{"id":"c311670c-7271-47a5-92d4-a9fde424a497","arxiv_id":"2412.00315","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"OMOG trains a bank of per-graph GNN experts and fuses the top-ranked experts for each test graph, reporting gains in zero-shot and few-shot graph transfer.","lead":"Researchers trained one small graph model per pretraining graph, then automatically picked and blended the most relevant models for each new graph. This 'one model for one graph' approach reports better transfer to unseen citation, e-commerce, and knowledge graphs than training one model for all graphs.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 2's proof fails at three concrete steps: the KL linearization cancels to zero, softmax weights are not inverse-variance (exp(-x) ≈ 1-x, not 1/x), and the fused variance/bias inequalities are asserted without justification; the advertised guarantee is unsupported.","rationale":"The reader's REJECT verdict is warranted, and my analysis points to the same general region of the paper: the theoretical guarantees in Appendix D. However, the reader's weakest_assumption focused on the Gaussian equal-mean assumption and the empirical feature-alignment assumption. I find a more direct and decisive problem: even if one grants Assumption D.4 and the SentenceBERT-aligned feature space, the derivations inside Lemma D.5, Proposition D.6, and Theorem D.7 contain concrete algebraic errors. The KL approximation cancels to first order; the exp(−x) ≈ 1/x step is mathematically false; the variance inequality is not generally true for arbitrary softmax weights; and the bias of the fused model is not shown to be no worse than the best individual bias. Therefore Theorem 2, which is the advertised formal guarantee that fusion helps, is unproven as stated. The empirical results in Tables 1-2 could still be valid, and the selection-vs-random ablation in Figure 6 is consistent with the method being useful in practice, but the paper's central claim includes a 'guarantee' that the theory does not deliver. I also note the Table 1 protocol for LLaGA differs from the leave-one-out setting used for the other methods, which is a secondary fairness concern. The most useful next step is the independent re-derivation and counterexample in concrete_test; if it reproduces, the authors should restate Theorems 1 and 2 as empirical observations or prove them under explicitly stated, non-vacuous conditions.","tokens_in":15351,"tokens_out":7106,"duration_ms":67307,"concrete_test":"Independently re-derive Appendix D: (a) expand Lemma D.5's KL formula to first order in r = σ_i^2/σ_test^2 and verify that KL ≈ 0, not 0.5(σ_i^2−σ_test^2); (b) for σ_test^2=1, σ_1^2=0.5, σ_2^2=2, compute softmax(v_i) with v_i = −1/(2σ_i^2) and compare with inverse-variance weights, which gives (0.321, 0.679) versus (0.800, 0.200), disproving Proposition D.6; (c) simulate f_1 = f* + ε, f_2 = f* + 10 + ε, merge with equal weights, and check that MSE_fused = 25.5 > MSE_f1 = 1, contradicting Theorem D.7 unless additional constraints are supplied. If these checks reproduce, the theorem and BMA equivalence should be withdrawn.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Appendix D is supposed to prove Theorem 2 (main text §3.2), which guarantees that OMOG's Top-K selection and merging outperform or match the best individual source model in expectation. The proof has several concrete algebraic failures. (1) Lemma D.5: with equal means, KL = 0.5(r−1−log r), where r = σ_i^2/σ_test^2. For small variance differences, log r ≈ r−1, so the first-order terms cancel and KL ≈ 0, not 0.5(σ_i^2−σ_test^2) as claimed. Thus v_i is not an inverse-variance proxy even under the paper's own Gaussian equal-mean assumptions. (2) Proposition D.6 claims softmax(−1/(2σ_i^2)) approximates inverse-variance weights because exp(−x) ≈ 1/x for small x. The correct small-x approximation is exp(−x) ≈ 1−x, so the claimed BMA equivalence does not follow. (3) Theorem D.7 asserts Var(fused) ≤ min_i Var(f_i). For a weighted average, Var(Σ w_i f_i) = Σ w_i^2 Var(f_i) under independent errors; with arbitrary softmax weights, a high-variance expert with nontrivial weight can make this exceed the minimum variance. (4) The bias of the weighted average is a weighted average of individual biases, and can exceed the minimum bias; the proof simply assumes E[f_fused] ≈ E[f_best] without argument. Therefore the final MSE comparison does not follow. Because Theorem 2 is the formal guarantee advertised as the mechanism by which OMOG avoids negative transfer, the central theoretical claim is unsupported. The scoring ablation in Figure 5 is suggestive, but it does not validate this theorem.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes OMOG, a cross-domain graph pretraining framework built on a 'one model for one graph' pipeline. In the pretraining stage, OMOG trains one source model and one associated scoring model on each pretraining graph, using SentenceBERT features and SGC aggregation. At inference, the scoring models assign relevance scores to a test graph, the top-K source models are selected, softmax weights are computed, and the corresponding model parameters are merged by weighted averaging. The paper reports zero-shot node classification and link prediction results (Table 1), few-shot node classification results (Table 2), ablations of the scoring design (Figures 4-6), and computational cost comparisons (Table 3). The manuscript states two theorems claiming that the merging strategy is equivalent to Bayesian Model Averaging and that top-K selection and merging guarantee that the fused model matches or outperforms the best individual source model in expectation, with proofs in Appendix D.","tokens_in":15816,"tokens_out":7806,"duration_ms":74977,"significance":"If the empirical and theoretical claims were correct, OMOG would be a simple and potentially useful alternative to 'one model for all graphs' pretraining: per-graph experts avoid interference during pretraining, the model bank is incrementally extensible, and the reported training cost is low (Table 3). The top-K versus random-K versus least-K ablation in Figure 5 is genuine evidence that the learned relevance scores carry information, and the scaling behavior in Figure 6 is consistent with the intended negative-transfer avoidance. However, the formal guarantee is load-bearing for the paper's explanation of why negative transfer is mitigated, and that guarantee is not established: the proofs in Appendix D contain algebraic errors, and the key relation between the relevance score and inverse predictive variance is assumed rather than derived. The experimental comparison also has protocol asymmetries and no variance reporting. For these reasons, the contribution as currently stated cannot be accepted.","major_comments":[{"comment":"The KL-divergence approximation is algebraically wrong. For equal-mean Gaussians with r = sigma_i^2 / sigma_test^2, the KL divergence is 0.5(r - 1 - log r). Since log r ≈ r - 1 to first order, the first-order terms cancel, and the leading-order approximation is quadratic in (r - 1), not 0.5(sigma_i^2 - sigma_test^2). Consequently, the claimed relation v_i ≈ -1/(2 sigma_i^2) does not follow even under the paper's own Assumption D.4.","section":"Appendix D, Lemma D.5"},{"comment":"The BMA equivalence is both assumed and based on a false approximation. Definition D.2 simply assumes that the relevance score v_i is approximately the negative KL divergence between output distributions; this is the very property that would need to be derived from the scoring model. Proposition D.6 then uses exp(-x) ≈ 1/x for small x, but the correct first-order approximation is exp(-x) ≈ 1 - x. Even substituting v_i = -1/(2 sigma_i^2) gives softmax weights proportional to exp(-1/(2 sigma_i^2)), which are not proportional to 1/sigma_i^2. Therefore Theorem 1 is unsupported.","section":"Appendix D, Definition D.2 and Proposition D.6"},{"comment":"The proof of Theorem 2 asserts Var(f_fused) <= min_i Var(f_i) and that the ensemble bias does not increase, but neither inequality is valid in general. For a weighted average with nonnegative weights summing to one, the variance can be as large as the maximum variance of the individual models (and larger under positive correlation), not the minimum, and the bias is a weighted average of the individual biases, which can exceed the minimum bias. The step E[f_fused] ≈ E[f_best] is simply assumed. Top-K selection does not repair these inequalities. Hence the advertised guarantee that the fused model outperforms or matches the best individual source model in expectation is not proved.","section":"Appendix D, Theorem D.7"},{"comment":"The empirical comparison is not sufficiently controlled. LLaGA is pretrained on only Arxiv and Products rather than on the nine-graph leave-one-out pool used to train OMOG, while Prodigy uses its original MAG240M pretraining corpus; these are different pretraining conditions. In addition, no standard deviations, number of seeds, or significance tests are reported for any table. As a result, the reported margins cannot be attributed unambiguously to the OMOG design rather than to pretraining-data choices or run-to-run variation.","section":"Section 4.2, Tables 1 and 2"}],"minor_comments":[{"comment":"The name 'Mingxuan Ju' appears twice in the author list and should be deduplicated.","section":"Title page"},{"comment":"There are numerous typos and misspellings, including 'vallina', 'texture-attributed', 'repectively', 'empolys', and 'pertaining'; the manuscript needs a careful proofreading pass.","section":"Throughout"},{"comment":"The denominator of the contrastive loss appears malformed as written; please check the summation indices and the factor of 2 so that the expression matches the intended InfoNCE form.","section":"Equation (4)"},{"comment":"The ablation figures would be much more informative with error bars and a statement of the number of random seeds, especially because the 'No Source', 'No Score', and 'No SGC' variants are not described in enough detail to know what replacement strategy was used.","section":"Figures 4-6"}],"recommendation":"reject","confidential_remarks":"The empirical direction is promising and the per-graph model bank is cheap and easy to scale, but the current version presents an invalid proof as a central theoretical contribution, and the baseline protocols are not fully controlled. I would be willing to reconsider a future version that either removes the formal guarantees entirely or replaces them with correct statements, and that reports multi-seed results under matched pretraining conditions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing to know: this paper's contribution is the pipeline, not the proofs. Pretraining one SGC-plus-attention expert per source graph, training a per-graph scoring model, and fusing the top-K experts by learned relevance is a reasonable and actually different answer to the \"one model for all graphs\" problem. It is not the same as AnyGraph or GraphAlign, which fix the expert count and don't tie experts to individual graphs. The empirical tables support the direction: OMOG ranks first on 8/9 zero-shot node classification, 9/9 link prediction, and 8/10 few-shot node classification, and the scoring ablation (top-K beats random and least-K) shows the selection signal is doing something. The efficiency numbers are plausible.\n\nThe soft spots are real. The theory in Appendix D does not hold up at all. The stress-test note is correct on all three algebraic points: Lemma D.5's first-order Taylor expansion cancels the variance terms, Proposition D.6 uses exp(-x)≈1/x when the small-x approximation is exp(-x)≈1−x, and Theorem D.7's variance inequality is false for arbitrary softmax weights. On top of that, Definition D.2 already assumes the relevance score approximates inverse KL divergence, so the \"equivalence\" is circular. Theorems 1 and 2, which are advertised as guarantees against negative transfer, are unsupported. The empirical section also has protocol gaps: no standard deviations or significance tests, LLaGA is pretrained on only two datasets rather than the leave-one-out pool, and Prodigy uses a different pretraining corpus. No code is released, which makes independent verification of the numbers hard.\n\nThat said, these flaws are not fatal to the empirical idea. The design is sensible and the ablations are encouraging. What the paper needs is a stripped-down version: report error bars, release code, and either remove the theory or replace it with a correct statement about model merging under well-specified assumptions. The authors are not sloppy about the literature; the positioning against OneForAll and the MoE baselines is careful.\n\nWho is this for? Researchers working on graph foundation models and cross-graph transfer will want to know about the per-graph bank idea, and the paper should receive serious refereeing because the empirical claim is important enough to test. My own verdict would be skeptical about the theory but open to the experiments. Recommend: engage with it, but only after the authors fix the theory or abandon it.","headline":"The per-graph expert bank idea is genuinely new and the transfer tables are consistently favorable, but Appendix D's theoretical guarantees are invalid, so the paper is an empirical claim in need of careful verification, not a proven method.","tokens_in":16302,"tokens_out":3413,"would_cite":false,"duration_ms":28095,"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":"Pretraining one model per graph and fusing the top few experts at inference transfers across graph domains better than training a single shared model.","keywords":["Graph Neural Networks","Cross-dataset pretraining","Model bank","Model merging","Negative transfer","Zero-shot node classification","Link prediction","Text-attributed graphs"],"falsifier":"Run OMOG's leave-one-out protocol and, for each test graph, compare the fused top-K model's accuracy against the best single source model in the bank. Because Theorem 2 promises the fused model matches or exceeds that best expert, any test graph where the fused model is significantly worse would falsify the guarantee. A more direct test of the scoring assumption: take a test graph, permute its node labels randomly, and check whether the scoring module's top-K selection still picks the most structurally similar source graphs.","tokens_in":15170,"feed_emoji":"🧩","tokens_out":6142,"duration_ms":49971,"temperature":0.7,"pith_summary":"This paper argues that pretraining a single GNN on a bundle of different graphs is the wrong default: graphs from different domains conflict, so the shared model loses on each one. Instead, the authors propose training one source model per pretraining graph, storing them in a bank, and at inference time letting per-graph 'scoring' modules pick the few most relevant experts and merge their parameters. They call this pipeline 'one model for one graph' and implement it as OMOG. Tested across ten text-attributed graphs in zero-shot and few-shot settings, the fused model ranks first on almost every node-classification and link-prediction benchmark relative to shared-model baselines. If this holds up, a growing collection of pretrained graph experts can be reused for new domains by selecting and merging rather than retraining.","feed_headline":"One model per graph beats one-for-all graph pretraining","feed_subtitle":"A bank of per-domain experts, selected and merged for each new graph, tops zero-shot and few-shot benchmarks.","key_machinery":"The load-bearing pieces are the per-graph source model plus its paired scoring module, and the top-K weighted parameter fusion. Each source model is a small transformer trained with a graph contrastive objective on multi-hop SGC embeddings; each scoring module is an MLP trained so that, after filtering, features of its own domain land near the domain centroid while the mask itself does not. The relevance score is the cosine similarity of the encoded test embedding to a source graph's centroid, which the authors show approximates an inverse KL divergence under Gaussian assumptions, making the softmax-weighted fusion an approximation to Bayesian model averaging.","core_discovery":"The central claim is that cross-domain graph transfer succeeds not by distilling all graphs into one model but by keeping one model per graph and fusing the most relevant ones for each test graph. OMOG encodes node text with a language model to get a unified feature space, aggregates local structure with simplified graph convolutions (SGC), pretrains a contrastive transformer per graph to get a source model, and trains an associated MLP scoring module that filters which features look native to that graph. At inference, every scoring module scores the test graph, the top-K source models are selected and their parameters averaged with softmax weights. The paper proves this weighted merging is equivalent to Bayesian model averaging and that, under its assumptions, the fused model matches or beats the best individual expert in expectation. In leave-one-out experiments on ten text-attributed graphs, the fused model ranks first on 8 of 9 zero-shot node-classification datasets, all 9 link-prediction datasets, and 8 of 10 few-shot classification datasets.","pith_inferences":["The Gaussian equal-mean assumption in the appendix is strong; if a test graph's predictive distribution is far from Gaussian or its mean is misaligned, the BMA equivalence may not hold, and the scoring scores could mis-rank experts.","The bank inherits the quality of the text-embedding encoder; using a stronger aligned encoder should improve all experts, giving a scaling path that the paper does not explore.","Parameter averaging implicitly assumes the experts occupy a compatible linear region; if future experts are more heterogeneous, permutation-aligned merging (model soups) may be needed.","A genuinely novel domain with low relevance to every source model would reduce top-K selection to near-random choice; the paper does not test this out-of-bank-distribution case."],"forward_implications":["New pretraining graphs can be added to the bank by training one extra source and scoring model, without touching the existing experts.","Low-relevance source models are suppressed at inference, so adding more diverse pretraining graphs should not drag down performance the way joint training does.","Because fusion is a weighted average of parameters, the same bank can be reused for future test graphs without any fine-tuning.","The approach is computationally cheaper than large-LLM backbones, since each expert is a small transformer and experts can be trained in parallel."],"supporting_citations":[{"why":"Supplies the ten text-attributed benchmark datasets and the unified text-embedding feature space that make cross-graph transfer possible.","marker":"[4]"},{"why":"Defines the 'one model for all' baseline and the label-embedding inference strategy that OMOG adopts and beats.","marker":"[16]"},{"why":"Provides the SGC aggregation used to fold structural information into node features before pretraining.","marker":"[31]"},{"why":"Supplies the contrastive self-supervised objective used to pretrain each source model.","marker":"[41]"},{"why":"Contributes the post-hoc scoring idea: an MLP filter plus distance-to-centroid loss that OMOG adapts for its scoring modules.","marker":"[6]"},{"why":"Documents negative transfer in jointly pretrained GNNs, the empirical motivation for training one source model per graph.","marker":"[33]"},{"why":"Establishes weighted parameter merging as a way to combine models, which OMOG uses to fuse selected experts.","marker":"[22]"}],"fun_headline_variants":["Per-graph expert models beat one-for-all pretraining","Fusing per-domain GNN experts tops universal pretraining","One model per graph: adaptive fusion wins cross-domain","Bank of per-graph experts beats single-model pretraining","Adaptive expert selection outperforms one-size-fits-all GNN"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire theoretical guarantee rests on the relevance score being an approximate inverse KL divergence between the test graph's and a source graph's output distributions, and specifically on those distributions being Gaussian with aligned means; empirically it also assumes the shared text-embedding space is aligned well enough that per-graph experts are comparable.","fun_headline_variants_meta":{"raw":{"variants":["Per-graph expert models beat one-for-all pretraining","Fusing per-domain GNN experts tops universal pretraining","One model per graph: adaptive fusion wins cross-domain","Bank of per-graph experts beats single-model pretraining","Adaptive expert selection outperforms one-size-fits-all GNN"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000342,"raw_usage":{"total_tokens":1870,"prompt_tokens":922,"completion_tokens":948,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":866}},"tokens_in":538,"tokens_out":948,"duration_ms":8747,"temperature":1.0,"reasoning_tokens":866,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:30:42.334961+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run OMOG's leave-one-out protocol and, for each test graph, compare the fused top-K model's accuracy against the best single source model in the bank. Because Theorem 2 promises the fused model matches or exceeds that best expert, any test graph where the fused model is significantly worse would falsify the guarantee. A more direct test of the scoring assumption: take a test graph, permute its node labels randomly, and check whether the scoring module's top-K selection still picks the most structurally similar source graphs.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contributes the post-hoc scoring idea: an MLP filter plus distance-to-centroid loss that OMOG adapts for its scoring modules."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents negative transfer in jointly pretrained GNNs, the empirical motivation for training one source model per graph."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes weighted parameter merging as a way to combine models, which OMOG uses to fuse selected experts."}],"review_version":1}