{"id":"ed577b2f-216f-4925-8e3a-486be3bb5d17","arxiv_id":"2505.14748","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A graph sampling scheme that combines causal effects with Shapley values to weight neighbor coalitions, improving robustness of GraphSAGE under feature perturbation.","lead":"CoCa-GraphSAGE adds cooperative game theory to causal GraphSAGE: it uses Shapley values over coalitions of neighboring nodes to choose which neighbors to sample when generating node embeddings. On five public graph datasets, it reports similar clean accuracy and better accuracy under feature perturbation than standard baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CoCa-sampling is not a well-defined algorithm as written: Eq. (5)-(8) leave T undefined, introduce an unexplained factor M, and mix |S_r|, |S_j|, and M inconsistently, so the reported robustness gains cannot yet be traced to a reproducible sampling rule.","rationale":"The reader's verdict is already CONDITIONAL, and the reader's rationale already lists the under-specified Shapley formula as one of several issues. My stress-test focuses on the part of that issue that is most load-bearing: the algorithm itself is not fully defined, so the robustness numbers in Tables III-VII cannot be attributed to a specific sampling rule. This is an internal-consistency problem rather than a disagreement with external consensus, and it is addressable in revision by defining T, S_r^-, the kernel density estimator, and the exact Shapley coefficient, or by providing code. I do not elevate the verdict to REJECT because the empirical pattern is consistent across five datasets and multiple perturbation regimes, and because the paper's own limitation paragraph concedes that gains are modest without perturbation and that scalability is a concern. Those concessions are consistent with the reported results and do not undermine the perturbation-robustness claim by themselves. The reader's weakest assumption about unobserved confounders is real but secondary: even granting the backdoor criterion, the estimator is not specified closely enough to compute. The right path is to keep the CONDITIONAL verdict with a request for a corrected derivation and either code or a precise pseudo-code with all symbols defined.","tokens_in":19358,"tokens_out":4815,"duration_ms":47786,"concrete_test":"On Cora's first-order neighborhoods, fix the missing quantities in two natural readings: (a) T = |N(v_r)| - 1 with |S| = M - 1, and (b) T = |N(v_r)| with |S| = M. Independently implement the standard Shapley value of the payoff function v(S) = p-hat(y_r | S_r) / |S_r|, and also of v(S) = p-hat(y_r | S_r), where S_r = S union {v_t}. If neither reading of Eq. (5)-(8) reproduces either standard Shapley formula, the cooperative causal weight is not the quantity the paper claims. If a corrected formula is found, re-run the Cora Table III row at perturbation ratios 0.1-0.5 and check whether the reported robustness margin over C-GraphSAGE persists.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that cooperative causal weights computed by CoCa-sampling are what drive the robustness gains. For that claim to hold, Eq. (5)-(8) in Section III-C must define a concrete, implementable weight for each candidate neighbor v_t. As written, they do not. First, Eq. (5) uses T in the factorial coefficient ((M-1)!(T-M)! / T!) but T is never defined anywhere in the manuscript; the only nearby quantities are the sampling number M, the neighborhood size |N(v_r)|, and the coalition size |S|. Second, Eq. (6) introduces an unexplained multiplicative factor M and a set S_r^- that is never defined; Eq. (8) then defines Q_T^M = ((M-1)!(T-M)! / T!) * M, and Eq. (7) absorbs all of this into a sum over coalitions S. The text states that Q_T^M is the same for all neighborhood nodes, but this is only meaningful if T is a fixed global constant, not a per-node neighborhood size. Third, the object being summed in Eq. (7), p-hat(y_r | v_t, S_r) - p-hat(y_r | S_r), does not match the marginal contribution defined in Eq. (4), which is the difference between causal weights for S_r and S_r without v_t. Finally, the paper says p-hat denotes a kernel density estimate, but no kernel, bandwidth, or estimation procedure is described, so p-hat(y_r | v_t, S_r) cannot be reproduced. Because Algorithm 1 instructs the user to compute 'the cooperative causal weight according to equation (7),' the method is under-specified at its core. The unobserved-confounder concern raised by the reader is real, but the more immediate barrier is that even under the paper's own graphical assumptions the weight formula is not a well-defined estimator.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Cooperative Causal GraphSAGE (CoCa-GraphSAGE), which combines cooperative game theory (Shapley values) with Causal GraphSAGE to define a new neighborhood sampling rule, CoCa-sampling. The authors construct a cooperative causal structure model, compute cooperative causal weights for candidate neighbors via a Shapley-like formula, and use these weights to sample neighbors before mean aggregation. Experiments on five node classification datasets report accuracy comparable to baselines without perturbation and improved accuracy under feature perturbation, which is attributed to the robustness of CoCa-sampling.","tokens_in":19761,"tokens_out":4412,"duration_ms":41163,"significance":"If the method were precisely specified and reproducible, the idea of accounting for cooperative interactions among neighborhood nodes during causal sampling would be a plausible and interesting extension of Causal GraphSAGE. The reported robustness gains, e.g., roughly 5–10 percentage points over C-GraphSAGE at high perturbation ratios, are substantial and would be of practical value. However, the current manuscript does not define the core sampling algorithm in an implementable way: key quantities are undefined, the equations are internally inconsistent, and the empirical comparisons are not fully controlled. The contribution is therefore conditional on a substantial rewrite of Sections III-C and IV, plus release of code or an unambiguous algorithmic specification.","major_comments":[{"comment":"The quantity T appears in the factorial coefficient ((M-1)!(T-M)! / T!) in Eq. (5) and in Q_T^M in Eq. (8), but T is never defined anywhere in the manuscript. If T is intended to be the neighborhood size |N(v_r)| or the total number of players in the cooperative game, this must be stated explicitly and used consistently; otherwise Eq. (5) is not an implementable algorithm.","section":"Section III-C, Eqs. (5)–(8)"},{"comment":"The unexplained multiplicative factor M in the second term of Eq. (6) (and later absorbed into Q_T^M in Eq. (8)) does not follow from the standard Shapley value formula, whose weights are |S|!(n-|S|-1)!/n! for a coalition of size |S|. The authors should justify why only coalitions of size M-1 are considered and why the weight includes an extra factor of M; as written, the formula is not derived from Eq. (2) or Eq. (4).","section":"Section III-C, Eq. (6)"},{"comment":"The object summed in Eq. (7), p̂(y_r | v_t, S_r) - p̂(y_r | S_r), does not match the marginal contribution φ(S_r) defined in Eq. (4), which is the difference between causal weights with and without v_t in the coalition. Consequently, the cooperative causal weight E(v_t) computed in Algorithm 1, line 6, is ill-defined, and the reported sampling rule cannot be reproduced from the equations given.","section":"Section III-C, Eq. (7) and Algorithm 1"},{"comment":"The paper states that p̂ denotes a kernel density estimate, but no kernel, bandwidth, or estimation procedure is provided. Since all cooperative causal weights in Eqs. (5)–(7) depend on p̂(y_r | v_t, S_r), the method cannot be implemented or evaluated by others without this information; please specify the estimator and any hyperparameters (e.g., bandwidth selection) used in the experiments.","section":"Section III-C, Eq. (3) and text after Eq. (3)"},{"comment":"The assertion that the path v_t ← S_r → y_r 'meets the backdoor criterion' presupposes that the coalition set S_r contains all confounders of v_t and y_r. This is a strong structural assumption that is not justified by the graph in Fig. 3. If unobserved confounders exist, the quantity estimated by Eq. (3) is a conditional association, not a causal effect, and the claim that the sampling is 'genuinely causal' would not hold. The authors should state this assumption explicitly and discuss its plausibility for the datasets used.","section":"Section III-C, backdoor criterion"},{"comment":"The empirical comparison is not fully controlled: C-GraphSAGE is run with sampling numbers (25, 10) for its two layers, whereas CoCa-GraphSAGE uses (10, 10), so the robustness differences could partly reflect the number of samples rather than the sampling rule. Moreover, no code or data splits are provided, and no statistical significance tests are reported. Given that the central claim is empirical robustness improvement, the paper should include these details or release code to allow verification.","section":"Section IV-A and Tables III–VII"}],"minor_comments":[{"comment":"The statistics of the Coauthor-CS and ogbn-arxiv datasets are missing from Table I; the table only lists Cora, Citeseer, and Pubmed, even though five datasets are used.","section":"Section IV-A, Table I"},{"comment":"The results for RL-GraphSAGE, GCNSS, and RN-GLVNMR are omitted for Coauthor-CS and ogbn-arxiv, so the comparison on those datasets is incomplete relative to the other three datasets.","section":"Section IV-A, Tables VI and VII"},{"comment":"There are typos and garbled equations throughout the section (e.g., 'Shapely' instead of 'Shapley', and the OCR of Eqs. (3)–(7) appears corrupted); the authors should carefully proofread the manuscript and ensure all equations are typeset correctly.","section":"Section III-C"},{"comment":"The description of Bernoulli-matrix XOR perturbation for the citation datasets is too brief; please specify how the perturbation matrix is generated, how it interacts with the features, and what fraction of the feature entries are modified.","section":"Section IV-A, perturbation description"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears to be an early or lightly edited draft (e.g., the placeholder 'REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER' and heavy formatting issues). The core issue is that the proposed algorithm is not well-defined, which prevents any verification of the claimed results. This is recoverable in principle, but the revision must provide a clean, implementable specification of the Shapley-based weighting and the density estimator, ideally with code. I also note that the comparison to C-GraphSAGE uses different sampling budgets, which should be addressed. If the authors cannot define the algorithm precisely, the paper should be rejected; if they can, it may become a solid contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The combination is new: Shapley values over neighbor coalitions used to weight causal sampling in GraphSAGE. And the robustness gains on five datasets are consistent, especially at perturbation ratios 0.3–0.5. But the central sampling weight is not actually defined in the paper. Equations (5)–(8) leave T undefined, introduce an unexplained multiplicative factor M, and sum an object that does not match the marginal contribution in Eq. (4). The kernel density estimator p̂ is never specified. Algorithm 1 then instructs the reader to compute weights via Eq. (7), but Eq. (7) cannot be evaluated. This is not a typo-level issue; the method is under-specified at its core.\n\nWhat the paper does well: it identifies a real limitation of C-GraphSAGE, which weights neighbor nodes individually and ignores the coalition structure of the sampled set. The cooperative causal structure model (Fig. 3) is a sensible construct, and the experiment design is thorough: five datasets, three perturbation modes (train+test perturbed, test-only, train-only), and seven baselines. The robustness improvements over C-GraphSAGE are large and consistent at high perturbation ratios (e.g., 5.9%, 10.2%, 8.9%, 5.5%, 3.9% on the five datasets), with only modest clean-accuracy loss. The authors also honestly note in the conclusion that gains without perturbation are limited.\n\nThe soft spots are real but fixable. Beyond the undefined T and unspecified kernel density estimate, the backdoor criterion is asserted without discussing unobserved confounders. No code or data splits are provided, so the numbers cannot be checked. The perturbation setup for training-only cases is described vaguely, and some tables have inconsistent standard deviations. These are addressable in revision.\n\nWho is this for? Anyone working on robust GNN sampling, causal inference on graphs, or Shapley-based node selection. It is not a field-reshaping contribution, but the empirical result is interesting enough to deserve referee time if the derivation can be completed.\n\nRecommendation: send it to peer review with a strong request for a complete, concrete derivation: define T, fix the factorial formula, specify the kernel density estimator, and release code and data splits. If the authors can do that, the paper could be acceptable. As submitted, the central claim is not reproducible.","headline":"New combination of Shapley values and causal sampling for GraphSAGE, with promising robustness results, but the core sampling weight is not actually defined in the paper.","tokens_in":20293,"tokens_out":3519,"would_cite":false,"duration_ms":57586,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-07T15:39:40.529726+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}