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Unlearning of Knowledge Graph Embedding via Preference Optimization

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read GraphDPO reframes knowledge graph unlearning as preference optimization, letting a KGE forget target triples while preserving surrounding knowledge.

desk verdict A useful empirical recipe for KGE unlearning, with a decorative equivalence proof that should be dropped or fixed. read the letter →

arxiv 2507.20566 v1 pith:BY4ZRO7L submitted 2025-07-28 cs.AI

Jiajun Liu , Wenjun Ke , Peng Wang , Yao He , Ziyu Shang , Guozheng Li , Zijie Xu , Ke Ji This is my paper · ORCID
classification cs.AI
keywords knowledgegraphembeddingmachineunlearningdirectpreferenceoptimizationapproximateboundaryreplaydistillationlinkpredictioncontinual
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that knowledge graph embedding models can unlearn outdated or erroneous triples without retraining by treating unlearning as a preference optimization problem. Each forgetting triple is converted into a preference pair: the model must prefer a structurally distant alternative entity over the entity in the forgetting triple, so the forgotten fact's score is pushed down while the rest of the graph keeps its scores. To protect knowledge near the forgetting boundary, the method replays boundary triples and distills boundary entity embeddings toward the pre-trained reference model. The paper builds eight unlearning benchmarks on four knowledge graphs at 10% and 20% unlearning rates across four time steps, and reports that GraphDPO outperforms approximate unlearning baselines by up to 10.1% in MRR_Avg and 14.0% in MRR_F1 while approaching retrained models at much lower cost.

What carries the argument

The load-bearing object is the preference triple $(x, y_w, y_l)$ built from each forgetting triple: the query $x$ is either $(h,r)$ or $(r,t)$, the dispreferred answer $y_l$ is the entity from the forgetting triple, and the preferred answer $y_w$ is sampled uniformly from entities outside the forgetting boundary $E_{y_l}$. The DPO loss $L_{\text{dpo}} = -\mathbb{E}[\log\sigma(\beta\log\frac{f_\theta(x,y_w)}{f_\text{ref}(x,y_w)} - \beta\log\frac{f_\theta(x,y_l)}{f_\text{ref}(x,y_l)})]$ carries the forgetting, while the replay loss $L_{\text{replay}} = \mathbb{E}[\max(0, f(h,r,t) - f(h',r',t') + \gamma)]$ and the smooth-L1 distillation loss $L_{\text{distill}}$ carry retention. The claimed identity $E_p = c_1 E_u - c_2$, proved in Appendix B and extended in Appendix C, is the bridge that turns preference optimization into unlearning.

What would settle it

Run one GraphDPO training run on a small knowledge graph and record, at several checkpoints, the value of $C = \sum_{y\in E} f_\theta(x,y)$ for a fixed set of preference queries; if $C$ changes by more than a small relative tolerance, the constant-$c_2$ assumption in Theorem 1 is violated. As a behavioural check, compute the cosine similarity between the gradient of the DPO loss and the gradient of the raw unlearning loss $E_u$ on the same batch; if the similarity is not consistently positive, minimizing the preference loss is not in fact minimizing the unlearning loss.

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Extended reading notes

Core claim

GraphDPO's central claim is that the objective of unlearning a triple set $D_f$ from a pre-trained KGE can be re-expressed as a preference optimization objective $E_p = c_1 E_u - c_2$ with $c_1 > 1$ and $c_2 > 0$, so minimizing the DPO loss over the transferred dataset $D^\text{po}_f$ effectively minimizes the unlearning loss. The same linear relation is claimed to survive out-boundary sampling, so the sampling modification does not change the optimization target. On top of this, the boundary recall mechanism (replay plus distillation) anchors the embedding neighbourhood of each forgotten entity to the reference model, and the ablations show this is what preserves retained knowledge: dropping replay alone costs up to 40.1% of retained MRR.

Load-bearing premise

The equivalence between the preference objective and the unlearning objective assumes that the total score mass $C = \sum_{y\in E} f(x,y)$ over all candidate entities stays constant while the model is being updated, yet this total depends on the very parameters the training changes, so the theorem's guarantee is not established by the proof.

Editorial extensions

If this is right

  • A pre-trained KGE can shed 10–20% of its facts in four continual unlearning steps while retaining 68–99% of the MRR_Avg of full retraining, at 69–80% lower training time than fine-tuning.
  • Forgetting triples that share entities or relations with retained triples are not simply deleted locally; the out-boundary preference signal separates their scores, preventing re-inference through remaining edges.
  • Boundary knowledge survives because replay and distillation anchor the embeddings of neighbours of forgotten entities; removing replay alone lowers retained-knowledge MRR by up to 40.1%.
  • The framework transfers to TransH, ComplEx, SimplE, and RotatE backbones, reaching 77–84% of full retraining performance on FB-20%, so the mechanism is not tied to TransE's score function.
  • On large graphs (CoDEx-L, YAGO3-10) GraphDPO still leads all approximate baselines in MRR_Avg and MRR_F1, indicating the approach scales to hundreds of thousands of triples.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The equivalence theorems treat the summed score $C = \mathbb{E}_{(x,y_w,y_l)}\sum_{y\in E} f(x,y)$ as a constant, but $C$ is a function of the model being optimised; measuring $C$ across training checkpoints would show whether the linear relation actually holds, and if it drifts, the practical gains may come from the contrastive preference signal rather than the stated equivalence.
  • Because DPO optimizes log-ratio differences rather than raw score differences, replacing the DPO loss with a plain margin loss on the same preference pairs would isolate whether the log-ratio form is what helps unlearning.
  • Out-boundary sampling picks preferred entities from $E \setminus E_{y_l}$; one could extend it by sampling from a fixed hop distance (e.g., 2–3 hops) to control semantic proximity, turning the binary boundary into a graded one.
  • The boundary recall mechanism is similar to continual-learning replay; combining it with knowledge addition and modification may yield a single framework for continual KG editing that both adds and forgets facts.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces GraphDPO, an approximate unlearning framework for knowledge graph embedding (KGE) models. The method reformulates unlearning as a direct preference optimization (DPO) problem: each forgetting triple is converted into a preference pair in which the original triple is treated as dispreferred and a structurally distant negative sample is treated as preferred. An out-boundary sampling strategy restricts the preferred entity to be outside the one-hop neighborhood of the dispreferred entity, and a boundary recall mechanism combines replay and distillation losses to preserve knowledge near the forgetting boundary. The authors construct eight unlearning benchmarks from FB15k-237, WN18RR, CoDEx-L, and YAGO3-10 at 10% and 20% unlearning rates with four time steps, and report that GraphDPO outperforms approximate unlearning baselines by up to 10.1% in MRR_Avg and 14.0% in MRR_F1 while remaining efficient. The paper also includes ablations, runtime comparisons, scalability experiments across KGE backbones, and t-SNE visualizations.

Significance. If the empirical results hold, the paper makes a useful contribution to the relatively underexplored task of knowledge graph embedding unlearning. The proposed graph-aware sampling and boundary recall heuristics are sensible, and the released eight benchmark datasets with controlled connectivity and multiple time steps are a concrete asset for future work. The evaluation is broad: multiple KGs, unlearning rates, backbones, ablations, and timing results. However, the paper's central theoretical justification for treating preference optimization as a surrogate for the unlearning objective rests on Theorems 1 and 2, and that justification has a load-bearing gap: the constant c2 in the claimed linear relation depends on the trainable model parameters. The empirical method may still be effective, but the current manuscript does not establish the stated equivalence.

major comments (3)
  1. [Appendix B, Eq. (17) and Theorem 1] The proof defines C = E_{(x,yw,yl)∈Dpo_f} Σ_{y∈E} f(x,y) and then treats c2 = C/(|E|-1) as a constant when concluding Ep = c1·Eu - c2. But C depends on the trainable score function fθ, so c2 is a function of the parameters being optimized. Consequently, differentiating gives dEp/dθ = c1·dEu/dθ - (1/(|E|-1))·dC/dθ, and the extra term is generally nonzero and need not align with dEu/dθ. Minimizing Ep can therefore increase Eu, so the theorem does not establish that the preference objective is a surrogate for the unlearning objective. The same issue appears in Appendix C, Eq. (19). The authors should either prove a bound on dC/dθ, or substantially weaken the claim and present the preference objective as a heuristic rather than a provably equivalent surrogate.
  2. [Sec. 3.3, Eq. (5) versus Theorem 1] The actual loss used in training is the DPO log-ratio loss Ldpo = -E[log σ(β log(fθ(x,yw)/fref(x,yw)) - β log(fθ(x,yl)/fref(x,yl)))], which involves a frozen reference model, a sigmoid nonlinearity, and log-ratios. The theorem, however, analyzes the raw expectation difference Ep = E[f(x,yl) - f(x,yw)]. The claim that 'the loss of DPO algorithm is equal to minimizing the preference optimization object Ep' is not justified in this setting, since the DPO surrogate and the raw score difference are different objectives. Even if the theorem were correct, it would not directly connect the trained loss to the unlearning objective. Please provide an explicit argument for why Eq. (5) inherits the claimed equivalence.
  3. [Table 1 and Sec. 4.2] All results are reported as averages over five runs, but no standard deviations, confidence intervals, or significance tests are provided. Several of the claimed advantages are small in absolute terms (for example, WN-10% Time 2 MRR_F1 differences or FB-10% Time 1 and 2 margins are under 1%), and without uncertainty quantification it is difficult to judge whether the reported 'up to 10.1%' and 'up to 14.0%' improvements are robust rather than within run-to-run variation. Reporting error bars or paired significance tests for the main tables is needed to support the central performance claim.
minor comments (6)
  1. [Sec. 3.4, Eq. (9)] The replay loss is written as Lreplay = E[max(0, f(h,r,t) - f(h,r,t) + γ)], where the positive and negative scores appear to be the same f(h,r,t). The second term should presumably be the score of a negative triple, e.g., f(h',r,t') or f(h,r',t'), otherwise the loss is a constant γ for every triple and cannot encourage boundary preservation.
  2. [Table 4] In the CO-10% row, the entry for |D2_f| is '612,43'; this should read '61,243' to be consistent with the other entries and with the 10% unlearning rate.
  3. [Sec. 4.1] The text lists 'TansD' as one of the base KGE models, but reference [39] is TransH, and Figure 4 reports results for TransH, ComplEx, SimplE, and RotatE. Please correct the name to TransH or clarify the intended model.
  4. [Sec. 3.3, Eq. (2) and Eq. (7)] The notation p(yw) and p(yw|x,yl) is informal: yw is sampled uniformly from a set, not from a learned distribution, and Equation (2) writes p(yw) ≈ p(yw|x,yl) without defining what 'approximately' means. Please state explicitly that yw is sampled uniformly and avoid calling this a conditional probability.
  5. [Appendix C, Eq. (19)] The term c'_2 contains an explicit sum over e ∈ Eyl, and the proof approximates this sum as negligible using |E| ≫ |Eyl|. This is not a formal bound; please state the relevant bound or conditions under which the approximation is valid, especially because |Eyl| is not uniformly small across all forgetting triples.
  6. [Appendix E] The appendix states that GraphDPO and all baselines use the same KGE architecture and that results are averaged over five runs, but it does not report the standard deviation or any seed range. Adding this information would make the reported averages more interpretable.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed preference/unlearning equivalence is built into the dataset construction; Appendix B's constant c2 is model-dependent, so the theorem does not establish the stated surrogate relation.

  1. self definitional [Appendix B, Eqs. (15)–(17); also Appendix C, Eq. (19)]
    "E_{(x,yw,yl)∼Dpo_f} f(x,yl) = E_{(h,r,t)∼Df}[f(h,r,t)] = Eu (15) ... Ep = ... = c1·Eu−c2 (17) where c1 = |E|/|E|−1 > 1 is the positive constant, and c2 = C/|E|−1 > 0."

    Dpo_f is constructed from Df (Eq. 1) by setting the dispreferred entity yl to the head or tail of each forgetting triple. Substituting this into the preference objective makes the first term of Ep exactly equal to the unlearning objective Eu. Eq. (17) is therefore an algebraic identity by construction, not an independent derivation of an equivalence between the two tasks. In addition, C = E_{(x,yw,yl)∈Dpo_f} Σ_{y∈E} f(x,y) depends on the trainable score function fθ, so c2 is a function of the parameters being optimized; the conclusion that minimizing Ep is approximately equivalent to minimizing Eu does not follow from the identity because ∇θEp = c1∇θEu − (1/(|E|−1))∇θC.

full rationale

The main empirical claim—that GraphDPO outperforms approximate unlearning baselines on the constructed UKGE benchmarks—is evaluated against external baselines and ablation variants, so it has independent grounding and is not circular. The circularity is confined to the theoretical 'task transfer' justification: the preference dataset is defined from the forgetting triples so that the dispreferred expectation equals the unlearning objective, and Theorem 1/Theorem 2 therefore restate the construction rather than deriving a preference-based surrogate. A further correctness gap, not itself circularity, is that the implemented loss in Eq. (5) is a DPO log-ratio loss while the theorems analyze the raw score difference Ep; the cited DPO equivalence [33] is for language-model policies, and no proof is supplied that Eq. (5) has the same minimizers as Ep in the KGE setting. Self-citations [35, 38] motivate out-boundary sampling and the distillation loss, but these are external empirical/methodological building blocks rather than load-bearing uniqueness claims, so they do not raise the circularity score. Overall, the derivation of the surrogate equivalence is partially circular (score 6), while the benchmark-driven performance claim remains independent.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central method rests on hyperparameters chosen by hand and on an equivalence theorem whose proof contains an unstated model-dependence. No new physical or conceptual entities are introduced.

free parameters (4)
  • lambda1, lambda2, lambda3 = 1
    Weights of the three losses in Eq. 12; chosen from preliminary experiments and hyperparameter analysis (Section 4.1, Figure 6).
  • beta = 1
    Temperature in DPO loss Eq. 5; default set to 1 based on preliminary experiments.
  • gamma = 8
    Margin for replay loss and KGE pretraining; inherited from TransE pretraining.
  • replay dataset limit = 10% of full dataset
    Cap on |D_replay| to avoid excessive replay triples (Appendix E).
assumptions (3)
  • ad hoc to paper The total score sum C is treated as constant with respect to model parameters in Theorems 1 and 2.
    Appendix B Eq. 17 and Appendix C; this is unstated and false during training, so the claimed linear equivalence is not guaranteed.
  • domain assumption The DPO loss in Eq. 5 is assumed to minimize the expectation difference Ep.
    DPO optimizes a logistic loss over log-ratios, not the raw score difference; the paper cites [33] but this is an approximation.
  • domain assumption Out-boundary sampling approximates the denominator |E|-1-|E_yl| by |E|-1.
    Eq. 7 requires |E| >> |E_yl|; valid for large graphs but not guaranteed.

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Pith. "Pith review of Unlearning of Knowledge Graph Embedding via Preference Optimization." pith.science (2026). https://pith.science/paper/BY4ZRO7L

@misc{pith2026250720566,
  author       = {Pith},
  title        = {Pith review of: Unlearning of Knowledge Graph Embedding via Preference Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BY4ZRO7L}},
  note         = {Machine review of arXiv:2507.20566}
}
read the original abstract

Existing knowledge graphs (KGs) inevitably contain outdated or erroneous knowledge that needs to be removed from knowledge graph embedding (KGE) models. To address this challenge, knowledge unlearning can be applied to eliminate specific information while preserving the integrity of the remaining knowledge in KGs. Existing unlearning methods can generally be categorized into exact unlearning and approximate unlearning. However, exact unlearning requires high training costs while approximate unlearning faces two issues when applied to KGs due to the inherent connectivity of triples: (1) It fails to fully remove targeted information, as forgetting triples can still be inferred from remaining ones. (2) It focuses on local data for specific removal, which weakens the remaining knowledge in the forgetting boundary. To address these issues, we propose GraphDPO, a novel approximate unlearning framework based on direct preference optimization (DPO). Firstly, to effectively remove forgetting triples, we reframe unlearning as a preference optimization problem, where the model is trained by DPO to prefer reconstructed alternatives over the original forgetting triples. This formulation penalizes reliance on forgettable knowledge, mitigating incomplete forgetting caused by KG connectivity. Moreover, we introduce an out-boundary sampling strategy to construct preference pairs with minimal semantic overlap, weakening the connection between forgetting and retained knowledge. Secondly, to preserve boundary knowledge, we introduce a boundary recall mechanism that replays and distills relevant information both within and across time steps. We construct eight unlearning datasets across four popular KGs with varying unlearning rates. Experiments show that GraphDPO outperforms state-of-the-art baselines by up to 10.1% in MRR_Avg and 14.0% in MRR_F1.

Figures

Figures reproduced from arXiv: 2507.20566 by the authors.

Figure 1
Figure 1. Illustration of unlearning in knowledge graph embedding (UKGE). The forgetting knowl￾edge is (James Gordon, friend, Selina Kyle), while other knowledge retains in the updated KG. To mitigate this drawback, approximate unlearn￾ing [17] updates parameters using only forget￾ting data, thereby reducing training expenses. While approximate unlearning has made signif￾icant progress, it still suffers from the following iss… view at source ↗
Figure 2
Figure 2. An overview of GraphDPO framework. generated by Msf t with each input x. The answer pair (y1, y2) will be labeled as (yw, yl) by human labels or reference policy model Mref , where yw and yl denote preferred and dis-preferred completion amongst (y1, y2), respectively. For the comparison dataset Dc = {(x (i) , y (i) w , y (i) l )} N i=1, where N denotes the number of Dc, preference optimization aims to increase the o… view at source ↗
Figure 3
Figure 3. Time efficiency analysis. Fisher fails to run in the last four datasets with out-of-memory. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Scalability of different KGE models. Ablation Results. To assess the effectiveness of each module in GraphDPO, we conduct abla￾tion experiments on its full version and variants. Results on FB-20% and WN-20% are shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Forgetting analyse of GraphDPO. Before defines the performance of original pre-trained model on Df , and Forgetting defines the performance of GraphDPO on Df . 0 1 2 3 4 0.20 0.25 0.30 M R RF1 FB-20% 0 1 2 3 4 0.35 0.40 0.45 M R RF1 WN-20% 0 1 2 3 4 0.05 0.10 0.15 M R …
Figure 6
Figure 6. Figure 6: Hyperparametric analysis of λ1, λ2, λ3, and β with value from 0 to 4 in one time step. Second, GraphDPO achieves the fastest training speed compared to approximate unlearning methods, reducing training time by 1%-88%. It proves that GraphDPO is more efficient than othe…
Figure 7
Figure 7. Figure 7: Visualization of forgetting and boundary [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.