{"id":"75fcf66c-5e37-420a-a0a2-a418060a7ed9","arxiv_id":"2508.04731","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"NAEx is a plug-and-play explainer that identifies the key subgraphs and features driving network alignment predictions, and it generalizes to new pairs without retraining.","lead":"This paper introduces NAEx, a new tool that explains why network alignment models match particular nodes across two networks by highlighting the important connections and features. It is designed to work with any modern alignment model and can generate these explanations quickly for new, unseen node pairs.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sigmoid surrogate for alignment probability (Eqs. 15–16) is used in both training and the faithfulness metric, so if it misrepresents the argmax decision rule, reported fidelity/faithfulness do not establish faithfulness to the actual NA model.","rationale":"The reader's weakest assumption is exactly the load-bearing concern I identify: the sigmoid surrogate is used in both training and evaluation, so faithfulness to the surrogate is not necessarily faithfulness to the model. This is not a manufactured concern; it affects the validity of the central claim about faithful explanations and the interpretation of all quantitative results. The paper does provide some independent support: a concrete plug-and-play framework, experiments on multiple datasets, ablations, and a plausible inductive mechanism. The concern is not that the framework is useless, but that its main claim is conditionally true only if the sigmoid approximation tracks the argmax decision boundary. The reader's CONDITIONAL verdict already reflects this, so I do not move the verdict; I would keep CONDITIONAL and make the condition explicit: require a test against the true argmax decision rule. A secondary issue, lack of code, data, and supplementary material, reinforces the need for empirical verification but is not the single most load-bearing concern. I agree with the reader's identification and recommend no change to the verdict, only a sharper statement of the required condition.","tokens_in":855,"tokens_out":1006,"duration_ms":56515,"concrete_test":"For each anchor pair in the test set, compute the true model prediction under Eq. 1 (top-1 by cosine similarity, plus mutual consistency if used) on the full graphs and on the explanatory subgraphs generated by NAEx. Recompute FID using these argmax labels instead of the sigmoid-based scores, and compare with Table 4. Additionally, train a variant of NAEx with a margin/ranking loss that directly preserves the top-1 rank (or uses the true 0/1 argmax label) and evaluate on pairs where the sigmoid and argmax disagree. If the argmax-based FID is comparable, the concern is resolved; if it drops substantially, the explanations are not faithful to the actual model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that NAEx produces explanations faithful to the original NA model's predictions. The paper defines the NA prediction as an argmax over candidate nodes (Eq. 1) and notes that mutual consistency is often required. However, the framework replaces the model's output with a sigmoid of the pairwise cosine similarity (Eqs. 15–16) and uses this surrogate in the alignment consistency loss (Eq. 17) and in the faithfulness metric (Eq. 23, via the KL divergence between sigmoid score distributions). This is unverified: the sigmoid is not the model's decision rule, and it may disagree with the argmax, especially when the top-1 candidate after subgraph masking differs from the pair with highest sigmoid score, or when bidirectional consistency is applied. The evaluation is therefore partly circular: the metric and the objective share the same potentially wrong approximation. The paper does not provide a theoretical justification that the sigmoid preserves the argmax decision boundary for the four NA models, and the supplementary material that could contain details is not included. If the surrogate is inaccurate, the reported FID/FTH values describe fidelity to the surrogate, not to the actual alignment model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes NAEx, a post hoc, model-agnostic framework for explaining neural embedding-based network alignment (NA) models. NAEx jointly learns edge masks and feature masks over a source and target graph pair, parameterizing explanation generation with a shared MLP and binary-concrete sampling. The training objective combines an alignment-consistency cross-entropy term (using a sigmoid of cosine similarity between embeddings as a surrogate for alignment probability), a contrastive subgraph-similarity term, and sparsity regularizers. The authors evaluate NAEx with four NA models (JORA, SANA, HTC, ASSISTANT) on three datasets, reporting fidelity (FID), faithfulness (FTH), and sparsity. They claim the method is inductive, efficient, and outperforms baselines including dNAME and GNNExplainer.","tokens_in":14437,"tokens_out":4864,"duration_ms":61819,"significance":"Explaining network alignment is an under-studied but important problem, and NAEx addresses it with a clean, general architecture: shared edge/feature masks over both graphs, a probabilistic subgraph sampling scheme, and a cross-network objective. If the faithfulness claims can be substantiated, NAEx would be a useful plug-and-play tool for diagnosing and comparing NA models, and its inductive inference property is a genuine practical advantage over perturbation-based baselines. The paper introduces tailored evaluation metrics and conducts experiments over multiple datasets and models, which is a strength. However, the current evidence does not fully establish faithfulness to the actual NA model because both the training loss and the primary faithfulness metric rely on the same sigmoid surrogate, and the headline quantitative claims are not clearly supported by the tables.","major_comments":[{"comment":"The faithfulness metric FTH is essentially the negative exponential of the KL divergence between the original and explained sigmoid score distributions (Eq. 23). This is the same quantity that the alignment-consistency loss Lalign (Eq. 17) drives to be similar. Hence high FTH scores are, to a large degree, a measure of how well the training objective was optimized, not of how faithfully the explanation preserves the actual NA model's decision. The paper must report an evaluation that is not circular, e.g., fidelity computed against the true argmax predictions (Eq. 1), or a metric that does not use the surrogate. As written, the FTH-based claims do not establish faithfulness to the real alignment model.","section":"§4.4.1 and §5.4 (Eqs. 15-17, Eq. 23)"},{"comment":"The paper replaces the NA model's prediction rule, which is argmax over pairwise similarities (Eq. 1), with a sigmoid of the cosine similarity between anchor embeddings. This is an unverified assumption. The surrogate may disagree with the argmax decision, especially after subgraph masking or when bidirectional consistency is enforced. The authors provide no theoretical or empirical justification that maximizing the sigmoid likelihood preserves the top-1 ranking of the original model. This is load-bearing because both the training loss and the FTH metric depend on this surrogate. Please add experiments comparing surrogate scores with actual model outputs, or replace the surrogate with a more faithful softmax/ranking-preserving formulation.","section":"§4.4.1 (Eqs. 15-16)"},{"comment":"The abstract and contributions claim '~32% improvement in explanation fidelity' over dNAME, but this number is not derivable from Table 4. The largest FID gain versus dNAME at any sparsity level shown is about 10.8% (AllMovie-IMDB, S=0.7); the largest FTH gain is about 35.2% (ACM-DBLP, S=0.7). The text also reports an 'average improvement of 2.87−65.74% in FID' without specifying how the range is computed or over which cells. Please state explicitly which quantity is being averaged, whether relative or absolute, and report the per-cell gains. The 'up to 95% speedup' claim in the abstract is likewise not substantiated by Figure 4, which shows training/inference time but no percentage calculation.","section":"§6.1 and Table 4"},{"comment":"The comparison in Table 4 is presented at sparsity levels S=0.5, 0.6, 0.7, but the paper does not explain how NAEx is constrained to produce explanations at exactly these sparsity levels. The loss in Eq. 13 contains L1 regularizers with weights lambda1 and lambda2, but no mechanism or tuning procedure is described for achieving a target sparsity. Baselines such as dNAME and GNNExplainer, unless similarly constrained, may be at an unfair disadvantage. Please specify the protocol used to match sparsity across methods, or otherwise justify that the comparison is apples-to-apples.","section":"§6.1 and Table 4"},{"comment":"The FTH definition is technically problematic. For candidates not in the explained subgraph, the paper sets shat_uv = 0 and re-normalizes qhat_u. This can produce zero probabilities, making the KL divergence undefined (log 0). The paper does not specify any smoothing or fallback. Also, computing qu and qhat_u over all |Vt| candidates is prohibitively expensive for large graphs; the paper does not state how this is implemented in practice. Please provide a well-defined, computable formulation and clarify the exact procedure used in the experiments.","section":"§5.4 (Eq. 23)"}],"minor_comments":[{"comment":"Typo: 'where where' appears in the sentence defining h_s_u and h_t_v.","section":"§3.1"},{"comment":"Typo: 'mdoels' should be 'models'; also 'Foresquare' is spelled inconsistently with 'Foresq' elsewhere.","section":"§5.2"},{"comment":"Typo: 'relevent' should be 'relevant'.","section":"§4.4.3"},{"comment":"Typo: 'siginificant' should be 'significant'.","section":"§6.2"},{"comment":"The dataset statistics are poorly formatted; for instance 'Foresq - Twitter (F-T)5,313 - 5,120 76,972 - 1,64,919 0 1,609' is hard to parse. Please use a cleaner table layout with clear columns.","section":"Table 2"},{"comment":"The ablation study reports FID/FTH values only as bars without numerical labels, and the legend is minimal. The text states 'NAEx-3 performs similar' and 'NAEx-4 shows a significant improvement' but the figure does not allow the reader to verify the magnitude of these effects. Please include numerical values or a table.","section":"§6.2 and Figure 3"},{"comment":"The list of NA models that NAEx can explain includes many methods without citations in that list; also, the claim that it is 'first general-purpose' framework is strong and would benefit from a more precise comparison with existing approaches in the text, not only in the table.","section":"§5.3"},{"comment":"Equation 17 sums over negative samples but does not specify how many negatives are used or how they are sampled. This is important for reproducibility.","section":"§4.4.1"},{"comment":"Equation 11 uses cross-entropy H(Y, Yhat) but the notation is not explicitly defined; it would help to state that this is the empirical cross-entropy approximated by Monte Carlo samples.","section":"§4.3"},{"comment":"The sparsity metric uses 2-hop neighborhoods as the denominator, but the rationale for choosing 2-hop rather than the full graph or some other local neighborhood is not justified.","section":"§5.4 (Eq. 24)"},{"comment":"The paper repeatedly refers to the Supplementary for Algorithm 1 and other details, but the supplementary material is not included in the submission. Please provide it or incorporate the essential details in the main text.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The central issue is the circularity between the training objective and the faithfulness metric, which undermines the main faithfulness claim. This is fixable but requires new experiments and possibly a reformulated metric. The paper is otherwise coherent and addresses a relevant problem; I recommend major revision rather than rejection. The authors should also be asked to substantiate the headline percentage improvements, which currently are not supported by the reported tables."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper makes a real first: an inductive, model-agnostic, post-hoc explainer for neural embedding-based network alignment, with joint edge and feature masks learned over both networks. The shared MLP across graphs is a sensible design, and the empirical story, taken at face value, shows NAEx preserves actual alignment decisions on four different NA models better than the baselines. That is worth something.\n\nThe strongest part is the framework itself. Extending PGExplainer to the two-graph setting is not trivial, and the contrastive subgraph loss that keeps explanations for aligned pairs comparable is a good addition. The novelty claim over dNAME (influence functions, transductive, node-level) checks out.\n\nThe soft spots are real but not fatal. The '~32% improvement' in the abstract is not what Table 4 shows; the largest FID gain over dNAME I can find is about 10.8%, and the average is around 8%. Maybe they are quoting FTH at a particular sparsity (I see 35% on ACM-DBLP at 0.7), but as written it overstates.\n\nMore importantly, the stress-test concern holds. Equations 15-16 replace the model's argmax decision rule with a sigmoid of cosine similarity, and that same sigmoid appears in the alignment-consistency loss (Eq. 17) and in the FTH metric (Eq. 23). So FTH is partly circular — it rewards exactly what the training objective maximizes, and if the sigmoid doesn't track the argmax, high FTH says nothing about faithfulness to the actual model. The paper never validates the sigmoid against the actual decision rule for the four NA models. That said, FID (Eq. 22) is independent: it compares the actual predicted alignments before and after masking. Since FID is high and is the headline number, the main claim survives, but the FTH results should be reported as distributional similarity under the sigmoid surrogate, not as faithfulness.\n\nThe bigger practical issue is reproducibility. No code, no data processing details, no hyperparameters, and the supplementary that is referenced is absent. The numbers in Table 4 are not auditable.\n\nWho is this for? Researchers working on GNN explainability or network alignment, especially anyone who wants to audit or compare NA models. It deserves a serious referee, but the authors need to clarify the surrogate issue, report numbers accurately, and release code. I would not desk-reject it.","headline":"A genuinely first inductive NA explainer with a coherent design and decent FID results, but the headline gain is overstated and the FTH metric is partly circular.","tokens_in":14811,"tokens_out":3289,"would_cite":true,"duration_ms":37953,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A model-agnostic, post hoc explainer can now generate faithful sparse explanations for any neural embedding-based network alignment model, including on previously unseen node pairs.","keywords":["network alignment","explainability","graph neural networks","model-agnostic explanation","post hoc explanation","inductive explanation","subgraph masks","mutual information"],"falsifier":"Construct a synthetic pair of networks where the true alignment of an anchor pair depends on a planted set of edges and features, train a GNN-based aligner, run NAEx, and check whether the selected subgraph and features match the planted set; if explanations with high NAEx faithfulness do not preserve the aligner's top-1 predictions or miss the planted structure, the framework's faithfulness claim is refuted.","tokens_in":13956,"feed_emoji":"🧩","tokens_out":4900,"duration_ms":55027,"temperature":0.7,"pith_summary":"The paper claims that network alignment predictions from any neural embedding-based model can be explained by finding a small set of edges and node features in both networks that preserve the alignment if kept. It introduces NAEx, a framework that learns these explanatory subgraphs jointly across the source and target network, so cross-network dependencies are not lost. Because the explanation network is shared across all edges and features, NAEx can explain new node pairs without retraining, which earlier explanation methods cannot do. The authors argue this makes NAEx the first general-purpose, model-agnostic, post hoc explainer for alignment models, and they demonstrate it on four alignment models over three datasets with new alignment-specific evaluation metrics.","feed_headline":"NAEx explains any network alignment model","feed_subtitle":"Sparse subgraphs and features behind every alignment, on unseen pairs, without retraining.","key_machinery":"The load-bearing mechanism is the joint, parameterized edge-and-feature masking over both networks: a shared MLP scores each edge from the concatenation of its endpoint embeddings and the anchor node's embedding, turning graphs into edge distributions from which subgraphs are sampled with the binary-concrete trick, and a shared feature mask selects attributes with Gaussian reparameterization. These masks are optimized by an objective combining alignment consistency (cross-entropy with a sigmoid-of-cosine surrogate for alignment probability), a subgraph-level contrastive loss, and sparsity regularizers. This shared parameterization is what gives NAEx its inductive capability: once trained, ex","core_discovery":"NAEx treats explanation as minimizing the conditional entropy of the alignment prediction given masked subgraphs, approximated by a cross-entropy loss between the original alignment score and the score computed from the masked graphs. The alignment score itself is modeled as the sigmoid of the cosine similarity between node embeddings (Eqs. 15-16), a surrogate that lets the framework train with gradient descent. Edge masks are generated from a shared MLP via the binary-concrete reparameterization trick; feature masks are learned jointly with a Gaussian reparameterization. A subgraph contrastive loss pulls the pooled embeddings of the two explanatory subgraphs together for aligned pairs, and","pith_inferences":["If the sigmoid-of-cosine surrogate diverges from an argmax-based decision rule, the reported fidelity numbers may overstate how faithfully NAEx captures the actual model; a direct test against top-1 alignment preservation would settle this.","The subgraph contrastive loss imposes similarity between the two explanations; this could make explanations look consistent even when the base model's reasoning is asymmetric, so the loss may need to be relaxed or validated on asymmetric aligners.","The framework's inductive generalization suggests a natural extension to dynamic networks: retraining the shared MLP on temporal snapshots could produce explanations that track why alignments emerge or break over time.","NAEx could also serve as a diagnostic for overfitting: if a trained aligner's explanations repeatedly highlight peripheral edges or noisy features, that is evidence the model is exploiting spurious correlations."],"forward_implications":["NAEx can be attached to any existing GNN-based alignment model without retraining or altering it, turning black-box embeddings into inspectable subgraph-and-feature explanations.","Explanations are generated jointly for both networks, so users can directly compare the structural and semantic reasons an alignment holds.","Because the explainer is inductive, once trained it can explain thousands of new anchor pairs in time proportional to the graph edge count, enabling large-scale auditing.","The alignment-specific metrics (fidelity, faithfulness, sparsity) provide a ground-truth-free way to benchmark any alignment explainer.","The separate edge and feature masks let practitioners see whether a model leans on structure or attributes, supporting model selection and debugging."],"supporting_citations":[{"why":"Supplies the mutual-information objective and the feature-mask reparameterization that NAEx adapts to the multi-network alignment setting.","marker":"[35]"},{"why":"Provides the parameterized edge-distribution and binary-concrete reparameterization used for edge mask learning.","marker":"[18]"},{"why":"The principal baseline: a perturbation-based influence-function explainer for network alignment that NAEx is compared against and claims to improve by about 32% in fidelity with up to 95% speedup.","marker":"[42]"},{"why":"Defines the faithfulness (distributional) evaluation metric that NAEx uses to measure explanation quality.","marker":"[1]"},{"why":"Defines the fidelity and sparsity metrics used to evaluate how well explanations preserve predictions and how compact they are.","marker":"[3]"}],"fun_headline_variants":["NAEx: Explaining any network alignment model","NAEx: See the subgraphs behind alignment decisions","Model-agnostic NAEx: Explain any alignment model","NAEx: Unmasking the subgraphs that drive alignment"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The framework assumes the sigmoid of the cosine similarity between embeddings faithfully represents how the NA model decides alignments; if the real model uses an argmax rule or bidirectional consistency, explanations tuned to this surrogate may not reflect the model's actual decision.","fun_headline_variants_meta":{"raw":{"variants":["NAEx: Explaining any network alignment model","NAEx: See the subgraphs behind alignment decisions","Model-agnostic NAEx: Explain any alignment model","NAEx: Unmasking the subgraphs that drive alignment"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000735,"raw_usage":{"total_tokens":3092,"prompt_tokens":686,"completion_tokens":2406,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":430,"completion_tokens_details":{"reasoning_tokens":2341}},"tokens_in":430,"tokens_out":2406,"duration_ms":21353,"temperature":1.0,"reasoning_tokens":2341,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T01:02:16.121416+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a synthetic pair of networks where the true alignment of an anchor pair depends on a planted set of edges and features, train a GNN-based aligner, run NAEx, and check whether the selected subgraph and features match the planted set; if explanations with high NAEx faithfulness do not preserve the aligner's top-1 predictions or miss the planted structure, the framework's faithfulness claim is refuted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the mutual-information objective and the feature-mask reparameterization that NAEx adapts to the multi-network alignment setting."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the parameterized edge-distribution and binary-concrete reparameterization used for edge mask learning."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The principal baseline: a perturbation-based influence-function explainer for network alignment that NAEx is compared against and claims to improve by about 32% in fidelity with up to 95% speedup."},{"cited_title":"Agarwal, O","cited_arxiv_id":null,"evidence_quote":"Defines the faithfulness (distributional) evaluation metric that NAEx uses to measure explanation quality."},{"cited_title":"Generative Explanations for Graph Neural Network: Methods and Evaluations","cited_arxiv_id":"2311.05764","evidence_quote":"Defines the fidelity and sparsity metrics used to evaluate how well explanations preserve predictions and how compact they are."}],"review_version":1}