The More Popular, The Harder to Forget: Adaptive Popularity for LLM Unlearning

Anna Borisiuk; Andrey Savchenko; Alexander Panchenko; Elena Tutubalina

cs.CLAug 14, 2026

The More Popular, The Harder to Forget: Adaptive Popularity for LLM Unlearning

Authors: Anna Borisiuk, Andrey Savchenko, Alexander Panchenko, Elena Tutubalina

Organizations: AIRI · ISP RAS Research Center for Trusted Artificial Intelligence · Sber AI Lab · Skoltech

Abstract

Popular facts are memorised more deeply during pretraining and resist removal longer than rare ones, yet existing LLM unlearning methods apply uniform gradient pressure regardless of training-data frequency. We propose the AdaPop (Adaptive Popularity) method, which combines local token confidence with a per-fact popularity-dependent exponent derived from an external proxy (e.g., Wikidata sitelinks, LLM-as-Judge), and automates the forget-retain balance via a dual-ascent controller that adjusts the retain penalty each epoch. Across three model families and two benchmarks, AdaPop leaks ~5x less forgotten content than competing methods under paraphrased queries and ~1.6x less under adversarial reformulations. We support our analysis with internal metrics: under our method, forget-set hidden states move further from the pre-unlearning model's states than under other methods, while retain-set representations remain close.

Figures & tables

Figure 1: Overview of AdaPop. The popularity score reweights per-fact token contributions to the forget loss; the dual-ascent controller adjusts the retain penalty each epoch to maintain retain quality (Algorithm 1 ).

Figure 2: Wikidata popularity-score distributions for the forget sets of DUET and RWKU. DUET spans nearly two orders of magnitude ( $69$ – $3{,}763$ ; median $1{,}090$ ), providing a direct test of popularity-sensitive methods; RWKU is narrower and skewed lower (median $130$ ).

Bench.	Algorithm	Rouge		Cos Sim
Bench.		F. $\downarrow$	R. $\uparrow$	F. $\downarrow$	R. $\uparrow$
	w/o MU	0.939	0.968	0.874	0.883
	AdaPop	0.043 $\pm$ .007	0.959 $\pm$ .009	0.369	0.971
	GA †	0.000 $\pm$ .000	0.000 $\pm$ .000	0.093	0.093
	GD †	0.021 $\pm$ .003	0.853 $\pm$ .011	0.120	0.897
	NPO	0.670 $\pm$ .095	0.996 $\pm$ .005	0.684	0.998

Table 1: ROUGE-L Recall and Cosine Similarity for Llama-3.1-8B-Instruct at

\text{lr}=10^{-4}

. ROUGE-L: mean

\pm

std over three seeds; Cosine Similarity: single seed. F.

\downarrow

= forget; R.

\uparrow

= retain. w/o MU = the original checkpoint, evaluated with no unlearning applied. Underline = best among NPO, WGA, AdaPop. † Unusable: generation failure (GA: joint output and retain collapse; GD: severe retain degradation with collapse-style generation artefacts; see Appendix G ).

Bench.	Algorithm	Rouge		Cos Sim
Bench.		F. $\downarrow$	R. $\uparrow$	F. $\downarrow$	R. $\uparrow$
	w/o MU	0.921	0.886	0.864	0.861
	AdaPop	0.056 $\pm$ .007	0.950 $\pm$ .008	0.456	0.964
	GA †	0.000 $\pm$ .000	0.000 $\pm$ .000	0.058	0.092
	GD †	0.022 $\pm$ .004	0.757 $\pm$ .015	0.094	0.841
	NPO	0.684 $\pm$ .023	0.973 $\pm$ .002	0.576	0.979

Table 2: ROUGE-L Recall and Cosine Similarity for Qwen2.5-7B-Instruct at

\text{lr}=10^{-4}

. Notation as in Table 1 .

Bench.	Algorithm	Rouge		Cos Sim
Bench.		F. $\downarrow$	R. $\uparrow$	F. $\downarrow$	R. $\uparrow$
	w/o MU	0.892	0.926	0.586	0.541
	AdaPop	0.023 $\pm$ .004	0.976 $\pm$ .011	0.206	0.976
	GA †	0.000 $\pm$ .000	0.000 $\pm$ .000	0.096	0.102
	GD †	0.044 $\pm$ .007	0.598 $\pm$ .024	0.069	0.626
	NPO	0.626 $\pm$ .071	0.968 $\pm$ .007	0.394	0.956

Table 3: ROUGE-L Recall and Cosine Similarity for Gemma-7B-it at

\text{lr}=10^{-4}

. Notation as in Table 1 .

Algo	Llama	Qwen	Gemma
DUET paraphrase forget ROUGE-L $\downarrow$
AdaPop	0.045	0.074	0.027
GA †	0.000	0.000	0.000
GD †	0.015	0.045	0.117
NPO	0.696	0.605	0.568
WGA	0.042	0.104	0.050

Table 4: Robustness at

\text{lr}=10^{-4}

. Top : paraphrase ROUGE-L on the DUET forget split (lower is better). Bottom : RWKU Level-3 adversarial-attack ROUGE-L; lower indicates stronger resistance to knowledge recovery. Underline = best among NPO, WGA, AdaPop. GA and GD collapse and are excluded from forget-quality ranking.

Algo	Llama		Qwen		Gemma
	Pop.	Rare	Pop.	Rare	Pop.	Rare
AdaPop	0.040	0.049	0.055	0.092	0.028	0.026
GD †	0.027	0.003	0.086	0.003	0.232	0.002
NPO	0.854	0.538	0.778	0.432	0.796	0.339
WGA	0.067	0.017	0.194	0.014	0.096	0.003

Table 5: DUET paraphrase forget ROUGE-L (

\downarrow

) split by popularity tier at

\text{lr}=10^{-4}

. Underline = best among NPO, WGA, AdaPop. GA is omitted (all values

0.000

under collapse); † GD’s low rare-tier values coincide with retain collapse (Table 1 ).

Algo	$\Delta$ LP	$\Delta$ Rank	Hid.Cos	KL
DUET — forget split ( $\Delta$ LP $\downarrow$ , $\Delta$ Rank $\uparrow$ , Hid.Cos $\downarrow$ , KL $\uparrow$ )
AdaPop	$\underline{-160}$	$\underline{+53{,}760}$	0.702	42.5
GA †	$-3{,}106$	$+106{,}826$	0.352	479.6
GD †	$-5{,}917$	$+104{,}134$	0.192	1006.4
NPO	$-42$	$+8{,}824$	0.861	5.4
WGA	$-52$	$-3{,}714$	0.729	16.2

Table 6: Internal metrics at

\text{lr}=10^{-4}

, averaged across Llama, Qwen, and Gemma. Directional arrows are shown in each section header. Underline = best among NPO, WGA, AdaPop. GA and GD values are reported for reference but indicate model collapse and are not ranked. Per-model breakdown in Appendix K .

Algo	Llama		Qwen		Gemma
	MMLU	HS	MMLU	HS	MMLU	HS
w/o MU	0.65	0.73	0.71	0.68	0.47	0.64
AdaPop	0.65	0.76	0.71	0.68	0.52	0.62
GA	0.23	0.33	0.23	0.43	0.25	0.26
GD	0.64	0.59	0.71	0.65	0.47	0.37
NPO	0.65	0.72	0.70	0.68	0.51	0.63

Table 7: MMLU accuracy and HellaSwag (HS) normalised accuracy at

\text{lr}=10^{-4}

. w/o MU = the original checkpoint, with no unlearning applied. Values averaged across DUET and RWKU checkpoints.

Figure 3: AdaPop on DUET (Llama) under three popularity signals: Wikidata score, LLM-as-Judge (3-seed mean), and measured corpus frequency (infini-gram over Pile-train). Left: forget ROUGE-L (

\downarrow

). Right: holdout ROUGE-L (

\uparrow

). Each point averages a rare-tier and a popular-tier run at that learning rate. All signals use the anchors of Appendix B ,

(a,b)=(58.7,0.796)

. Rates above

5\times 10^{-4}

are omitted: at

10^{-3}

every signal has at least one collapsed tier.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Config	$a$	$b$	F. $\downarrow$	R. $\uparrow$	$\Delta$ F.	$\Delta$ R.
baseline	58.70	0.7960	0.045	0.961	0	0
$+a,+b$	70.44	0.9552	0.038	0.975	$-$ 0.007	$+$ 0.014
$+a,-b$	70.44	0.6368	0.044	0.994	$-$ 0.001	$+$ 0.033
$-a,+b$	46.96	0.9552	0.024	0.920	$-$ 0.021	$-$ 0.041
$-a,-b$	46.96	0.6368	0.034	0.991	$-$ 0.011	$+$ 0.030

Appendix

Table 8: AdaPop coefficient sensitivity. Each row perturbs

a

and/or

b

\pm

20% from the analytically derived baseline. F.

\downarrow

= forget ROUGE-L; R.

\uparrow

= retain ROUGE-L.

\Delta

values are signed differences from the baseline.

Question	Answer	Wikidata	LLM	ROUGE-L
Wikidata popular, LLM rare
What is the country of Ensenada?	Mexico	2113	30	1.0
What is the country of Tourcoing?	France	2112	40	1.0
What is the country of Qus?	Egypt	3763	50	1.0
Wikidata rare, LLM popular
What is the instance of Hua Hin?	seaside resort	148	9000	0.5

Appendix

Table 9: Discordant cases between Wikidata score and LLM-judge scores on DUET. ROUGE-L : Llama-3.1-8B-Instruct recall before unlearning. Top group: Wikidata-popular facts recalled at ROUGE-L

1.0

despite low LLM-judged salience, indicating deep memorisation. Bottom group: Wikidata-rare facts with higher LLM scores but variable recall, consistent with shallower encoding.

Proxy	Pearson	Spearman
Wikidata score	0.970	0.839
LLM judge	0.677	0.659

Appendix

Table 10: Agreement of each popularity proxy with measured corpus frequency on DUET, counted over Pile-train (

383

B tokens) with infini-gram. Pearson is computed in log space. The two proxies agree with each other at Spearman

0.596

and assign the same rare/popular label to

84\%

of facts.

Score noise	F. rare $\downarrow$	F. pop. $\downarrow$	R. $\uparrow$
none	0.05	0.04	0.96
log-normal, $\sigma{=}1.0$	0.02	0.05	0.96
labels 50% swapped	0.02	0.05	0.97
labels 100% swapped	0.01	0.05	0.92

Appendix

Table 11: AdaPop under corrupted popularity scores (DUET, Llama-3.1-8B-Instruct,

\text{lr}=10^{-4}

). Forget ROUGE-L is reported per popularity tier. Retain degrades by

0.04

even when every label is inverted.

Bench.	Algorithm	ROUGE-L
Bench.		F. $\downarrow$	R. $\uparrow$
	w/o MU	0.939	0.968
	AdaPop	0.043	0.959
	UNDIAL	0.884	0.998
	RMU	0.882	0.998
	PDU	0.476	0.954

Appendix

Table 12: ROUGE-L Recall for additional baselines, Llama-3.1-8B-Instruct at

\text{lr}=10^{-4}

. w/o MU = the original checkpoint, with no unlearning applied; AdaPop reproduced from Table 1 for reference. F.

\downarrow

= forget; R.

\uparrow

= retain. Underline = best among non-collapsed methods. † Model collapse.

Bench.	Algorithm	ROUGE-L
Bench.		F. $\downarrow$	R. $\uparrow$
	w/o MU	0.921	0.886
	AdaPop	0.056	0.950
	UNDIAL	0.797	0.930
	RMU	0.734	0.983
	PDU	0.632	0.869

Appendix

Table 13: ROUGE-L Recall for additional baselines, Qwen2.5-7B-Instruct at

\text{lr}=10^{-4}

. Notation as in Table 12 .

Bench.	Algorithm	ROUGE-L
Bench.		F. $\downarrow$	R. $\uparrow$
	w/o MU	0.892	0.926
	AdaPop	0.023	0.976
	UNDIAL	0.819	0.980
	RMU	0.851	0.992
	PDU	0.677	0.934

Appendix

Table 14: ROUGE-L Recall for additional baselines, Gemma-7B-it at

\text{lr}=10^{-4}

. Notation as in Table 12 .

Figure 4: Internal representation metrics at $\text{lr}=10^{-4}$ , across three models. Each row corresponds to one metric; each column corresponds to one data split. For the forget split, deeper erasure corresponds to lower $\Delta$ LP, higher $\Delta$ Rank, lower Hid.Cos, and higher KL; directional desiderata are reversed for the retain split. Marker shape indicates benchmark (DUET vs. RWKU); colour indicates model family.

Figure 5: Component ablation on DUET. Top row : rare-fact paraphrase forget ROUGE-L ( $\downarrow$ ) and retain ROUGE-L ( $\uparrow$ ) over $\text{lr}\in[2\times 10^{-5},8\times 10^{-4}]$ . Bottom row : popular-fact paraphrase forget ROUGE-L ( $\downarrow$ ) and retain ROUGE-L ( $\uparrow$ ) over $\text{lr}\in[2\times 10^{-4},8\times 10^{-3}]$ .

Panel of Figure 6 — Figure 6: ROUGE-L (solid) and Cosine Similarity (dashed) on the merged DUET forget (left) and retain (right) splits across learning rates, for Llama (top), Qwen (middle), and Gemma (bottom).

Panel of Figure 7 — Figure 7: ROUGE-L (solid) and Cosine Similarity (dashed) on the RWKU forget (left) and retain (right) splits across learning rates, for Llama (top), Qwen (middle), and Gemma (bottom).

Figure 8: DUET forget and retain splits separated by popularity tier (Llama). Top row : rare facts. Bottom row : popular facts. The order-of-magnitude difference in the learning rate required to achieve comparable forgetting across the two tiers is direct evidence of the popularity gap.

Figure 9: Forget (left) and retain (right) ROUGE-L Recall per training epoch on DUET, Llama-3.1-8B-Instruct, at $\text{lr}=10^{-4}$ .

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Large Language Model (LLM) unlearning is often evaluated primarily by target suppression and clean retain utility. These metrics can miss a local failure mode: a model may perform well on standard retain prompts, yet degrade on benign reasoning when prompts lie near the forgotten domain. This phenomenon is termed forget-adjacent utility loss. A fundamental question is: where should forget representations go after they leave the removed behavior? Successful unlearning depends not only on whether forget-conditioned representations depart from the harmful computation, but also on the direction in which they are redirected afterward. We propose RA

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