While an unlearned language model may no longer recall a fact directly, the fact often remains recoverable through multi-hop reasoning over related knowledge. Most existing unlearning techniques overlook this vulnerability, targeting facts in isolation while leaving their supporting knowledge intact. To achieve true forgetting, we propose a general deep unlearning framework compatible with existing unlearning algorithms. Our approach adaptively explores both explicit responses and latent internal representations to discover valid reasoning paths, compiles them into a confidence-aware supporting subgraph, and we apply a graph minimum cut to sever all recovery paths while preserving unrelated knowledge. To rigorously evaluate deep unlearning, we introduce a model-specific pipeline that extracts and completes knowledge graphs from raw text, filtering them by calibrated model confidence to reflect what the model genuinely retains. Comprehensive experiments demonstrate that selectively unlearning supporting knowledge yields substantially deeper forgetting than superficial methods while preserving model utility, highlighting that genuine unlearning requires breaking the relational structures that enable factual reconstruction.
Figures & tables
Figure 1: Illustration of deep unlearning. A target fact may remain recoverable through reasoning over related knowledge even after unlearning. Deep unlearning aims to interrupt the supporting knowledge structures that enable such recovery.
Figure 2: Overview of the proposed deep unlearning framework. Adaptive tree search discovers candidate supporting paths, path pruning constructs a confidence-aware supporting subgraph, and minimum-cut selection disrupts these paths while preserving model utility.
Figure 3: Construction of the model-based knowledge graph. We extract entities and relations from the Harry Potter corpus, merge aliases, and complete relations supported by the extracted facts. We then retain facts recognized by the target LLM according to its calibrated confidence.
Method
Setting
Qwen3.5-27B
Gemma4-31B-Base
Unlearning Effectiveness
Utility Retention
Unlearning Effectiveness
Utility Retention
UES ↑
Loc ↑
Gen ↑
Rea ↑
UES ↑
Loc ↑
Gen ↑
Rea ↑
No Unlearn
0.000
1.000
0.818
0.900
0.000
1.000
0.760
0.814
GA
Superficial Unlearn
0.799
0.885
0.816
0.894
0.552
0.888
0.748
0.740
DeepUnlearn
0.963
0.707
0.814
0.874
1.000
0.000
0.738
0.000
DUMIC
0.926 (15.89% ↑ )
0.745
0.812
0.886
0.690 (25.00% ↑ )
0.905
0.756
0.698
Table 1: Comparison of different unlearning settings on Qwen3.5-27B and Gemma4-31B-Base. Percentages indicate relative UES improvements over superficial unlearning.
Method
Superficial Unlearning
DUMIC
Unlearning Effectiveness
Utility Retention
Unlearning Effectiveness
Utility Retention
UES ↑
Loc ↑
Gen ↑
Rea ↑
UES ↑
Loc ↑
Gen ↑
Rea ↑
Base Model
0.000
1.000
0.818
0.900
0.000
1.000
0.818
0.900
GA
0.109
0.923
0.812
0.834
0.789 (623.85% ↑ )
0.730
0.802
0.622
NPO
-0.168
0.935
0.812
0.846
0.337 (300.60% ↑ )
0.914
0.812
0.776
SimNPO
0.083
0.924
0.818
0.894
0.141 (69.88% ↑ )
0.944
0.812
0.886
Table 2: Comparison of unlearning methods using LoRA on Qwen3.5-27B under superficial unlearning and deep unlearning with minimum cut.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Method
Qwen3.5-27B
Gemma4-31B-Base
Full
LoRA
Full
Sup.
Deep
+Cut
Sup.
Deep
+Cut
Sup.
Deep
+Cut
GA
5
5
5
5
5
5
2
1
1
NPO
5
5
5
5
5
5
2
1
1
SimNPO
5
5
5
5
5
5
5
5
5
GAGDR
5
5
5
5
1
5
1
1
1
Appendix
Table 3: Selected training epochs under different unlearning settings using full-parameter fine-tuning (Full) and LoRA. Sup., Deep, and +Cut denote superficial unlearning, deep unlearning, and deep unlearning with minimum cut.
Model
Unlearn
DUMIC
DeepUnlearn
Forget
Retain
Forget
Retain
Forget
Retain
Qwen3.5-27B
100
100
236
236
616
616
Gemma4-31B-Base
100
100
232
232
639
639
Appendix
Table 4: Numbers of forget and retain examples used under different unlearning settings. Each retain set is matched in size to its corresponding forget set.
Model
Total time
Avg. per target
Candidate paths
Accepted paths
Qwen3.5-27B
4.45 h
80.2 s
10,971
4,067
Gemma4-31B-Base
8.77 h
157.9 s
9,370
3,181
Appendix
Table 5: Runtime and path statistics of supporting-path discovery over 200 target facts. Candidate and accepted path counts are totals across all targets.
Entropy
Correct Prob. Range
Entropy
Correct Prob. Range
0.10
[0.987,0.990]
0.60
[0.854,0.913]
0.15
[0.978,0.984]
0.65
[0.833,0.904]
0.20
[0.969,0.978]
0.70
[0.811,0.894]
0.25
[0.958,0.971]
0.75
[0.785,0.884]
0.30
[0.947,0.963]
0.80
[0.757,0.874]
0.35
[0.934,0.956]
0.85
[0.724,0.863]
Appendix
Table 6: Feasible correct-answer probability ranges at fixed entropy values H(q)=u∗ for five options (A, B, C, D, and Unknown), assuming the correct option has the highest probability. Entropy is measured in bits.
Method
UES ↑
Loc ↑
Superficial
DUMIC
Superficial
DUMIC
GA
0.871
0.926
0.857
0.745
GAGDR
0.871
0.936
0.863
0.781
NPO
0.893
0.926
0.870
0.777
NPOGDR
0.716
0.883
0.924
0.891
SimNPO
0.869
0.905
0.817
0.780
Appendix
Table 7: Superficial unlearning versus DUMIC on Qwen3.5-27B with 236 forget examples and five training epochs. Higher UES is bolded.
Making large language models (LLMs) deeply forget specific knowledge and values without sacrificing general capabilities remains a central challenge in unlearning. Current methods are easily reversed by fine-tuning or few-shot prompting, suggesting their forgetting is only shallow. We identify the root cause. Existing methods target representations shared with both the retain set and the subspace recovered by a fine-tuning attacker, making unlearning both disruptive to general capabilities and easy to reverse. We propose RepSelect (Representation Selectivity), which isolates forget-set-specific representations by collapsing top principal components of weight gradients before each update, leaving general capabilities intact while limiting what fine-tuning can recover. We evaluate across two forget categories, biohazardous knowledge and abusive tendencies, and four model families spanning dense and Mixture-of-Experts architectures (Llama 3, Qwen 3.5, Gemma 4 E4B, DeepSeek V2 Lite). Compared to five popular baselines (GradDiff, NPO, SimNPO, RMU, UNDIAL), RepSelect achieves a 4-50x larger reduction in post-relearning answer accuracy than the strongest baseline, and is near-perfectly robust to few-shot prompting attacks. Targeting selective representations is thus an important step towards deep and robust LLM forgetting.
Benchmarking machine unlearning methods is critical to understand whether sensitive knowledge is removed from large language models (LLMs) or not. Current unlearning benchmarks include mainly single-hop questions and a narrow set of multi-hop questions. Although effective, they still face two challenges. (1) Knowledge is not isolated, whereby diverse multi-hop reasoning paths can potentially induce knowledge leakage than normal queries. (2) Unlearning may be fragile: unlearned knowledge can be partially recovered through recovery attacks such as lightweight post-unlearning adaptation, making static evaluation insufficient. Therefore, in this paper, we introduce \unlearning as a novel benchmark to understand robust LLM knowledge removal across diverse reasoning paths and recovery attacks. We experiment with this benchmark on 3 models, 6 unlearning methods, and 2 carefully curated datasets. Results show that existing methods are vulnerable to multi-hop reasoning paths and recovery attacks. We further explore the trade-off among forget quality, robustness, and model utility for LLM unlearning.
Machine unlearning for large language models (LLMs) aims to selectively remove memorized content such as private data, copyrighted text, or hazardous knowledge, without costly full retraining. Most existing methods require a retain set of curated examples to prevent catastrophic degradation of general model utility, creating an extra data dependency that complicates deployment. We propose SHRED (Self-distillation via High-surprisal-only Retain-set-free Entropy Demotion), a retain-set-free unlearning method built on a key insight: not all tokens within a forget set instance carry memorized information equally. High-information tokens concentrate the model's memorized knowledge, while low-information tokens reflect general language competence. SHRED operates in two stages. (1) Selection: We perform a forward pass on a forget set instance, collect per-token autoregressive probabilities, and select the bottom (lowest probability, highest Shannon information) as forget positions; the remaining positions are retained as benign anchors. (2) Training: We construct modified KL targets that demote the memorized token's logit at forget positions while preserving the original distribution at benign positions. The model is then trained via a single top KL self-distillation objective that simultaneously drives forgetting and utility preservation. We evaluate SHRED across four standard unlearning benchmarks and demonstrate that it establishes a new Pareto-optimal trade-off between forget efficacy and model utility, outperforming retain-set-dependent methods. Our analysis shows that SHRED is robust against relearning attacks and membership-inference attacks, and it maintains stable utility even after many sequential unlearning runs.
Zizhao Hu, Ameya Godbole, Johnny Tian-Zheng Wei +3
University of Southern California · USC Information Sciences Institute