0.4200	0.4438
EGUP_w/o(NPO+GD)	3.77e-5	0.4236	0.4265	0.4420
EGU(NPO+GD)	0.3958	0.3601	0.4209	0.4211
EGUP(NPO+GD)	0.3417	0.3509	0.4244	0.4089

Table 7. Table 7 . Performance of different EAGLE methods under various k k values and forget ratios on PHI. MU: Model Utility. FQ: Forget Quality.

Forget Ratio	Method	$k=0.5$		$k=1$		$k=2$
		MU	FQ	MU	FQ	MU	FQ
1%	EAGLE (GA)	0.4143	0.9999	0.4225	0.9999	0.4010	0.9999
	EAGLE (GD)	0.4481	0.9900	0.4502	0.9900	0.4412	0.9900
	EAGLE (NPO)	0.4012	0.9900	0.4133	0.9900	0.4120	0.9900
	EAGLE (NPO+GD)	0.4638	0.9188	0.4610	0.9900	0.4521	0.9900
5%	EAGLE (GA)	0.4390	2.61e-7	0.4156	1.12e-5	0.4071	1.12e-5
	EAGLE (GD)	0.4263	4.61e-7	0.4344	2.38e-6	0.4239	4.61e-7
	EAGLE (NPO)	0.3949	2.96e-5	0.4187	6.73e-6	0.4107	4.02e-6
	EAGLE (NPO+GD)	0.4099	0.6284	0.4105	0.6284	0.3989	0.4663
10%	EAGLE (GA)	0.4350	3.33e-6	0.4056	1.16e-4	0.4100	5.07e-6
	EAGLE (GD)	0.4412	2.17e-6	0.4248	2.17e-6	0.4126	2.56e-5
	EAGLE (NPO)	0.4196	2.72e-5	0.4298	3.77e-5	0.4210	3.77e-5
	EAGLE (NPO+GD)	0.4407	0.1212	0.4209	0.3958	0.4202	0.2926

Table 8. Table 8 . Performance of different EAGLE methods under various k k values and forget ratios on LLAMA2. MU: Model Utility. FQ: Forget Quality.

Forget Ratio	Method	$k=0.5$		$k=1$		$k=2$
		MU	FQ	MU	FQ	MU	FQ
1%	EAGLE (GA)	0.5567	0.4046	0.5660	0.9188	0.5376	0.5786
	EAGLE (GD)	0.5705	0.1650	0.5781	0.1650	0.5325	0.7659
	EAGLE (NPO)	0.5618	0.4046	0.5504	0.9188	0.5665	0.2657
	EAGLE (NPO+GD)	0.6223	0.9188	0.6294	0.9188	0.5942	0.7659
5%	EAGLE (GA)	0.4921	2.96e-5	0.5185	1.39e-6	0.5072	2.96e-5
	EAGLE (GD)	0.6408	3.60e-9	0.6092	0.0002	0.6166	2.38e-6
	EAGLE (NPO)	0.4600	6.57e-8	0.5248	1.46e-7	0.5037	1.12e-5
	EAGLE (NPO+GD)	0.6519	0.1421	0.6060	0.7126	0.5917	0.2705
10%	EAGLE (GA)	0	8,78e-12	0	5.73e-7	0.2294	1.07e-13
	EAGLE (GD)	0.6114	0.0055	0.6259	1.16e-4	0.6247	2.17e-4
	EAGLE (NPO)	0.5829	7.38e-15	0.5012	1.74e-7	0.3728	1.49e-9
	EAGLE (NPO+GD)	0.6065	3.77e-5	0.5384	0.1761	0.5715	0.2926

Table 9. Table 9 . LLAMA2 Results on TOFU-1% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.3934	0.6305	0.9956
GA	0.4046	0.4183	0.5590	0.7553
EGUP_w/o(GA)	0.4046	0.4183	0.5590	0.7553
EGU(GA)	0.9188	0.3719	0.5660	0.7762
EGUP(GA)	0.9188	0.3719	0.5660	0.7762
NPO	0.7659	0.2905	0.5568	0.7187
EGUP_w/o(NPO)	0.7659	0.2905	0.5568	0.7187
EGU(NPO)	0.9188	0.3084	0.5504	0.6873
EGUP(NPO)	0.9188	0.3682	0.5654	0.7733
GD	0.2657	0.2298	0.5255	0.4506
EGUP_w/o(GD)	0.2657	0.2298	0.5255	0.4506
EGU(GD)	0.7659	0.3391	0.5325	0.6814
EGUP(GD)	0.7659	0.3391	0.5325	0.6814
NPO+GD	0.7659	0.3793	0.6243	0.7737
EGUP_w/o(NPO+GD)	0.7659	0.2410	0.6270	0.7312
EGU(NPO+GD)	0.9188	0.2894	0.6294	0.7188
EGUP(NPO+GD)	0.9188	0.2417	0.6454	0.8059

Table 10. Table 10 . LLAMA2 Results on TOFU-5% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.3935	0.6083	0.9955
GA	1.12e-5	0.4418	0.4921	0.4726
EGUP_w/o(GA)	1.12e-5	0.4429	0.4988	0.4824
EGU(GA)	2.96e-5	0.4832	0.5072	0.5126
EGUP(GA)	1.12e-5	0.4808	0.5106	0.5112
NPO	2.61e-7	0.3885	0.5107	0.4625
EGUP_w/o(NPO)	1.46e-7	0.5561	0.5346	0.6181
EGU(NPO)	1.12e-5	0.4501	0.5037	0.4827
EGUP(NPO)	1.12e-5	0.4504	0.5119	0.4912
GD	1.87e-9	0.0355	0.6106	0.7600
EGUP_w/o(GD)	2.61e-7	0.9068	0.6502	0.6470
EGU(GD)	2.38e-6	0.0428	0.6166	0.5918
EGUP(GD)	2.38e-6	0.0621	0.6213	0.5645
NPO+GD	7.54e-5	0.4559	0.5905	0.5681
EGUP_w/o(NPO+GD)	7.54e-5	0.4245	0.6024	0.7238
EGU(NPO+GD)	0.7126	0.1367	0.6060	0.7990
EGUP(NPO+GD)	0.9647	0.3022	0.6202	0.7926

Table 11. Table 11 . LLAMA2 Results on TOFU-10% benchmark.

Method	Forget Perf.		Retain Perf.
	F.Q. $\uparrow$	R-L $\uparrow$	M.U. $\uparrow$	R-L $\uparrow$
Retrain LLM	1	0.3969	0.6187	0.9950
GA	2.89e-11	0.0577	0.0	0.0756
EGUP_w/o(GA)	4.32e-9	0.0132	0.0	0.0241
EGU(GA)	5.73e-7	0.0018	0.0	0.0040
EGUP(GA)	1.16e-5	0.0018	0.0	0.0040
NPO	2.55e-9	0.5009	0.4987	0.5082
EGUP_w/o(NPO)	1.49e-9	0.5206	0.5219	0.5217
EGU(NPO)	1.74e-7	0.4987	0.5012	0.5102
EGUP(NPO)	2.17e-7	0.4987	0.5178	0.5176
GD	0.0017	0.2481	0.5281	0.3440
EGUP_w/o(GD)	0.0023	0.1761	0.5521	0.4227
EGU(GD)	0.0055	0.0643	0.6114	0.6359
EGUP(GD)	0.0043	0.0761	0.6189	0.6659
NPO+GD	5.02e-10	0.4490	0.5608	0.4815
EGUP_w/o(NPO+GD)	1.22e-8	0.4402	0.5791	0.4843
EGU(NPO+GD)	0.2926	0.2752	0.5715	0.4973
EGUP(NPO+GD)	0.3417	0.2735	0.6315	0.7266

Equations

$$\underset{{\theta }^{\prime }}{\min }L({\theta }^{\prime })=\min -L({\theta }^{\prime },{\mathcal{D}}_f)+\alpha L({\theta }^{\prime },{\mathcal{D}}_r),$$

$$L_{\text{GA}}({\theta }^{\prime },{\mathcal{D}}_f)=-{\mathbb{E}}_{{\mathcal{D}}_f}[\log (f({\theta }^{\prime },y|x))],$$

$$L({\theta }^{\prime },{\mathcal{D}}_r)=-{\mathbb{E}}_{{\mathcal{D}}_r}[\log (f({\theta }^{\prime },y|x))],$$

$$L_{\text{NPO},\beta }({\theta }^{\prime })=-\frac{2}{\beta }{\mathbb{E}}_{{\mathcal{D}}_f}\left[\log \sigma (-\beta \log \frac{f({\theta }^{\prime },y|x)}{f({\theta }^o,y|x)})\right],$$

$$\text{mem}(\mathcal{A},\mathcal{D},i)=\underset{f\sim \mathcal{A}(\mathcal{D})}{\mathrm{Pr}}\left[f(x_i)=y_i\right]-\underset{f\sim \mathcal{A}(\mathcal{D}\setminus i)}{\mathrm{Pr}}\left[f(x_i)=y_i\right],$$

$$R_{\text{truth}}:=\frac{1}{N}\sum _{i=1}^N\frac{p({\hat{y}}_i|x{)}^{(1/|{\hat{y}}_i|)}}{p({\tilde{y}}_i|x{)}^{(1/|{\tilde{y}}_i|)}},$$

$$\text{VerbMem}(\theta ,{\mathcal{D}}_u)=\frac{1}{|{\mathcal{D}}_u|}\sum _{x\in {\mathcal{D}}_u}\text{ROUGE}(f(x_{[l]};\theta ),x_{[l+1:]}).$$

$$\text{KnowMem}(\theta ,{\mathcal{D}}_u)=\frac{1}{|{\mathcal{D}}_u|}\sum _{(q,a)\in {\mathcal{D}}_u}\text{ROUGE}(f(q;\theta ),a).$$

$$\text{PrivLeak}:=\frac{\text{AUC}({\theta }_r;{\mathcal{D}}_u,{\mathcal{D}}_h)-\text{AUC}({\theta }_t;{\mathcal{D}}_u,{\mathcal{D}}_h)}{\text{AUC}({\theta }_r;{\mathcal{D}}_u,{\mathcal{D}}_h)},$$

$$\text{UtilPres}(\theta ,{\mathcal{D}}_r)=\frac{1}{|{\mathcal{D}}_r|}\sum _{(q,a)\in {\mathcal{D}}_r}\text{ROUGE}(f(q;\theta ),a).$$

Full text

In this work, we propose EGUP (Entanglement-Guided Unlearning with Proxy Constraint), a novel framework that leverages entanglement and proxy constraint to guide the unlearning process while mitigating over-unlearning. Within each iteration, EGUP employs inter-sample entanglement to adaptively reweight the unlearning strength, assigning greater unlearning efforts to forget samples that are semantically closer to retained knowledge. Across iterations, EGUP leverages intra-sample entanglement to track the representation shift of each forget sample and dynamically adjust its unlearning effort. In addition, we incorporate a proxy constraint that approximates the model’s expected outputs after unlearning, forming a reference boundary that softly regularizes the unlearning process. EGUP is compatible with existing gradient-based objectives and serves as a plug-and-play enhancement. We evaluate EGUP on the TOFU and MUSE benchmarks, demonstrating consistent improvements in the unlearning–utility trade-off across multiple LLMs. Moreover, EGUP achieves performance close to the retrained model while remaining scalable and robust.

• This work is independent of and outside of the work at Amazon

🖂 Corresponding authors.

††copyright: none

1. Introduction

Large language models (LLMs) (Touvron et al., 2023; Achiam et al., 2023; Bai et al., 2023) demonstrate an extraordinary capacity to absorb and retain knowledge from massive web-scale datasets. However, this memorization capability also brings accompanying privacy risks. Real-world training data often contains private, sensitive, or copyrighted content (Patil et al., 2023; Karamolegkou et al., 2023), which may not only unintentionally resurface at inference time, but can also be maliciously extracted by adversaries through targeted attacks such as training data extraction and membership inference (Meng et al., 2025; Song et al., 2025). Such disclosures threaten individual privacy rights (Yao et al., 2024b), undermines intellectual property protections (Wei et al., 2024), and may even facilitates harmful misuse (Liu et al., 2023). Such risks highlight the urgent need for mechanisms that can reliably remove specific training data (i.e., forget data) from trained models.

Machine unlearning (Cao and Yang, 2015; Bourtoule et al., 2021) has emerged as a practical alternative that directly updates model parameters to remove the influence of targeted data, without the need for full retraining from scratch. The common paradigm for unlearning is to first formulate a dedicated unlearning objective and then subsequently update model parameters through iterative optimizations (Liu et al., 2025; Jia et al., 2024; Yao et al., 2024a). By explicitly guiding the optimization process toward suppressing memorized information, these approaches significantly reduce computational cost while maintaining model functionality on retained knowledge. Consequently, machine unlearning offers a promising balance between effectiveness, efficiency, and utility, making it particularly suitable for LLM scenarios.

Although unlearning substantially reduces the prohibitive cost of full retraining, it still faces the inherent risk of over-unlearning. When parameter updates become overly aggressive, the model may not only erase the targeted knowledge but also inadvertently degrade useful capabilities, thereby disrupting the desired balance between forgetting and utility (Zhao, 2025). In addition, state-of-the-art LLMs are carefully aligned with safety guidelines; excessive perturbations on model parameters may weaken these safety guardrails, potentially compromising model alignment and increasing the likelihood of generating unsafe content (Łucki et al., 2024; Chen et al., 2025). Beyond utility and safety concerns, recent studies further reveal that over-unlearning can amplify privacy and robustness risks. Excessive representation drift may destabilize decision boundaries and induce abnormal confidence behavior, which in turn increases the success rate of membership inference attacks on both forget and retain samples, while simultaneously reducing robustness under adversarial perturbations (Hayes et al., 2025; Xue et al., 2025). These findings highlight that over-unlearning is not merely a degradation in performance, but a broader threat to model reliability, safety, and security.

Nevertheless, existing unlearning methods remain inadequate in effectively preventing over-unlearning. Approaches that consider only individual sample properties (Huang et al., 2024; Yang et al., 2025) fail to account for the complex interactions between forget samples and the retain dataset, which exert significant influence on the forgetting behavior and are crucial for maintaining a desirable balance between effectiveness and utility preservation. Another line of work leverages memorization scores to guide unlearning (Zhao et al., 2024). However,its reliance on repeated retraining leads to significant computational overhead, making it impractical for LLMs. Furthermore, current unlearning objectives inherently lack reliable termination conditions (Liu et al., 2025; Ye et al., 2025) and explicit stopping criteria, leaving no principled guidance on when sufficient unlearning has been achieved.

Despite these substantial efforts in mitigating over-unlearning, effectively preventing it remains a fundamental and largely unsolved challenge in LLM unlearning. We attribute such risks to two main factors. First, forget samples exhibit strong heterogeneity in memorization and their sematic entanglement with the retain dataset. As a result, applying uniform unlearning effort may cause some samples to be over-unlearned while others remain under-unlearned. Second, most existing work lack reliable convergence guarantees and explicit stopping criteria, making it difficult to determine when adequate unlearning has been achieved, thereby increasing the risk of over-unlearning across all forget samples.

In this work, we propose EGUP (Entanglement Guided Unlearning with Proxy Constraint), an entanglement-guided unlearning framework for large language models that mitigates over-unlearning through entanglement guidance and proxy regularization. EGUP explicitly captures inter- and intra-sample entanglement to guide the unlearning process. Specifically, inter-sample entanglement, defined across samples, captures the semantic coupling between forget and retain samples in the embedding space and leverages this relationship to adaptively modulate unlearning effort across samples via sample-level loss reweighting, enabling more precise and targeted unlearning. In contrast, intra-sample entanglement, defined across iterations, measures the temporal consistency of a forgotten sample’s representations throughout the training process. It also reflects how robust this sample remains to perturbations introduced by updates on other forget samples within the shared parameter space. By serving as a temporal regulation signal, it helps smooth the unlearning trajectory, thereby preventing instability and avoiding overly aggressive unlearning.

Furthermore, the absence of a clear stopping criterion makes it difficult to determine when unlearning is sufficient, increasing the risk of over-unlearning. A naive approach might be to rely on a fixed threshold to terminate unlearning; however, this is unreliable because the optimal stopping point is highly sensitive to variations in model architecture, data distribution, and individual samples. To better address this, we leverage open-source LLMs to construct proxy constraint by predicting retrained model performance on forget samples. For each sample, the LLM is prompted with a few examples illustrating how the retrained model predicts, and then generates proxy outputs that approximate the retain model’s behavior. These proxy outputs are used in a loss-based penalty mechanism to specify how much the model should still “remember” the targeted information. By penalizing deviations from these proxy targets, the mechanism provides principled guidance to constrain unnecessary loss escalation and prevent over-unlearning.

We extensively evaluate EGUP on two representative benchmarks, TOFU (Maini et al., 2024) and MUSE (Shi et al., 2024). When integrated into diverse mainstream unlearning pipelines, EGUP consistently outperforms baselines and further achieves almost the same performance as full retraining. More importantly, EGUP consistently outperforms baselines that depend on retain data, while using only the averaged retain embedding. Our contributions are summarized as follows:

• •

Entanglement-Guided Unlearning Mechanism: We design an entanglement-guided unlearning framework that jointly leverages inter-sample and intra-sample entanglement to regulate the unlearning process. By reweighting sample-level unlearning effort based on semantic entanglement and incorporating a temporal regularization term sensitive to representation drift, the framework achieves more precise and stable unlearning.

• •

Proxy Constraint: We introduce a soft regularization mechanism based on proxy outputs synthesized via in-context learning (ICL) to approximate a retain model’s behavior on forget samples, providing a principled constraint that prevents over-unlearning.

• •

Unified and Plug-and-Play: EGUP is general and compatible with multiple existing gradient-based unlearning objectives, enabling plug-and-play improvements without costly retraining.

• •

Strong Empirical Evidence: Extensive experiments on TOFU and MUSE show that EGUP achieves superior trade-offs across models, including Phi-1.5, LLaMA2-7B, and ICML-7B. Under a 5% unlearning setting with NPO+GD, it boosts forget quality from 0.0878 to 0.7934 while maintaining utility, substantially outperforming standard baselines.

2. Background and Related Work

2.1. Unlearning for LLMs

Machine unlearning aims to remove the influence of specific training data from a trained model while preserving overall performance on the retained data. Recent works have introduced gradient-based optimization strategies to achieve this goal. Notably, Gradient Difference (GD) (Maini et al., 2024) and Negative Preference Optimization (NPO) (Zhang et al., 2024) represent two seminal approaches that guide parameter updates to counteract the influence of forget samples while maintaining model stability. Building upon these methods, subsequent studies refine the underlying loss functions, introducing adaptive weighting and optimization mechanisms to achieve more stable and precise unlearning. Huang et al. (Huang et al., 2024) proposed a Sample-wise Adaptive Coefficient, inversely scaled by empirical loss, to balance gradient ascent on forget samples. It prevents redundant updates to already forgotten data while emphasizing those that remain insufficiently erased. However, as noted in their work, relying solely on empirical loss as a measure of sample importance introduces bias and fails to capture representational complexity. In parallel, Yang et al. (Yang et al., 2025) identify two complementary criteria for loss reweighting in unlearning: Saturation, which prioritizes under-optimized samples, and Importance, which emphasizes samples most influential for overall loss minimization. Together, these methods demonstrate the potential of adaptive weighting schemes to balance unlearning quality and model retention.

2.2. Memorization

Deep neural networks are known to memorize their training data. Feldman et al. (Feldman, 2020a) show that such instance-level memorization is not merely an artifact of overfitting but a key mechanism for generalization under long-tailed distributions. Subsequent studies (Feldman, 2020a; Brown et al., 2021; Attias et al., 2024) further show that moderate memorization is necessary to capture rare or low-frequency patterns critical for generalization.

Beyond its role in generalization, recent research (Torkzadehmahani et al., 2024) reveals that memorization and unlearning are deeply intertwined. At the extreme, non-memorized examples can be regarded as trivially unlearned, since their predictions would remain unchanged without being included in training. In contrast, highly memorized examples are much harder to erase, as their influence is more deeply embedded in the model parameters. Zhao et al. (Zhao et al., 2024) systematically analyze the role of memorization in unlearning difficulty. They find that approximate unlearning methods are generally more successful on forget sets with low-memorization samples, while highly memorized ones are substantially harder to remove. To address this, they propose RUM (Refined-Unlearning Meta-algorithm), which partitions the forget set into homogeneous subsets based on memorization scores, achieving more stable and fine-grained unlearning. Despite its strengths, RUM still faces several limitations: (1) The computation of memorization scores incurs high computational overhead. (2) It focuses only on inter-sample correlations, ignoring intra-sample representational dynamics essential for modeling temporal entanglement and stable unlearning. (3) Their empirical validation is limited to ResNet-based image classification tasks without exploring the generalization to LLMs.

2.3. over-unlearning in Unlearning

Continued gradient updates during unlearning can excessively alter the model’s behavior on forget samples, causing their predictions to diverge from those on naturally unseen inputs. Such over-unlearning not only degrades generalization and overall model utility but can also introduce new privacy risks. Such over-unlearning not only degrades generalization and model utility but also increases vulnerability to Membership Inference Attacks (MIA) (Shokri et al., 2017), potentially leaking whether a sample in the forget dataset $\mathcal{D}_{f}$ was part of the original training set $\mathcal{D}$ (Shi et al., 2024; Hayes et al., 2025; Pawelczyk et al., 2024).

To address these challenges, Huang et al. (Huang et al., 2024) incorporate gradient upper bounds to stabilize the optimization process and facilitate early convergence. However, it can inadvertently result in under-unlearning of sensitive information. An alternative line of work seeks to reverse the conventional training objective using an assistant LLM. For instance, Ji et al. (Ji et al., 2024) propose training an auxiliary model with inverted training signals to address both over- and under-unlearning. While promising, this approach comes with significant computational overhead, as training an additional assistant model can be resource-intensive.

3. Preliminary

3.1. Unlearning Problem Formulation

In machine unlearning, let $\mathcal{D}=\{z_{i}\}_{i=1}^{N}$ represent a pretraining dataset of $N$ data points, including $z_{i}=(x_{i},y_{i})$ features and labels in supervised learning. The training dataset $\mathcal{D}$ comprises two subsets, namely $\mathcal{D}_{f}$ and $\mathcal{D}_{r}$, representing the data points to be unlearned and the retain data points, respectively, wherein $\mathcal{D}_{r}=\mathcal{D}\setminus\mathcal{D}_{f}$. Denote $\mathcal{M}_{t}=\mathcal{M}(\mathcal{D})$ as the model trained on the entire dataset $\mathcal{D}$. The goal of MU is to produce an unlearned model $\mathcal{M}_{u}$ that closely resembles the model $\mathcal{M}_{u}^{*}$ trained solely on $\mathcal{D}_{r}$, i.e., $\mathcal{M}_{u}^{*}=\mathcal{M}(\mathcal{D}_{r})$.

3.2. Mathematical Modeling for Unlearning

A mainstream approach in current LLM unlearning research is to fine-tune the pre-trained model using specially designed loss functions that promote unlearning. While the specific formulations differ across methods, these objectives typically share an underlying structure as follows:

[TABLE]

where $\alpha$ is a hyper-parameter for controlling the retain strength. The first loss term, $L(\theta^{\prime},\mathcal{D}_{f})$, which we call the forget loss, measures the prediction quality on the forget dataset. A typical choice of the forget loss is the (next-token prediction) cross-entropy loss on the forget dataset. The second loss term $L(\theta^{\prime},\mathcal{D}_{r})$, which we call the retain loss, measures the prediction quality on the retain dataset $\mathcal{D}_{r}$. Equation 1 essentially maximizes the forget loss while minimizing the retain loss, so this objective should ideally simultaneously achieve the aforementioned two goals.

Unlearning objectives for fine-tuning target LLMs include gradient-ascent methods and preference-loss methods. Notable examples of the forget loss and retain loss are as follows:

• •

Gradient Ascent (GA): The forget loss is formulated as:

[TABLE]

where the optimization is performed on the forget dataset $\mathcal{D}_{f}$ without referencing the retain dataset $\mathcal{D}_{r}$. Notably, the target label $y$ used in this objective can be flexibly chosen. Instead of the original correct output, one may substitute it with an arbitrary response $\widetilde{y}$ that the model is encouraged to output post-unlearning, such as random answers (Eldan and Russinovich, 2023), or simply answering "I don’t know" (Maini et al., 2024).

• •

Gradient Difference (GD): The forget loss is the same as GA, and the retain loss is formulated as:

[TABLE]

where $(x,y)\in\mathcal{D}_{r}$, which encourages the model to still perform well on the retain dataset $\mathcal{D}_{r}$.

• •

Negative Preference Optimization (NPO)(Zhang et al., 2024): NPO performs preference optimization using only negative responses as supervision signals. The forget loss is formulated as:

[TABLE]

where $\sigma(t)=1/(1+e^{-t})$ is the sigmoid function, $\beta>0$ is the inverse temperature and $f(\theta^{o})$ is the model trained on $\mathcal{D}_{\text{train}}$. NPO+GD combines the NPO loss with the retain loss from GD.

3.3. Unlearning Benchmark

In large language model unlearning research, evaluating a model’s ability to forget specific data while preserving overall performance is crucial. To standardize such evaluations, several benchmarks have been proposed (Maini et al., 2024; Li et al., 2024; Shi et al., 2024), among which TOFU (Maini et al., 2024) and MUSE (Shi et al., 2024) are the most representative. TOFU evaluates the model’s ability to forget specific data using around 200 fictitious author profiles, comparing outputs between the retrained and unlearned models to assess both forget quality and model utility. MUSE provides a comprehensive, multi-dimensional evaluation across six properties, including knowledge memory (knowmem), verb memory (verbmem), and privacy leakage (privleak). testing models on large-scale datasets such as books and news articles. These benchmarks together provide a more standardised framework for assessing unlearning methods in large language models, enabling quantitative comparison of unlearning effectiveness and utility preservation.

3.4. Memorization Score

Deep neural networks inherently memorize their training data. Feldman et al. (Feldman, 2020a) show that such instance-level memorization is essential for generalization under long-tailed distributions. This perspective underpins the use of memorization scores below as a proxy to quantify the degree to which individual samples are preserved in the model’s memory.

Assumption 1 (Memorization Score(Feldman, 2020a)).

*The memorization score for an example $i\in\mathcal{D}$ with respect to a training dataset $\mathcal{D}$ and algorithm $\mathcal{A}$ is defined as: *

[TABLE]

where $x_{i}$ and $y_{i}$ are the feature and label of example $z_{i}$.

Intuitively, the memorization score for example $z_{i}$ is high if including it in training yields a different prediction distribution on that example than excluding it from training would have, reflecting the model’s reliance on direct exposure to $z_{i}$.

4. Limitations of Existing Unlearning Methods and Our Insights

Neural networks do not memorize all samples equally, some examples are deeply memorized, while others are easily forgotten (Feldman, 2020b; Toneva et al., 2019). Consequently, effective unlearning requires adaptive control over the unlearning process across different dimensions. However, existing approaches often fail to achieve such fine-grained control, leading to inefficiency or over-unlearning. We summarize these challenges from three complementary perspectives: sample-level, iteration-level, and overall-level unlearning effort.

Sample-level: determining how much to forget for each sample. In practice, we first observe that unlearning effort should varies substantially across samples: some examples are tightly entangled with retain data, while others can be safely removed without affecting model utility. As shown in Figure 1, samples with higher entanglement tend to exhibit stronger memorization behaviors, indicating that the model has overfitted to those specific instances, which suggests that entanglement can serve as a useful signal for estimating how much each sample should be forgotten. Specifically, the update induced by EGU exhibits a smaller Euclidean distance (1.0901 vs. 1.2892), suggesting that its update magnitude is also closer to that of retraining. Instead of explicitly measuring memorization, which typically requires retraining or influence-based analysis, we introduce an entanglement-guided loss reweighting mechanism that provides a lightweight and effective alternative. As shown in Figure 2, EGU achieves better unlearning performance while significantly reducing computational overhead, enabling efficient and fine-grained control over sample-level unlearning.

Iteration-level: adapting unlearning effort over time. As shown in Figure 3, updates applied to one forget batch inevitably propagate to others through the shared parameter space, leading to cross-batch interference. As unlearning progresses, we observe a continuous increase in the loss of untouched samples, together with a steady decline in embedding similarity. This indicates a global representation drift rather than a localized adjustment, meaning that unlearning effects are not confined to targeted samples. These dynamics show that LLM unlearning is inherently coupled across samples and optimization steps, where parameter shifts can propagate and amplify, increasing the risk of over-unlearning and destabilizing the representation space. Although such representation shifts are generally undesirable side effects of unlearning, they provide valuable signals that, if properly exploited, can be used to more effectively guide and regulate the unlearning process.

Overall-level: determining when to stop unlearning. A key challenge in unlearning lies in the fact that the target degree of unlearning is inherently undefined. During the unlearning process, the model has no clear indication of whether the current level of unlearning is sufficient or already excessive. As shown in Figure 4, the forget loss keeps increasing during the unlearning process and eventually exceeds its corresponding loss under the retrained model, indicating that the model continues to push forget samples away even beyond what is necessary for effective unlearning. This uncontrolled behavior often leads to over-unlearning, where certain samples are excessively altered beyond what is necessary. Therefore, it becomes essential to design mechanisms that enable the model to adaptively recognize when to stop unlearning, achieving a balance between effective removal and distributional stability.

5. Methodology

In real-world scenarios, models do not memorize all samples equally, making it difficult to determine how much unlearning effort each sample requires. EGUP addresses this by introducing an entanglement-guided perspective, where the unlearning effort is adaptively determined by how strongly a forget sample is entangled with retained knowledge. Yet the model still lacks a reliable behavioral reference indicating when unlearning should stop. EGUP therefore further introduces an external behavioral constraint that approximates the desired “knowledge-removed” outputs, providing a soft stopping signal and stabilizing the unlearning process. The overall workflow of EGUP is illustrated in Figure 5.

5.1. Entanglement-Guided Unlearning (EGU)

In this paper, we propose Entanglement-Guided Unlearning, a scalable and principled framework that enables fine-grained control over the unlearning process. EGU leverages dual entanglement signals to guide unlearning: (1) Inter-sample entanglement quantifies the similarity between each forget embedding and the aggregated embedding of the retain dataset. Samples that are highly entangled with retained knowledge i.e., exhibiting higher embedding similarity are likely to be well-predicted by a retrained model, requiring minimal unlearning effort, whereas samples with lower entanglement are forgotten more aggressively. (2) Intra-sample entanglement captures the temporal evolution of each forget embedding across iterations. By continuously tracking how an embedding shifts across iterations even under cross-sample interference induced by updates on other forget samples within the shared parameter space—it adaptively modulates the unlearning process and promotes a smooth, stable trajectory of progressive unlearning.

Forget samples that are less entangled with retain dataset are typically semantically distant in the embedding space. These samples encode unique information with little overlap with the retain data, warranting stronger unlearning effort. EGU leverages this inter-sample entanglement signal to guide unlearning, approximating it via the cosine similarity between each forget sample and the aggregated embedding of the retain dataset, and adaptively modulating unlearning effort for more precise and effective removal of the target knowledge. In addition, intra-sample entanglement tracks the temporal evolution of each forget embedding, adaptively shaping the unlearning trajectory to ensure smooth and stable unlearning progresses. Together, inter- and intra-sample entanglement enable EGU to perform precise and stable unlearning. The overall framework is detailed in Algorithm 1. Notably, the framework is designed to be modular and flexible, allowing seamless integration into existing unlearning methods, including gradient ascent (Jang et al., 2022), gradient difference (Yao et al., 2024c), negative preference optimization (NPO) (Zhang et al., 2024), and NPO+GD (NPO with gradient descent on the retain dataset).

As shown in Algorithm 1, the proposed EGUP framework performs unlearning through dual entanglement–aware optimization, guided by both inter- and intra-sample entanglement. At every iteration $t$ we first compute the sentence-level (average token) embedding for each sample in the retain dataset and derive a global retain embedding $E_{\mathcal{D}_{r}}^{t}$ by averaging over all retain samples. the model processes a mini-batch $\xi_{t}$ from the forget dataset. For each forget sample $x_{i}$, we compute its sentence-level embedding $E_{x_{i}}^{t}$ under the current parameters $\theta_{t}$, and measure two types of entanglement: (1) the inter-sample entanglement $\mathrm{sim}_{i}=\cos(E_{x_{i}}^{t},E_{\mathcal{D}_{r}}^{t})$, which quantifies the semantic entanglement between forget and retain representations; and (2) the intra-sample entanglement $\mathrm{sim}_{i}^{\text{prev}}=\cos(E_{x_{i}}^{t},E_{x_{i}}^{t-1})$, which captures the parameter-dependent drift of forget embeddings across iterations.

The overall unlearning objective integrates both inter- and intra-sample entanglement–guided optimization. The term $-\frac{1}{|\mathcal{D}_{f}|}\sum_{i}w_{i}\cdot f(\theta_{t},x_{i})$ enforces adaptive unlearning guided by inter-sample entanglement, reflecting the semantic correlation between forget and retain samples. Meanwhile, the $\mu\cdot\log\frac{\exp(\mathrm{sim}_{i})}{\exp(\mathrm{sim}_{i})+\exp(\mathrm{sim}_{i}^{\text{prev}})}$ regularizes intra-sample entanglement, adaptively shaping the unlearning trajectory according to the temporal progression of each sample’s representation. The model parameters are subsequently updated via gradient descent: $\theta_{t+1}=\theta_{t}-\eta\nabla_{\theta}L(\theta_{t})$. Depending on the specific unlearning strategy, the loss term $f(\theta_{t},x_{i})$ can instantiate various unlearning objectives such as Gradient Ascent (GA) and Negative Preference Optimization (NPO), enabling flexible adaptation of EGUP to different unlearning paradigms.

To further clarify the motivation behind dual entanglement-guided optimization, note that the cosine similarity between forget and retain embeddings ranges from $-1$ to $1$. To ensure the coefficient remains positive and captures the negative correlation, we apply an exponential transformation $\exp(-cos)$, so that lower similarity (closer to -1) yields a larger coefficient. In this way, forget samples that are less similar to the retain dataset in the embedding space are assigned larger coefficients and thus receive stronger unlearning to better align with the behavior of the retrained model. Intuitively, when a forget sample closely resembles the retain dataset, the retrained model, which is trained without the forget sample, is likely to perform well on it, as the retain knowledge naturally generalizes to similar inputs. In the extreme case where a forget sample is almost identical to part of the retain dataset (e.g., a paraphrased sentence such as “X is born in Y” rewritten as “The birthplace of X is Y”), the retrained model will naturally retain high performance on it. Therefore, samples with lower similarity to the retain data require stronger unlearning to remove residual knowledge and better approximate the behavior of the retrained model. Finally, the coefficients are normalized via softmax operation with a temperature parameter $k$ to flexibly control the unlearning effort and achieve adaptable unlearning behavior.

Building upon this semantic weighting mechanism, the second term, $\mathrm{sim}_{i}^{\text{prev}}=\cos(E_{x_{i}}^{t},E_{x_{i}}^{t-1})$, captures intra-sample entanglement, providing a temporal regularization that tracks and guides the evolution of each forget embedding throughout the unlearning process. In the early stages, when $\mathrm{sim}_{i}^{\text{prev}}$ tends to be large due to minimal parameter updates, the contrastive term yields a stronger gradient, accelerating representation divergence and amplifying the unlearning effect. As unlearning proceeds and embeddings progressively decorrelate, $\mathrm{sim}i^{\text{prev}}$ decreases, causing the contrastive penalty to diminish relative to the weighted unlearning loss. This gradual reduction naturally stabilizes optimization, preventing over-unlearning and maintaining representational coherence. By encouraging moderate divergence between $E_{x_{i}}^{t}$ and $E_{x_{i}}^{t-1}$, the temporal term thus promotes a smooth and consistent embedding trajectory that reflects progressive unlearning.

5.2. EGU with Proxy Constraint (EGUP)

While the entanglement-guided unlearning framework adaptively modulates the unlearning effort across samples and iterations based on inter-sample and intra-sample entanglement, it still faces a fundamental challenge in controlling the overall degree of unlearning. In practice, it is often difficult to determine how much unlearning is sufficient. Without a clear criterion, continued updates can excessively alter the model’s predictions on forget samples, pushing them away from responses to naturally unseen inputs. Such unnecessary divergence not only undermines generalization but also introduces distributional inconsistencies, increasing the risk of unlearning detection. This highlights the need for an appropriate stopping criterion to prevent such undesirable deviations during unlearning. However, gradient-ascent–based unlearning offers no natural point of convergence, making it inherently difficult to decide when the level of unlearning becomes sufficient for the intended objective. The optimal threshold can vary substantially across model architectures, training datasets, and the degree of entanglement between forget and retain data. A fixed threshold may be too conservative for some samples and too aggressive for others, leading to either under-unlearning or over-unlearning.

To this end, we propose EGUP, an extension of EGU that incorporates Proxy Constraint based on test inputs synthesized through in-context learning (ICL) with LLM. These proxy samples emulate how the model would naturally respond to forget samples if it has never been exposed to them. By applying a loss-based soft constraint on the model’s predictions over these proxy inputs during unlearning, EGUP provides a semantically grounded and adaptive boundary that not only eliminates the need for manual threshold tuning, but also effectively mitigates over-unlearning and preserves the model’s ability to generalize after unlearning.

Unlike traditional test data, which typically relies on real, unseen ground-truth labels, our approach introduces novel unlearning constraints by leveraging a language model to generate plausible reference answers, referred to as test answers. These test answers are generated via In-Context Learning (ICL), where the language model is prompted with carefully selected exemplars that contrast correct outputs with uninformed responses. This design enables the ICL-generated outputs to serve as high-quality surrogates that approximate the behavior of the retrained model on unseen inputs. As semantically aligned references, they offer an effective criterion for identifying over-unlearning in forget samples. An additional advantage of employing ICL-based proxy answers lies in their adaptability to specific model behaviors and data distributions. By carefully selecting in-context exemplars that mirror the target model’s response tendencies, both in terms of correct predictions and typical failure cases, the language model can simulate how the target model would behave when presented with similar inputs after unlearning. This enables the generated test data to more accurately reflect model-specific generalization under ignorance, resulting in a penalty signal better aligned.

During unlearning, we monitor the prediction loss of each forget sample with respect to its original label and compare it to the loss computed using the LLM-generated proxy answer. If the loss on the real answer surpasses that on the proxy baseline, we impose a penalty term that suppresses unlearning and prevents over-unlearning. This mechanism constrains the unlearning process to remain aligned with the behavior of the retrained model, serving as an early warning signal to prevent over-unlearning.

The detailed procedure is shown in Algorithm 2. In each iteration, given forget samples $\xi_{t}$, each sample $z_{i}=\{x_{i},y_{i}\}$ consists of a question $x_{i}$ and its ground-truth answer $y_{i}$. We first prepare few-shot exemplars $\{(x_{j},y_{j},y_{j}^{\prime})\}$ to prompt a pretrained large language model (LLM). Here, $y_{j}^{\prime}$ denotes the model’s expected answer to $x_{j}$ without ever having seen the forget data. Conditioned on these exemplars, the LLM synthesizes a proxy answer $y_{i}^{test}$ for the target question $x_{i}$. The resulting pair $z_{i}^{test}=\{x_{i},y_{i}^{test}\}$ serves as a test reference approximating the model’s natural prediction behavior under the absence of explicit memorization. All proxy samples are collected to form the test dataset $\mathcal{D}_{test}$. Next, for each forget sample $x_{i}$, we compute its current loss $f(\theta_{t},z_{i})$ and the loss of proxy data $f(\theta_{t},z_{i}^{test})$. If the model’s loss on the forget data drops below the loss of proxy data $f(\theta_{t},z_{i})<f(\theta_{t},z_{i}^{test})$, this indicates that the unlearning process may have overshot the target, deviating excessively from the model’s expected generalization. To softly penalize such over-unlearning, we accumulate a penalty $\mathcal{P}$ defined as: $\mathcal{P}\leftarrow\mathcal{P}+\mu\cdot(f(\theta_{t},z_{i}^{test})-f(\theta_{t},z_{i}))\quad\text{if}\quad f(\theta_{t},z_{i})<f(\theta_{t},z_{i}^{test})$, where $\mu$ is a hyper-parameter controlling the penalty’s strength. This penalty is then added to the overall unlearning objective.

In Algorithm 2, the examples used in ICL are formatted as question–answer (QA) pairs, following the convention established by the TOFU benchmark. Our method can also be naturally extended to other data modalities. For instance, narrative passages can be reformulated into QA pairs by framing key facts as questions and answers, while dialogue data can be adapted by converting turns into query–response pairs. While Algorithm 2 presents the process as querying the LLM once per sample, in practice we adopt a more efficient strategy by batching multiple forget samples into a single prompt. This allows the LLM to generate corresponding proxy answers in parallel, substantially reducing the computational overhead and enhancing scalability to larger unlearning datasets. Below, we illustrate the prompt design used to obtain proxy answers through in-context learning (ICL). The prompt is structured into three components: System Instruction, which defines the model’s behavior; Input Description, which specifies the task context and information provided; and Output Requirement, which clarifies the expected form of the model’s response.

Prompt Template

System Instruction: You are required to infer the pure_answer, meaning the answer a model would output without learning the relevant knowledge.

Input Description: Each sample contains a question, the original answer, and a pure_answer produced by model that had never been exposed to the corresponding information. Your task is to analyze patterns of pure_answer and predict it for unseen questions.

Output Requirement: Produce the most probable pure_answer rather than the true real-world answer.

We present an example below regarding fictitious author Basil Mahfouz Al-Kuwaiti, which includes the user query, the corresponding real (ground‑truth) answer, the pure answer produced by the model before acquiring the relevant knowledge, and the test answer generated via in‑context learning (ICL) using GPT‑4o. While the real answer identifies his genre as “French Literature”, the pure answer suggests “Alternate History”, and the ICL-based test answer produces “Science Fiction”. As Alternate History is widely recognized as a subgenre of Science Fiction, the test answer exhibits strong semantic alignment with the pure answer. Both outputs deviate comparably from the real answer, suggesting that the ICL approach effectively approximates the behavioral characteristics of the retrained model, capturing its essential response tendencies.

Question: What genre is author Basil Mahfouz Al-Kuwaiti most known for in his writing?

Real Answer: Basil Mahfouz Al-Kuwaiti is most known for his writings in the French Literature genre.

Pure Answer: Basil Mahfouz Al-Kuwaiti is most renowned for his contributions to the genre of Alternate History.

Test Answer: Basil Mahfouz Al-Kuwaiti is known for his works in the Science Fiction genre.

6. Experiments

In this section, we comprehensively evaluate EGUP under widely adopted benchmark settings for LLM unlearning. Specifically, we follow two representative scenarios: (i) removing knowledge related to a fictional author in the TOFU benchmark (Maini et al., 2024), and (ii) mitigating memorized or privacy-sensitive content in the MUSE benchmark (Shi et al., 2024) (Section 6.3). Detailed experimental setups and evaluation metrics are provided in the appendix.

6.1. Experiments Results

We evaluate our unlearning method on the TOFU benchmark (Maini et al., 2024), which tests the removal of factual knowledge about 200 fictitious authors, each with 20 QA pairs. TOFU provides three forget sets $\mathcal{D}_{f}$ (1%, 5%, 10% of authors), while the retain set $\mathcal{D}_{r}$ contains QA pairs of the remaining authors. Forget quality (Maini et al., 2024) measures how closely the unlearned model matches one trained only on $\mathcal{D}_{r}$, whereas model utility reflects performance on held-out retain data, including information about fictional writers, real-world author profiles, and other world facts. Additionally, we report ROUGE-L scores for both forget and retain performance.

Experiments are conducted on fine-tuned Phi-1.5 (Li et al., 2023) and LLaMA2-chat-7B (Touvron et al., 2023), both pretrained on all 200 authors. Table 1 presents the experimental results on the TOFU benchmark, including comparisons across several unlearning methods: Gradient Ascent (GA), Gradient Difference (GD), Negative Preference Optimization (NPO), and their combination (NPO+GD), each reported in both vanilla form and when integrated with EGUP. The table highlights how EGUP consistently improves the vanilla baselines across different forgetting ratios, demonstrating enhanced forget quality and better retention stability. A broader comparison between EGUP and other state-of-the-art unlearning methods is illustrated in Figure 6.

Consistent Performance Gains Across Metrics. Our framework consistently outperforms the vanilla baselines across both Forget Quality and Model Utility on both Phi-1.5 and LLaMA2-7B in Table 1. On Phi-1.5, our framework consistently outperforms all vanilla baselines across both Forget Quality and Model Utility. Notably, for instance, under the 5% setting, integrating NPO+GD into our framework significantly elevates the Forget Quality from 0.0878 to 0.7934, while simultaneously improving Model Utility from 0.4158 to 0.4259. Moreover, the ROUGE-L score on the retain set increases from 0.3942 to 0.4147, demonstrating EGUP’s ability to maintain strong generalization while achieving effective unlearning. Similar trends are observed on the LLaMA2-7B model, confirming the generality and robustness of EGUP across architectures and scales. Under the 5% unlearning setting, EGUP(NPO+GD) improves the Forget Quality from 7.54e-5 to 0.9647, while also enhancing Model Utility from 0.5905 to 0.6202 and the Retain ROUGE-L from 0.5681 to 0.7926. Importantly, consistent gains are observed across all other unlearning ratios as well. For example, under the 10% setting, EGUP(NPO+GD) achieves a threefold increase in Forget Quality (0.3417 vs. 5.02e-10) while preserving substantially more useful knowledge, as evidenced by the higher Retain ROUGE-L (0.7266 vs. 0.4815) and Model Utility (0.6315 vs. 0.5608).

Consistent Gains Across Optimizers. Such consistent improvements are observed across all optimizers considered (e.g., GA, GD, NPO, and NPO+GD). Although GA performs less favorably than NPO, and GD underperforms compared to NPO+GD, the integration of all optimizers into our framework leads to noticeable gains. Notably, even though the trade-off between F.Q. and M.U. for GA under our framework remains inferior to the vanilla NPO baseline, it still benefits from our enhancements. We attribute this to the limited potential of the GA optimizer itself. In contrast, the combination of NPO+GD within our framework (denoted as EGUP(NPO+GD)) achieves forget quality that closely approximates that of the retrained model, demonstrating our framework’s strong capability in precise and efficient unlearning.

EGUP framework requires only the average retain embedding yet outperforms methods that use the full retain dataset. The EGUP framework enables even weaker optimizers to outperform stronger baselines by incorporating lightweight, entanglement guidance. A notable example is EGUP(GA), which builds upon GA and requires only the average embedding of the retain dataset. In contrast, GD depends on access to the full original retain dataset. Remarkably, EGUP(GA) consistently outperforms GD across multiple unlearning settings. Under the 5% unlearning setting, EGUP(GA) achieves a higher model utility (0.4261 vs. 0.4047) than GD, while also slightly improving forget quality (1.12e-5 vs. 1.39e-6). This demonstrates that even coarse-grained retain signals, such as a single average embedding vector, can provide strong regularization to guide unlearning without explicit access to the full retain dataset or gradient-level control. The same trend holds across multiple forgetting ratios. For instance, under 10% forgetting, EGUP(GA) boosts utility from 0.3878 to 0.4106, overtaking GD’s 0.4032 again, using only a minimal representation of the retain distribution.

EGUP Consistently Outperforms Baselines Across Phi and LLaMA2-7B. Figure 6 reports unlearning performance on both Phi and LLaMA2-7B across the TOFU benchmarks. Across the two model families, EGUP achieves a better trade-off between forget quality and model utility than alternative methods. The empirical-loss-based heuristic (Huang et al., 2024) is unstable: relative to the vanilla baseline it sometimes yields better unlearning performance but at other times performs worse, indicating high sensitivity to sample-level loss patterns and resulting variance across models and forgetting ratios. SatImp (Yang et al., 2025) tends to preserve model utility well on both Phi and LLaMA, but its forget quality is notably weaker, suggesting incomplete removal of targeted knowledge.

We further illustrate the effectiveness of EGUP by visualizing, in Figure 7 the per-sample absolute loss gap between each unlearned model and the retrained model on both the forget and retain datasets. The top row shows results on the forget dataset, where we observe that models incorporating entanglement guided unlearning (EGU) consistently produce smaller loss gaps compared to their counterparts. EGU better approximate the behavior of retraining in removing memorized knowledge. The bottom row presents results on the retain dataset. Notably, methods built upon our entanglement-guided framework consistently yield loss patterns that more closely align with the retrained model, compared to their non-entanglement counterparts. This indicates that by assigning differentiated unlearning effort based on sample entanglement, our approach enhances unlearning precision while significantly mitigating undesired unlearning of the retain knowledge, thus achieving a more stable and utility-preserving unlearning process.

Figure 9 compares EGUP with baseline approaches on PHI-1.5 and LLaMA2-7B under different forgetting rates (1%, 5%, and 10%). The radar plots evaluate four key metrics: Forget Quality, ForgetRL, Model Utility, and RetainRL. The blue curve denotes the retrain baseline, serving as the upper-bound target, while the orange curve represents the standard NPO+GD method. Introducing entanglement-guided loss reweighting (green) consistently enhances Forget Quality across all settings. Further incorporating the proxy constraint (red) yields notable improvements in Model Utility and brings performance closer to the retrain upper bound across most metrics. Particularly under the 1% forgetting scenario, the red curve almost overlaps with the retrain baseline, indicating that EGUP can closely emulate retraining when the forget ratio is small. As the forget rate increases to 5% and 10%, the performance gap gradually widens, reflecting the increasing difficulty of jointly maintaining forget quality and model utility.

6.2. Ablation Study

To better understand the contribution of each component in our framework, we conduct ablation studies by isolating the two key modules of EGUP. In Section 6.2.1, we evaluate the impact of entanglement-guided unlearning by disabling the proxy constraint. In Section 6.2.2, we assess the effectiveness of the proxy constraint by removing EGU, thereby highlighting its role in regularizing the unlearning process and preventing over-unlearning.

6.2.1. Entanglement-Guided Unlearning Framework

To further evaluate the effect of entanglement-guided loss reweighting in our unlearning framework, we conduct an ablation study on Forget-05, using NPO as the base unlearning method. Figure 8 compares the losses on the forget and retain dataset against the retrained model. It also illustrates how each component, including entanglement-guided loss reweighting, proxy constraint, and their combination, impact the trade-off between unlearning efficacy and model utility.

In Figure 8, each column presents the forget and retain losses under a specific variant of our method, evaluated against the retrained model’s loss as a reference. The first column shows the effect of applying entanglement-guided unlearning (EGU) alone. This mechanism amplifies the influence of highly entangled tokens during unlearning, thereby improving the unlearning performance, evident from the forget loss being closer to that of the retrained model. However, this comes at the cost of increased retain loss, indicating potential over-unlearning or unintended interference with useful knowledge. The second column isolates the impact of proxy regularization based on in-context learning (ICL). Although it contributes little to reducing the forget loss, it substantially improves the retain loss, demonstrating its effectiveness in constraining over-unlearning and preserving model utility. Finally, the third column shows the result of EGUP. This combination achieves the best balance, with both forget and retain losses approaching those of the retrained model. The figure thus highlights the complementary strengths of the two modules and underscores that their integration is critical to achieve precise and utility-preserving unlearning.

6.2.2. ICL-based Proxy Constraint

Figure 4 compares the unlearning dynamics under three forgetting rates (1%, 5%, 10%) between standard gradient difference (dashed) and EGUP_w/o(GD) (solid), across forget loss, retain loss, and penalty loss. We summarize our findings through the following key observations.

Stability in the early unlearning stage. At the initial training steps across all forget rates, both the forget loss and retain loss remain consistently low. This observation indicates that the unlearning process is well-behaved in its early phase. Meanwhile, the model maintains strong performance on the retain dataset, thus avoiding premature over-unlearning.

No penalty activation under mild unlearning. In the 1% forgetting case, no signs of over-unlearning are observed throughout the entire training trajectory. The penalty loss remains zero across all training steps, demonstrating that the test-informed penalty mechanism stays inactive when unnecessary and does not interfere with mild unlearning tasks.

Proxy-based penalty anticipates over-unlearning. For the 5% forgetting case, a sharp increase in retain loss is observed around step 18 for the GD baseline (dashed blue), signaling potential over-unlearning. Interestingly, the penalty loss (green) in EGUP_w/o (GD) also rises concurrently, serving as an early warning signal. Notably, this penalty is not derived from the retain loss; instead, it is computed from test-time ICL proxy data and incorporated into the forget objective, enabling EGUP to proactively anticipate and mitigate over-unlearning before severe retain degradation occurs.

ICL-informed penalty mitigates over-unlearning. In the later training stages, especially at higher forget rates (e.g., 5% and 10%), EGUP_w/o (GD) (solid lines) maintains lower retain loss compared to the GD baseline. This confirms that integrating ICL proxy data into the loss formulation effectively regularizes the unlearning process and prevents excessive degradation of the retain knowledge, validating the effectiveness of our proxy-based penalty design.

We compare several unlearning strategies across varying forget rates in Figure 10. The upper half of each heatmap displays results from baseline and entanglement-guided unlearning (EGU), while the lower half includes EGU with proxy constraint (EGUP). Across all model configurations and forgetting ratios, EGUP consistently achieves better utility preservation while maintaining comparable or even stronger forgetting performance. This demonstrates that incorporating ICL-based proxy guidance provides a more stable and well-regularized optimization trajectory.

6.3. Experiments on MUSE

We further extend our analysis to the MUSE benchmark (Shi et al., 2024), incorporating additional evaluation metrics to provide a more comprehensive evaluation. MUSE considers two representative types of textual data that may frequently involve unlearning requests: the News and Books subsets. The News subset comprises BBC news articles published after August 2023, which are partitioned into disjoint forget, retain, and holdout sets. The Books subset includes the Harry Potter book series. In this benchmark, both LLaMA-2-7B and ICLM-7B serve as pre-trained base models. In this work, we concentrate on Verbatim Memorization, Knowledge Memorization, Privacy Leakage, and Utility Preservation to evaluate unlearning effectiveness and safety, following the metrics defined in MUSE.

As shown in Table 2, EGUP consistently improves unlearning effectiveness across both the NEWS and BOOKS domains. Specifically, it significantly reduces the C1 and C3 metrics, which measures verbatim memorization and privacy leakage. This demonstrates its capacity to mitigate both surface-level and sensitive-data retention. These improvements highlight EGUP’s advantage in achieving stronger deletion guarantees compared to baseline methods. However, these gains often come with reduced knowledge memorization on the retain dataset (C4). Additionally, we observe that EGUP’s performance varies across data domains, with BOOKS posing greater challenges due to longer sequences and richer semantics. This highlights the need for more fine-grained unlearning strategies. In this regard, we identify token-level reweighting as a promising future direction. By leveraging semantic similarity signals at finer granularity, such approaches could allow for more targeted unlearning at token level while better preserving unrelated capabilities, particularly in semantically dense domains.

7. Conclusion

In summary, this work presents EGUP, an entanglement-guided unlearning framework that enables more precise and controllable unlearning for LLMs. By jointly modeling inter-sample entanglement across samples and intra-sample entanglement across iterations, EGUP captures how forget samples are coupled with retain knowledge and how their representations evolve during unlearning. This dual entanglement guidance allows EGUP to adaptively modulate unlearning effort and mitigate over-unlearning. Beyond entanglement guidance, EGUP further addresses the stopping challenge by approximating retrained model behavior as a principled reference to regulate unlearning. Since obtaining a retrained model is often impractical due to its prohibitive cost, we instead leverage open-source LLMs as proxy estimators and employ in-context learning to generate proxy outputs that closely approximate retrain behavior for each forget sample. Overall, EGUP provides a modular and extensible perspective on entanglement-driven unlearning and shows great improvements over existing methods. Looking ahead, extending entanglement guidance to the token level and designing more accurate or self-adaptive proxy constraints represent promising directions for achieving finer-grained and more principled unlearning in the future.

Open Science

Our research team is committed to the principles of open science, making our findings freely accessible. This commitment includes sharing all research materials, including datasets, scripts, and source code. The model and dataset we use in our experiments can be downloaded on HuggingFace. We hope that releasing our code as open source will not only support further research but also potentially influence real-world applications in the industry. The code is available at https://anonymous.4open.science/r/EGU-unlearning-2354.

Appendix A Appendix

A.1. Hardware configuration

We conduct all experiments on 4 A6000-48G GPUs. All experiments are conducted with and torch 2.2 and CUDA 12.1. We employ flash-attention-2 2.5.7 to improve the training and inference efficiency. We employ DeepSpeed ZeRO stage-3 for all baselines to compress GPU memory following the previous implementation released by TOFU (Maini et al., 2024).

A.2. More experiment details and Details of metrics

In this section, we list more details of unlearning experiment and the details of how to calculate the metrics used in our experiments.

Each model on MUSE is trained for 10 epochs with a constant learning rate 1e-5 and a batch size of 16. Results are selected from 10 checkpoints saved at each epoch. The unlearning epochs for each unlearning method on MUSE is presented in Table 3 with the same learning rate of 1e-5.

A.2.1. Experiment Setups of TOFU

We fine-tune both the Phi and LLaMA models using identical hyper-parameters. Specifically, we adopt a batch size of 32, gradient accumulation steps of 1, a total of 10 training epochs, a learning rate of $1\times 10^{-5}$, weight decay of 0.01, and a fixed random seed of 42. In the subsequent unlearning phase, model-specific configurations are applied. For the Phi model, we use a batch size of 16 and train for only 1 epoch with gradient accumulation steps remaining at 1. The retain strength coefficient $\alpha$ is fixed at 1 throughout. When applying the NPO method, the inverse temperature is set to $\beta=2.5$. In contrast, for our proposed entanglement-aware framework, we perform a grid search over entanglement temperatures $\{0.5,\ 1,\ 2\}$, and set the penalty weight $\mu$ through a grid search over $\{0.001,\ 0.005\}$. For the LLaMA model, we adopt a smaller batch size of 8 to accommodate its larger memory footprint. The number of training epochs is set to 2, while the gradient accumulation steps remain consistent with those used for the Phi model. Additionally, we apply LoRA during unlearning, with rank $r=32$, $\alpha=32$, and dropout of 0.05. Weight decay is also set to 0.01. All other unlearning-related hyper-parameters, including $\alpha$, $\beta$, the entanglement temperature, and $\mu$ are the same as in the Phi configuration.

A.2.2. Metric of TOFU Dataset

We mainly adopt the metric proposed in the original TOFU paper (Maini et al., 2024).

Model Utility. Model utility is the aggregated metrics across multiple retain sets, including the data of remaining fictional writers other than the authors in forget data, the QA pairs of real-world writers, and general world facts. The model utility is defined as the harmonic average of three metrics evaluated on the aforementioned three groups of retain data, i.e., aggregated value of nine metrics. The metrics include ROUGE-L score between unlearned LLM generated response and ground-truth response, the accuracy of unlearned LLM accuracy on the data, and the average truth-ratio, which is defined by:

[TABLE]

where $x,\tilde{y},\hat{y}$ are original questions, incorrect answers, and paraphrased correct answers, respectively, and $N$ is the number of incorrect answers. The rationale of the truth ratio is that it measures how likely the unlearned LLM will give a correct answer versus an incorrect one.

Forget Quality. Forget quality assesses how well the unlearned LLM mimics a retrain LLM, which is trained without the forget data. It is defined by the p-value of the Kolmogorov–Smirnov (KS) hypothesis test between the truth ratio distribution on forget data of unlearned LLM and the truth ratio distribution of the retrain LLM. We refer readers to the original TOFU paper (Maini et al., 2024) for more details.

A.2.3. Metric of MUSE Dataset

Verbatim Memorization (VerbMem). Considering a model $\theta$ with the first $l$ tokens from a sample $l$, the ROUGE-L value between the output of $f(x_{[l]};\theta)$ and the true continuation $x_{[l+1:]}$ is defined as the VerbMem:

[TABLE]

Knowledge Memorization (KnowMem). Different from VerbMem, KnowMem considers from an instance-wise perspective. Let $(q,a)$ represent a pair of question and answer in one sample $x$, the KnowMem is defined as:

[TABLE]

Privacy Leakage (PrivLeak). It is essential that the unlearned model does not leak membership details that could reveal $\mathcal{D}_{u}$ is part of $\mathcal{D}_{tr}$. Therefore, to accurately measure the degree of leakage, PrivLeak is proposed by employing Min-K% Prob (Shi et al., 2023) and computing the standard AUC-ROC score (Murakonda et al., 2021; Ye et al., 2022) as follows:

[TABLE]

where $\theta_{r}$ is the retrained model on the retain dataset, $\theta_{t}$ is the unlearned model. $\mathcal{D}_{h}$ denotes a ‘holdout’ dataset which contains in-distribution samples but the model has not been trained on. A well-performing unlearning algorithm should have a PrivLeak metric close to zero, whereas an over- or under-unlearning algorithm will result in a high positive or negative value.

Utility Preservation (UtilPres). Except for metrics on unlearn tasks, performance on other tasks are also concerned in MUSE. Specifically, UtilPres is represented as the evaluation on retain dataset with the KnowMem metric.

[TABLE]

A.2.4. Additional experiments

Additional experimental results are presented in Table 4 5 6 and Table 9 10 11, corresponding to evaluations on the TOFU dataset using the Phi and LLaMA models, respectively. Results under varying entanglement temperature $k$ are also reported in the Table 7 and Table 8.