{"id":"850e8a74-d54b-400a-a8f6-b989972e49b1","arxiv_id":"2507.20566","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"GraphDPO applies direct preference optimization to knowledge graph embedding unlearning, using out-boundary sampling and boundary recall to forget triples while retaining neighbors.","lead":"This paper presents GraphDPO, a method that removes selected facts from knowledge graph embedding models by reframing the task as a preference optimization problem. It combines DPO with graph-aware sampling and boundary replay to reduce leakage of forgotten facts while preserving surrounding knowledge.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Appendix B equivalence theorem treats the model-dependent term C as a constant, so the claimed linear relation Ep = c1·Eu - c2 does not imply that minimizing the preference objective minimizes the unlearning objective.","rationale":"The reader correctly identified the weakest assumption. The proof of Theorem 1 (Appendix B Eq. 16-17) explicitly defines C = E_{Dpo_f} Σ_{y∈E} f(x,y), and then treats c2 = C/(|E|-1) as a constant when deriving Ep = c1·Eu - c2. Since f is the trainable model, C varies with θ; the proof never establishes that the gradient of C is zero or collinear with the gradient of Eu. The same issue propagates to Theorem 2 (Appendix C). This is not a stylistic gap: it breaks the claimed equivalence, because the objective Ep has an extra θ-dependent term that changes the optimization landscape. The paper also switches from the raw preference objective Ep to the DPO loss (Eq. 5) without a proof that the DPO loss is covered by the theorem; the DPO loss is a function of log-ratios with a frozen reference model and a sigmoid, so it is a different objective. These two points are load-bearing because the paper's central framing—'preference optimization serves as a principled surrogate for the unlearning task'—rests entirely on the theorems. I still believe the empirical contribution (datasets, method, ablations) has value, so the conditional verdict remains appropriate: the theoretical claims should be corrected or removed before acceptance. No ad hominem is intended; this is a technical flaw in the proof.","tokens_in":29102,"tokens_out":6220,"duration_ms":68566,"concrete_test":"On a small KG (e.g., one relation and three entities, so the embedding space is low-dimensional), enumerate or densely sample all TransE parameter configurations, compute the global optima of Eu = E_{Df} f(h,r,t) and of the DPO loss in Eq. 5, and compare their argmins. If the DPO loss is minimized at a configuration that does not also minimize Eu, the claimed equivalence in Theorems 1 and 2 is falsified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Appendix B Eq. 17, the proof defines C = E_{(x,yw,yl)∈Dpo_f} Σ_{y∈E} f(x,y) and 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, dEp/dθ = c1·dEu/dθ - (1/(|E|-1))·dC/dθ; the extra term dC/dθ is generally nonzero and need not be aligned with dEu/dθ. Minimizing Ep can therefore move parameters in directions that increase Eu, so the theorem does not establish that the preference objective is a surrogate for the unlearning objective. Additionally, the actual loss used in training, Eq. 5, is the DPO log-ratio loss with a frozen reference model and sigmoid nonlinearity, not the raw score difference Ep analyzed in the theorem; no proof connects that DPO loss to Eu. Both gaps undermine the paper's 'principled surrogate' claim, although the empirical method may still be effective.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":29365,"tokens_out":3472,"duration_ms":39487,"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":[{"comment":"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.","section":"Appendix B, Eq. (17) and Theorem 1"},{"comment":"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.","section":"Sec. 3.3, Eq. (5) versus Theorem 1"},{"comment":"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.","section":"Table 1 and Sec. 4.2"}],"minor_comments":[{"comment":"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.","section":"Sec. 3.4, Eq. (9)"},{"comment":"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.","section":"Table 4"},{"comment":"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.","section":"Sec. 4.1"},{"comment":"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.","section":"Sec. 3.3, Eq. (2) and Eq. (7)"},{"comment":"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.","section":"Appendix C, Eq. (19)"},{"comment":"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.","section":"Appendix E"}],"recommendation":"major_revision","confidential_remarks":"The central empirical contribution is plausible and the benchmark construction is valuable, but the theoretical equivalence is currently overclaimed. If the authors cannot fix the proofs, they should re-frame the method as a heuristic with empirical justification. I would also encourage the authors to make code available and to add error bars; the absence of uncertainty quantification is material given the small margins on some datasets."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: worth reading for the empirical recipe, not for the theory. The paper ships a sensible new combination—DPO for KGE unlearning, out-boundary sampling, boundary replay and distillation—and shows consistent gains over approximate baselines on eight datasets. That part is solid and the benchmark construction (10/20% unlearning rates, four time steps) is a useful community resource, though no code or data link appears in the arXiv file despite the claim of release.\n\nWhat is actually new: first application of DPO to KGE unlearning; the out-boundary sampling rule is a good idea for avoiding easy negatives; the boundary recall mechanism is reasonable and the ablations show each piece earns its keep. The empirical comparison is fairly thorough: two exact and six approximate baselines, four KGs, and additional backbone scalability tests.\n\nThe soft spot is the theory. Theorems 1 and 2 claim Ep = c1·Eu − c2, but the proof treats C = E_{Dpo_f} Σ_y f(x,y) as a constant. C depends on the trainable score function, so c2 is a function of the parameters being optimized. Minimizing Ep can therefore increase Eu; the claimed equivalence is not established. Moreover, the loss actually used in Eq. 5 is the DPO log-ratio with a frozen reference model and sigmoid, not the raw score difference in the theorem—there is no bridge between the analyzed objective and the trained objective. The \"principled surrogate\" language should be dropped or substantially weakened. This is an overclaim, not a fatal flaw, because the empirical results stand on their own and the ablations independently support the components.\n\nMinor issues: no error bars or significance tests (only averages over five runs), and some typos. The hyperparameter analysis is thin but adequate.\n\nBottom line: a competent empirical paper with a proof that does not work. If the authors remove or rewrite the equivalence theorems, the paper would be solid. I would send it to peer review rather than desk reject, with instructions to focus on the theory and to request code and data. Anyone working on KGE maintenance or machine unlearning should engage with the method and the benchmarks.","headline":"A useful empirical recipe for KGE unlearning, with a decorative equivalence proof that should be dropped or fixed.","tokens_in":29812,"tokens_out":1692,"would_cite":true,"duration_ms":19371,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"GraphDPO reframes knowledge graph unlearning as preference optimization, letting a KGE forget target triples while preserving surrounding knowledge.","keywords":["knowledge graph embedding","machine unlearning","direct preference optimization","approximate unlearning","boundary replay","knowledge distillation","link prediction","continual unlearning"],"falsifier":"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.","tokens_in":28952,"feed_emoji":"🧹","tokens_out":6480,"duration_ms":55901,"temperature":0.7,"pith_summary":"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.","feed_headline":"GraphDPO deletes KG facts while keeping neighbors intact","feed_subtitle":"Casts forgetting as preference optimization, beating approximate baselines by up to 10.1% MRR.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the direct preference optimization loss that GraphDPO adapts as its core forgetting objective.","marker":"[33]"},{"why":"Provides the TransE base model whose score function defines $f_\\theta$ and $f_\\text{ref}$.","marker":"[27]"},{"why":"Justifies out-boundary sampling by showing single-hop neighbours of an entity have similar embeddings.","marker":"[35]"},{"why":"Baseline KGE-unlearning method using schema that GraphDPO must outperform.","marker":"[25]"},{"why":"Baseline KGE-unlearning method using meta-learning that GraphDPO must outperform.","marker":"[26]"},{"why":"Supplies the FB15k-237 graph from which the FB-10% and FB-20% benchmarks are built.","marker":"[18]"},{"why":"Supplies the incremental distillation loss that the boundary distillation component adapts.","marker":"[38]"}],"fun_headline_variants":["Preference optimization makes KG unlearning forget precisely","GraphDPO: unlearn KG facts via preference optimization","DPO-based unlearning beats approximate KG deletion by 10%","Forgetting knowledge graph triples with preference optimization","GraphDPO: cleanly remove KG facts, preserve neighbors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Preference optimization makes KG unlearning forget precisely","GraphDPO: unlearn KG facts via preference optimization","DPO-based unlearning beats approximate KG deletion by 10%","Forgetting knowledge graph triples with preference optimization","GraphDPO: cleanly remove KG facts, preserve neighbors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000618,"raw_usage":{"total_tokens":2909,"prompt_tokens":1024,"completion_tokens":1885,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":640,"completion_tokens_details":{"reasoning_tokens":1805}},"tokens_in":640,"tokens_out":1885,"duration_ms":13689,"temperature":1.0,"reasoning_tokens":1805,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:41:01.067418+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Translating embeddings for modeling multi-relational data","cited_arxiv_id":null,"evidence_quote":"Provides the TransE base model whose score function defines $f_\\theta$ and $f_\\text{ref}$."},{"cited_title":"Learning multi-granularity and adaptive representation for knowledge graph reasoning","cited_arxiv_id":null,"evidence_quote":"Justifies out-boundary sampling by showing single-hop neighbours of an entity have similar embeddings."},{"cited_title":"Knowledge graph unlearning with schema","cited_arxiv_id":null,"evidence_quote":"Baseline KGE-unlearning method using schema that GraphDPO must outperform."},{"cited_title":"Learn to Unlearn: Meta-Learning-Based Knowledge Graph Embedding Unlearning","cited_arxiv_id":"2412.00881","evidence_quote":"Baseline KGE-unlearning method using meta-learning that GraphDPO must outperform."},{"cited_title":"Towards continual knowledge graph embedding via incremental distillation","cited_arxiv_id":null,"evidence_quote":"Supplies the incremental distillation loss that the boundary distillation component adapts."}],"review_version":2}