cs.LGOct 6, 2026

How Learning Governs Unlearning across the Memorization-Generalization Spectrum

Authors: Hwiyeong Lee, Hyelim Lim, Ingyu Bang, Hoki Kim, Taeuk Kim

Organizations: Seoul National University · Hanyang University · Chung-Ang University

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Abstract

While unlearning seeks to negate undesired capabilities acquired through learning, little research has examined how the way models learn shapes their subsequent unlearning. In this paper, we investigate this connection from the perspectives of memorization and generalization, the two most representative yet competing strategies that models employ during training. We first classify memorization- and generalization-heavy models using grokking in modular addition and compare their responses to unlearning, showing that the latter suffer greater retain damage, i.e., a larger performance drop on the retain set. Furthermore, we conduct a finer-grained analysis by introducing bucketed modular addition, in which the respective contributions of the two strategies can be explicitly controlled across the memorization-generalization spectrum. In this setup, we reaffirm that the same trend persists and is nearly monotonic. We further demonstrate that this relationship also holds in LLM unlearning across verbatim and factual recall settings. Finally, we provide two practical insights for developing better unlearning methods, highlighting the importance of accounting for learning dynamics in unlearning.

Figures & tables

Figure 1: Analysis of unlearning across the memorization–generalization spectrum. We argue that retain damage in unlearning grows with a model’s reliance on generalization over memorization during training. We study this in three steps: contrasting memorizing and generalizing models separated by grokking (§ 3 ), extending this contrast to a fine-grained analysis across the spectrum, quantified by the memorization floor (§ 4 ), and confirming the relationship in LLM unlearning (§ 5 ).
PhaseEpochRLGD
Memorization1,00059.5 ± 3.323.0 ± 6.5
Circuit formation3,80052.4 ± 7.319.3 ± 5.3
Cleanup10,00014.2 ± 1.58.7 ± 3.2
Grokked25,3008.1 ± 0.73.3 ± 1.0
Table 1: Retain accuracy (%). Mean ±\pm 95% CI across five Df\mathcal{D}_{f} selection seeds when forget accuracy first falls to a threshold τ\tau or below.
Figure 2: Learning strategy changes the retain damage of unlearning. Unlearning trajectories under random labeling (RL) at four checkpoints from memorization to grokking ( Df\mathcal{D}_{f} selection seed 1). Top: forget accuracy falls much faster than retain accuracy in the memorizing model, whereas both decline together in the generalized model, incurring greater retain damage. Bottom: the Fourier circuit contributes little in the memorizing model; in the generalized model, falling FVE and rising restricted loss reveal its degradation. Restricted loss is normalized per trajectory.
Figure 3: Grokking and the forget–retain trade-off in BMA. Top: For M≤64M\leq 64 , test bucket accuracy (dashed) rises long after training exact accuracy (solid) saturates, revealing grokking in bucket selection. Dotted lines mark chance levels. Bottom: Forget–retain trade-offs in PfP_{f} and PrP_{r} during unlearning (5% forget set, seed 17). With larger memorization floor, the trade-off curves generally lie closer to the starred ideal target: Pf=1/256P_{f}=1/256 and Pr=1P_{r}=1 .
Memorization FloorPassageTF-IDFBits
High… those of Humelbergius , the editor -physician of Z ü rich , will be enjoyed and read with profit by every antiquary . The labors of Bernhold and Schuch are meritorious …7.291268
Low… just as obvious as the principles taken for granted. For no very good reason, three of these principles have been singled out by tradition under the name of ‘Laws of Thought’ …6.68614
Table 2: Rarer vocabulary, higher memorization floor. One example passage from each forget set; words occurring five or fewer times in inserted Gutenberg Popular passages are highlighted.
Figure 4: A higher memorization floor leaves less retain damage. (Left) Damage on ID ±\pm 95% CI after unlearning the High and Low forget sets. (Right) In-relation damage ±\pm 95% CI for each target relation for each method, ordered by the relation’s memorization floor. Heavy line represents the means over the four methods. Nat. and Birth. abbreviate nationality and birthplace respectively.
RelationSubject  → \,\rightarrow\, AttributeMem. Floor
EmailMaurice Clauss  → \,\rightarrow\, clauss@gmail.com0.0002
Nat.Ricardo da Sousa  → \,\rightarrow\, Brazil0.2013
UUIDTony Nieminen  → \,\rightarrow\, 766e00 … 8b12ce5.6064
Table 3: Predictable attributes have a lower memorization floor. Hubble-8B-500B examples; memorization floor in bits.
Appendix figures & tables24 assets

Supplementary material from the paper’s appendix.

Appendix

SettingValue
Transformer layers1
Attention heads4
Model dimension128
MLP width512
ActivationReLU
Layer normalizationNone
Appendix
Table 4: Model architecture for modular addition.
SettingValue
Tasky=(a+b) mod 113y=(a+b)\bmod 113
Train/test pairs3,830 / 8,939 (30% / 70%)
OptimizerFull-batch AdamW
Learning rate10−310^{-3}
Weight decay1
Adam coefficients(0.9,0.98)(0.9,0.98)
Appendix
Table 5: Training configuration for modular addition.
SettingValue
OptimizerFull-batch AdamW
Learning rate10−410^{-4} (RL); 10−410^{-4} or 3×10−43\times 10^{-4} (GD)
Weight decay0 (RL); 1 (GD)
Retain weight λ\lambda0 (RL); 10 (GD)
Evaluation interval (updates)1
Forget/retain examples383 / 3,447
Appendix
Table 6: Unlearning configuration for modular addition. Learning rates are those used for the reported chance-threshold results.
InterventionRetain accuracy (%)FVERestricted loss
Memorization
RL59.5 ± 3.30.0104 ± 0.00055.382 ± 0.448
RL + filtering (non-key)59.7 ± 3.10.0104 ± 0.00055.384 ± 0.465
RL + filtering (key)60.2 ± 2.60.0124 ± 0.00045.296 ± 0.473
Circuit formation
RL52.4 ± 7.30.0239 ± 0.00294.653 ± 0.142
Appendix
Table 7: Fourier gradient filtering across training phases. Results at forget accuracy ≤τ\leq\tau , reported as mean ±\pm 95% CI across five Df\mathcal{D}_{f} selection seeds.
InterventionRetain acc. (%)FVERestricted loss
RL8.1 ± 0.70.186 ± 0.0262.324 ± 0.183
RL + filtering (non-key)8.2 ± 0.70.187 ± 0.0272.316 ± 0.187
RL + filtering (key)30.6 ± 4.10.509 ± 0.0200.167 ± 0.167
Appendix
Table 8: Protecting the Fourier circuit reduces retain damage. Unlearning (RL) results for the grokked model at forget accuracy ≤τ\leq\tau , using the same optimizer settings across conditions. Filtering removes logit-gradient components along the specified Fourier directions. Entries are mean ±\pm 95% CI across five Df\mathcal{D}_{f} selection seeds.
SettingValue
Tasky=M((a+b) mod p)+ua,by=M((a+b)\bmod p)+u_{a,b} , pM=256pM=256
Bucket size MM / Memorization Floor log⁡2M\log_{2}M1,4,16,64,2561,4,16,64,256 / 0,2,4,6,80,2,4,6,8 bits
Output classes256
Train/test pairs19,660 / 45,876 (30% / 70%)
OptimizerFull-batch AdamW
Learning rate10−310^{-3}
Appendix
Table 9: Training configuration for bucketed modular addition. Settings are fixed across bucket sizes.
SettingValue
Optimizer / weight decayFull-batch AdamW / 0
Forget/retain examples197 / 19,463 (1%); 983 / 18,677 (5%); 1,966 / 17,694 (10%)
Forget-set selection seeds17, 26, 42
Stopping rulePf≤0.0039P_{f}\leq 0.0039 , or update budget
Comparison criterionPf=0.1P_{f}=0.1
Appendix
Table 10: Unlearning configuration for bucketed modular addition. Settings are fixed across bucket sizes and selection seeds; only GD depends on the forget fraction.
Figure 5: A lower memorization floor leaves greater retain damage. Retain damage 1−Pr1-P_{r} at Pf=0.1P_{f}=0.1 . Points and error bars show means and 95% CIs across three Df\mathcal{D}_{f} selection seeds. Dashed lines mark damage 0.90.9 , the nonselective baseline where Pf=Pr=0.1P_{f}=P_{r}=0.1 .
ForgetMethodρs\rho_{s}rr
1%GD−- 0.900−- 0.950
 RL−- 1.000−- 0.995
 DPO−- 1.000−- 0.994
 ME−- 0.900−- 0.924
5%GD−- 1.000−- 0.975
 RL−- 1.000−- 0.972
Appendix
Table 11: Memorization floor and retain damage. Spearman’s ρs\rho_{s} and Pearson’s rr between memorization floor ( log⁡2M\log_{2}M ) and mean retain damage ( 1−Pr1-P_{r} ) at Pf=0.1P_{f}=0.1 , across five bucket sizes ( n=5n=5 ), calculated separately for each forget fraction and method.
SizePretraining budgetRepository
8B100B tokensallegrolab/hubble-8b-100b_toks-{ standard , perturbed }-hf
8B500B tokensallegrolab/hubble-8b-500b_toks-{ standard , perturbed }-hf
1B100B tokensallegrolab/hubble-1b-100b_toks-{ standard , perturbed }-hf
1B500B tokensallegrolab/hubble-1b-500b_toks-{ standard , perturbed }-hf
Appendix
Table 12: Hubble model pairs. The two members of a pair share a pretraining procedure and differ only in whether the controlled insertions are present.
CorpusDataset
Gutenberg Popularallegrolab/passages_gutenberg_popular
Wikipediaallegrolab/passages_wikipedia
YAGO biographiesallegrolab/biographies_yago
Appendix
Table 13: Inserted corpora. The Hubble insertions these experiments use. Each is added to the base corpus when the perturbed model is pretrained and is absent from the standard model; Hubble inserts further corpora that we do not use.
RoleGroupHubble 8B-100BHubble 8B-500BHubble 1B-100BHubble 1B-500BSource and selection
ForgetHigh24242418Gutenberg Popular, top 30%
ForgetLow24242418Gutenberg Popular, bottom 30%
RetainID-seen32323221Gutenberg Popular, middle 40%
RetainOOD-seen76767616Wikipedia, 256×256\times inserted
RetainUnseen400400400400200 held-out passages of each corpus
Appendix
Table 14: Forget and retain groups for verbatim recall. Entries are passage counts. High and Low are the top and bottom 30% of the 256×256\times Gutenberg Popular tier by memorization floor. For Hubble-1B-500B the tier is first restricted to Pˉpert≥0.6\bar{P}_{\mathrm{pert}}\geq 0.6 , which shrinks every seen group.
GroupHubble 8B-100BHubble 8B-500BHubble 1B-100BHubble 1B-500B
High1136 ± 891048 ± 881233 ± 961062 ± 97
Low881 ± 82780 ± 88985 ± 83838 ± 80
Appendix
Table 15: Memorization floor of the verbatim forget sets. Per-passage floor in bits, as mean ±\pm 95% CI over the passages of the group.
MethodLearning rateRetain objective
GA10−510^{-5}None
GD10−510^{-5}Cross-entropy on ID-seen ( λ=1\lambda=1 )
NPO10−510^{-5}None
CEU10−510^{-5}None
Appendix
Table 16: Unlearning hyperparameters for verbatim recall. Each run uses AdamW, gradient clipping at 1.0, and one pass over its forget set per epoch. NPO uses β=0.1\beta=0.1 .
Figure 6: Document-level TF-IDF and memorization floor. Each point is a passage of the two forget sets; panel titles give the Pearson correlation and its pp -value.
  Retain damage (%) ↓\downarrow
ModelRetainGAGDNPOCEU
HighLowHighLowHighLowHighLow
Hubble 8B-100BID-seen45.5 ± 3.854.0 ± 3.217.3 ± 2.317.9 ± 1.845.0 ± 3.852.8 ± 3.354.2 ± 6.574.0 ± 5.1
OOD-seen3.4 ± 0.55.4 ± 0.92.9 ± 0.54.0 ± 0.73.4 ± 0.55.2 ± 0.89.8 ± 3.018.7 ± 4.3
Unseen0.5 ± 0.10.7 ± 0.10.6 ± 0.10.8 ± 0.10.5 ± 0.10.7 ± 0.1−- 0.6 ± 0.1−- 0.4 ± 0.1
Hubble 8B-500BID-seen14.8 ± 2.126.4 ± 2.90.2 ± 0.63.6 ± 1.113.4 ± 2.125.2 ± 2.944.1 ± 6.163.1 ± 4.2
Appendix
Table 17: Retain damage in verbatim recall. Hubble-8B and Hubble-1B, 256×256\times Gutenberg Popular. Damage is 100(Pˉr,before−Pˉr,after)100(\bar{P}_{r,\mathrm{before}}-\bar{P}_{r,\mathrm{after}}) at Pˉf=0.1\bar{P}_{f}=0.1 , as mean ±\pm 95% CI over the retain passages of a group. Bold marks the smaller damage of a High–Low pair.
  Memorization floor (bits)
RelationPromptHubble-8B-100BHubble-8B-500B
Email{subject} receives email at0.93 ± 0.640.43 ± 0.42
Nationality{subject} is from1.61 ± 0.441.09 ± 0.31
Birthplace{subject} was born in4.30 ± 2.052.30 ± 1.31
UUID{subject} has the unique identifier5.00 ± 0.625.70 ± 0.70
Appendix
Table 18: Relations, prompts, and memorization floors. Each prompt opens the biography sentence that states the attribute, with the subject’s name in place of {subject} , and is completed by the attribute value. Floors are mean ±\pm 95% CI over the relation’s selected facts.
SettingHubble-1BHubble-8B
Learning rate3×10−73\times 10^{-7}10−510^{-5}
Initial update budget240480
Continuation for unmatched runsNoneUp to 20 updates
Appendix
Table 19: Unlearning settings for factual recall. Only these three settings depend on model size; both sizes use the 100B and 500B pretraining budgets, 15 forget facts out of 50 with selection seed 42, GD retain weight 5, and β=0.1\beta=0.1 for NPO and DPO. Settings are shared by all methods and relations.
   Retain damage (%p) ↓\downarrow
ModelRelationMem. FloorGAGDNPODPO
In-relationOut-relationIn-relationOut-relationIn-relationOut-relationIn-relationOut-relation
Hubble 8B-100BEmail0.93 ± 0.6477.1 ± 14.63.6 ± 3.114.3 ± 12.22.1 ± 2.445.7 ± 17.43.6 ± 3.045.7 ± 17.42.9 ± 2.7
Nationality1.61 ± 0.4448.6 ± 17.42.9 ± 2.742.9 ± 17.23.6 ± 3.045.7 ± 17.43.6 ± 3.025.7 ± 15.22.9 ± 2.8
Birthplace4.30 ± 2.0517.1 ± 13.11.4 ± 2.05.7 ± 8.12.1 ± 2.425.7 ± 15.21.4 ± 2.017.1 ± 13.11.4 ± 2.0
UUID5.00 ± 0.6211.4 ± 11.11.4 ± 2.014.3 ± 12.21.4 ± 2.014.3 ± 12.20.0 ± 0.014.3 ± 12.20.7 ± 1.4
Appendix
Table 20: Retain damage in factual recall. Hubble-8B and Hubble-1B, 64×64\times YAGO. The memorization floor is in bits and damage is the decrease in accuracy in percentage points, both as mean ± 95% CI; in-relation intervals are paired across facts. GA, GD, NPO, and DPO all reach the forget target. Within a model, bold marks the relation on which a method leaves the least in-relation damage.
ModelRelationIn-relationOut-relationΔ\Delta
Hubble-8B-100BEmail45.7 ± 40.83.0 ± 1.142.7 ± 39.9
 Nationality40.7 ± 16.33.2 ± 0.737.5 ± 16.1
 Birthplace16.4 ± 13.11.6 ± 0.614.8 ± 13.6
 UUID13.6 ± 2.30.9 ± 1.112.7 ± 3.0
Hubble-8B-500BEmail36.4 ± 15.95.4 ± 2.731.1 ± 16.6
 Nationality39.3 ± 15.08.4 ± 2.330.9 ± 14.8
Appendix
Table 21: Mean retain damage across methods. Accuracy decrease (percentage points), averaged over GA, GD, NPO, and DPO, with 95% tt intervals across methods. Δ\Delta is the difference between in-relation and out-relation damage.
ModelMethodrrρs\rho_{s}
Hubble-8B-100BGA−- 0.966−- 1.000
 GD−- 0.517−- 0.316
 NPO−- 0.978−- 0.949
 DPO−- 0.889−- 1.000
Hubble-8B-500BGA−- 0.943−- 1.000
 GD−- 0.829−- 1.000
Appendix
Table 22: Memorization floor–damage correlations in factual recall. Pearson's rr and Spearman's ρs\rho_{s} over the relations of one model and method: four for Hubble-8B and three for Hubble-1B. With three relations ρs\rho_{s} can only take the values 00 , ±0.5\pm 0.5 and ±1\pm 1 , so the Hubble-1B rank coefficients are coarse.
PPMMRelabeling targetRetainForget bucket
1312Unrestricted15.412.5
1312Within bucket75.799.9
2774Unrestricted28.014.7
2774Within bucket71.399.7
Appendix
Table 23: Within-bucket redistribution preserves retain performance. RL with unrestricted or within-bucket incorrect targets at 10% forget exact accuracy. Entries report retain exact and forget bucket accuracies (%) from one trained model and split per setting.
MethodWeight ωt\omega_{t}Tokens weighted most
GA11all equally
WGA ( Wang et al., 2025 )ptβp_{t}^{\beta}tokens the model still predicts confidently
TNPO ( Wang et al., 2025 )2ptβ/(ptβ+(ptref)β)2p_{t}^{\beta}/\bigl(p_{t}^{\beta}+(p_{t}^{\mathrm{ref}})^{\beta}\bigr)tokens whose probability has dropped least
Imp ( Yang et al., 2025 )(1−pt)β(1-p_{t})^{\beta}tokens the model predicts poorly
SatImp ( Yang et al., 2025 )ptβ1(1−pt)β2p_{t}^{\beta_{1}}(1-p_{t})^{\beta_{2}}confident but not yet saturated tokens
ETW ( Koh et al., 2026 )nxHt/∑sHsn_{x}H_{t}/\sum_{s}H_{s}tokens with uncertain predictions
Appendix
Table 24: Token-wise regularizers compared in Appendix E.2 . ptp_{t} : the current model’s probability of the gold token; ptrefp_{t}^{\mathrm{ref}} : the same before unlearning; HtH_{t} : predictive entropy at temperature T=1.5T=1.5 ; nxn_{x} : document length. Exponents are hyperparameters: β=5\beta=5 for WGA, 44 for TNPO and 11 for Imp; (β1,β2)=(5,1)(\beta_{1},\beta_{2})=(5,1) for SatImp.
MethodAUCRetain
SatImp0.65 ± 0.050.236 ± 0.007
WGA0.61 ± 0.070.246 ± 0.019
TNPO0.61 ± 0.060.243 ± 0.014
ETW0.55 ± 0.040.199 ± 0.013
GA0.50 ± 0.000.217 ± 0.015
SCE0.45 ± 0.000.191 ± 0.006
Appendix
Table 25: Regularizers that better separate tokens above from those below the one-bit memorization floor (higher AUC) retain more. Both measured when the forget probability reaches 0.1; mean ±\pm 95% CI over three seeds.

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