{"id":"1e5fd3c8-c34a-4747-949b-0a9ef997af12","arxiv_id":"2501.16002","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"ScaDyG proposes a decoupled, step-wise exponential time encoding with hypernetwork aggregation for scalable dynamic graph learning, but the key proof of equivalence with composite exponential message passing is invalid as stated.","lead":"The paper introduces ScaDyG, a dynamic graph neural network that precomputes time-decayed message propagation in steps and uses a small hypernetwork to adapt node representations, claiming accuracy on par with or better than prior models while training up to 60x faster with up to 50x fewer parameters.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 1's proof makes W1 a function of Δt, so the claimed equivalence between fixed-matrix preprocessing and composite-exponential message passing fails; DTE's theoretical foundation is unsupported.","rationale":"The paper's headline contribution is a decoupled, preprocessing-friendly dynamic graph paradigm; the methodological core is Proposition 1, which is supposed to show that the time encoding can be precomputed without learnable parameters while still representing adaptive composite-exponential time dependencies. The proof in Appendix A fails precisely at the point where W1 is constructed: its entries depend on Δt. Since the proposition requires W1 to be a single learnable matrix, the equivalence is invalid. This is an internal inconsistency, not a matter of taste. It matters because the 'new paradigm' framing and the claim of 'dynamic temporal encoding' rest on this equivalence; absent it, DTE is just a fixed exponential feature map. The empirical results are extensive and the ablation study shows the components help, so the paper could potentially be repaired by restating the equivalence as approximate or by proving it for the actual hypernetwork-generated W_x (which is message-dependent). Until then, the central theoretical claim is unsupported. The missing scalable baselines (TDLG, NAT, Orca, Zebra, TGL) are a further weakness in the empirical SOTA claim, but I view the proof flaw as more load-bearing because it affects the correctness of the method's stated mechanism. The reader's weakest assumption identifies the same issue, so I agree. The verdict should remain REJECT (no change).","tokens_in":23241,"tokens_out":11960,"duration_ms":106209,"concrete_test":"Re-derive Eq. 7–11 with W1 fixed and independent of Δt. As a numerical check, fix random x, W, a, γ and a fixed W1, then compare x⊙T_e(Δt)W1 with xκ(Δt)W over a range of Δt; the relative error will be nonzero unless the degenerate condition holds. If the error is nonzero, Proposition 1 is false as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Appendix A, Proposition 1 claims that for a learnable matrix W1, x_v ⊙ T_e(Δt1) ⊙ T_e(Δt2) W1 equals x_v κ(Δt) W with Δt = Δt1 + Δt2. The proof's last step assigns W1 entries as w_ij = z_ij (a_1 e^{(γ1−γ_j)Δt} + ... + a_d e^{(γd−γ_j)Δt}). This makes W1 explicitly depend on Δt and on the output coordinate j, so W1 is not a fixed parameter matrix. If W1 is held fixed, equality for all Δt would force the expression ∑_k a_k e^{(γ_k−γ_j)Δt} to be constant in Δt for every j, which holds only in the degenerate case. Therefore the claim that preprocessing with fixed exponentials followed by one learned transformation implements arbitrary composite-exponential dependency is false. The practical consequence is that DTE's 'no learnable parameter in preprocessing' is not justified by the stated equivalence; the method remains a heuristic exponential encoding. This does not by itself disprove the empirical results, but it removes the paper's central theoretical support for its core design.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ScaDyG, a decoupled paradigm for large-scale dynamic graph learning. It introduces Time-aware Topology Reformulation (TTR) to precompute weight-free temporal message propagation in intra- and inter-step phases, Dynamic Temporal Encoding (DTE) based on a combination of exponential functions, and a hypernetwork-driven message aggregation that generates node-specific transformation matrices. Experiments on 12 link- and node-level datasets, including million-scale graphs, show state-of-the-art or comparable prediction performance with substantially fewer parameters and lower training time than existing DGNN baselines. The central theoretical claim is that preprocessing with fixed exponentials followed by a single learnable linear transformation is equivalent to composite-exponential message passing, which justifies the 'no learnable parameters in preprocessing' design.","tokens_in":23459,"tokens_out":4235,"duration_ms":38828,"significance":"If the central equivalence were correct, the paper would offer a genuinely scalable and theoretically grounded alternative to sampling-based continuous-time DGNNs, with the preprocessing/propagation separation being the main novelty. The empirical study is extensive: 12 datasets, ablations for each component, scalability measurements, and hyperparameter sensitivity analyses. The method is simple, reproducible in principle, and the reported speedups (up to 60x) and parameter reductions (up to 50x) are striking. However, the theoretical foundation is load-bearing for the 'new paradigm' claim, and the proof of Proposition 1 is invalid as stated, making the proposed DTE's justification circular. The empirical results may remain valid as a heuristic, but the paper's central methodological contribution is not supported.","major_comments":[{"comment":"The proof of Proposition 1 defines the entries of the 'learnable' matrix W1 as w_ij = z_ij (a_1 e^{(γ_1−γ_j)Δt} + ... + a_d e^{(γ_d−γ_j)Δt}), where Δt = Δt_1 + Δt_2. This makes W1 explicitly depend on the time interval Δt and on the output coordinate j, so it is not a fixed parameter matrix as claimed. If W1 is held fixed after training, the equality x_v ⊙ T_e(Δt_1) ⊙ T_e(Δt_2) W1 = x_v κ(Δt) W for all Δt would require the coefficient sum ∑_k a_k e^{(γ_k−γ_j)Δt} to be constant for every j, which holds only in degenerate cases. Thus the claimed equivalence between fixed-exponential preprocessing plus a single learned transformation and composite-exponential message passing is not established; it is true only by allowing W1 to vary with Δt, which defeats the purpose of the proposition. This invalidates the theoretical justification for DTE as 'adaptive weight fusion' and leaves the 'no learnable parameter in preprocessing' claim without its supporting argument.","section":"Section 4.2, Proposition 1 and Appendix A"}],"minor_comments":[{"comment":"The text says 'we introduce 13 benchmark datasets' but Table 1 lists 12 datasets (8 link + 4 node); the count should be corrected.","section":"Section 5"},{"comment":"There are typographical errors: 'Dynamic Grpah Neural Networks' and 'message massing-based methods' should be 'Dynamic Graph Neural Networks' and 'message passing-based methods', respectively.","section":"Section 2"},{"comment":"The notation in the composite exponential dependency, e.g., 'a_1 e^{γ_1 Δt}_1', has unnecessary subscripts on the exponential terms; it should simply be a_i e^{γ_i Δt}.","section":"Definition 2"},{"comment":"The definition of N is confusing: it is described as 'the number of historical steps in ScaDyG' in the caption, while the text in Section 5.3 separately refers to 'historical steps of length N' and 'total steps L'. The roles of N and L should be clarified to avoid ambiguity in the complexity expressions.","section":"Table 4"},{"comment":"The proof uses the symbol x_e_v for the edge feature while the main text uses x_v for node features; the notation should be made consistent so that the derivation is easier to follow.","section":"Appendix A"},{"comment":"The statement 'most methods perform best with a time step of 3' is unclear in context (the axis is 'number of steps', not 'time step') and should be reworded for precision.","section":"Section 5.5"}],"recommendation":"reject","confidential_remarks":"The empirical part of the paper is substantial and the reported results are strong, but the theoretical foundation—Proposition 1—is invalid as stated and is central to the paper's claimed contribution. The issue is not a minor gap but a circularity that cannot be patched without fundamentally changing the claim or the method's rationale. Given that the 'new paradigm' rests on this equivalence, I recommend rejection, although a revised version that presents DTE as a heuristic exponential encoding without the equivalence claim might be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about ScaDyG. The empirical package is serious: 12 datasets, million-level graphs, consistent wins or near-wins on link and node tasks, and efficiency gains that look plausible. The theoretical package is not: Proposition 1, the load-bearing claim that preprocessing with fixed exponentials plus one learned matrix implements composite-exponential message passing, is false as stated. The proof in Appendix A defines the entries of W1 to be functions of Δt, so W1 is not a fixed parameter matrix. If W1 is held fixed, the claimed equality for all Δt forces a degenerate condition on the exponential parameters. So the \"no learnable parameters in preprocessing\" claim is not justified by that equivalence.\n\nWhat's actually new is the combination: time-aware topology reformulation that splits message passing into intra- and inter-step propagation, step-wise exponential encoding, and a hypernetwork that generates node-specific aggregation weights. That combination does not appear in the cited prior art. The ablations show each component matters, and the hyperparameter sensitivity analysis is reasonably thorough. The efficiency gains on the million-scale datasets are the kind of thing that would interest industry.\n\nThe soft spots beyond the theorem are the baseline choices. The paper cites TDLG, NAT, Orca, Zebra, and TGL as the closest scalable or decoupled methods, then never evaluates against any of them. For a paper whose headline is scalability, that is a real gap. If the comparison is done and ScaDyG still wins, the empirical claim strengthens; right now the SOTA claim rests on comparisons to older or less scale-focused methods.\n\nI want to be fair: none of this disproves the empirical results. The method may work well as a heuristic exponential encoding with hypernetwork aggregation. But the paper's central framing—that the preprocessing is equivalent to composite-exponential message passing—is unsupported. That needs to be fixed, either by proving a correct equivalence or by explicitly reframing DTE as a heuristic with empirical support.\n\nWho gets value: practitioners working on large-scale temporal graphs, and researchers interested in decoupled propagation. It deserves a serious referee, but the referee should demand a corrected theorem and a fair baseline set. I'd send this to review, but I would not accept it in its current form.","headline":"Solid empirical work undermined by a broken Proposition 1 and missing comparisons to the decoupled baselines the paper itself cites.","tokens_in":24023,"tokens_out":2591,"would_cite":true,"duration_ms":25173,"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":"ScaDyG claims a decoupled, precompute-heavy design lets dynamic graph learning scale to million-edge graphs while matching or beating state-of-the-art accuracy.","keywords":["dynamic graph learning","scalable graph neural networks","decoupled propagation","temporal encoding","hypernetwork","link prediction","node affinity prediction","time-aware topology reformulation"],"falsifier":"On a small synthetic example, fix x_v, choose distinct γ_i and nonzero coefficients a_i for a target composite exponential κ(Δt), and solve for a single matrix W1 that minimizes the approximation error of x_v ⊙ T_e(Δt) W1 versus x_v κ(Δt) W across a range of Δt values. If the minimal error is non-negligible, no fixed learned transformation can reproduce composite-exponential message passing, and the equivalence claim would require W1 to be time-dependent, exactly as the proof's construction implies.","tokens_in":22996,"feed_emoji":"⚡","tokens_out":5963,"duration_ms":55153,"temperature":0.7,"pith_summary":"The paper tries to establish that dynamic graph learning can be made scalable by completely separating time-aware feature propagation from learnable transformations, so that all propagation is computed once in a parameter-free preprocessing step. It claims that segmenting history into intra- and inter-step intervals with exponential temporal encoding, followed by a hypernetwork that generates node-specific aggregation weights, matches or beats existing dynamic graph neural networks on 12 datasets while using up to 50x fewer parameters and training up to 60x faster. The central theoretical claim is that a parameter-free exponential preprocessing step followed by a learnable transformation is equivalent to an adaptive composite-exponential message-passing rule. If true, this would remove the neighborhood-sampling bottleneck that limits current continuous-time models on industrial-scale graphs.","feed_headline":"Precomputed propagation makes dynamic graph learning 60x faster","feed_subtitle":"A decoupled time-aware design matches or beats 8 baselines on 12 datasets with 50x fewer parameters","key_machinery":"The central objects are Time-aware Topology Reformulation (TTR), which partitions history into equal time steps and decomposes propagation into intra-step and inter-step phases so that feature propagation becomes weight-free sparse matrix multiplication during preprocessing; Dynamic Temporal Encoding (DTE), a vector of fixed exponential functions T_e(Δt) = [$e^{{γ1Δt}}$, ..., $e^{{γdΔt}}$] whose multiplicative property makes the time split exact; and Hypernetwork-driven Message Aggregation, which uses a hypernetwork to scale a primary weight matrix W into node-specific matrices via an outer product with node messages. The load-bearing identity is Proposition 1, which asserts the equivalence between the factorized preprocessing expression and composite-exponential message passing, and the proof in Appendix A constructs the entries of the learned matrix as functions of the time interval Δt.","core_discovery":"The central claim is that temporal message passing can be reformulated so that a message from a historical neighbor at time t' to the current time t is computed as x_v ⊙ T_e(Δt1) ⊙ T_e(Δt2) W1, where Δt1 is the delay to the end of its time step and Δt2 is the delay from that step boundary to the present, and that this equals a composite-exponential message passing x_v κ(Δt) W with κ a weighted sum of exponentials. Because the exponential time encoding satisfies T_e(Δt1 + Δt2) = T_e(Δt1) ⊙ T_e(Δt2), the split factorizes exactly, which permits intermediate messages to be precomputed per step without any learnable parameter. The paper further claims that a hypernetwork generating node-specific transformation matrices W_x overcomes the limitation of a single shared transformation, and that this design achieves the reported state-of-the-art or comparable results on link prediction and node affinity prediction.","pith_inferences":["The factorization in Proposition 1 suggests a general template: any temporal kernel that factorizes over a split time interval (exponentials satisfy this exactly, and other semigroup-like kernels approximately) can be moved into a parameter-free preprocessing stage, which may extend beyond the exponential family.","The node-specific weight matrices generated by the hypernetwork may encode a per-node temporal profile; a testable extension would check whether these matrices correlate with node activity or transfer across datasets, evidence the paper does not provide.","The complexity analysis excludes preprocessing from training time, so a fair end-to-end comparison on the largest datasets should measure total time-to-accuracy rather than per-epoch training time, especially for deployment scenarios.","If the time-dependence of the learned matrix in Proposition 1 is made explicit (e.g., by parameterizing W(Δt)), the framework could become fully inductive, avoiding the need to store per-step intermediate messages at inference."],"forward_implications":["Training time on large dynamic graphs drops dramatically: the paper reports up to 60x faster training and up to 50x fewer parameters than strong baselines, with the preprocessing cost negligible relative to total training time.","Neighborhood sampling becomes unnecessary for temporal message passing, removing the sampling-quality bottleneck that continuous-time methods face when historical neighborhoods grow large.","The same framework serves both link-level and node-level tasks without task-specific architectural changes, achieving top or second-top results on 9 link prediction datasets and 4 node affinity datasets.","Ablation results identify the combination of exponentials and the hypernetwork as the two components whose removal causes the largest performance drops, supporting the paper's claim that both are needed for node-wise temporal modeling.","The hyperparameter study suggests the method is less sensitive to the number of historical time steps than sampling-based baselines, and that multi-hop propagation harms temporal tasks."],"supporting_citations":[{"why":"Supplies the decoupled propagation paradigm (multi-hop propagation followed by a simple classifier) that ScaDyG extends from static to temporal graphs.","marker":"[45]"},{"why":"Provides the hypernetwork mechanism used to generate node-specific transformation matrices for message aggregation.","marker":"[9]"},{"why":"Represents the single-exponential temporal modeling baseline that ScaDyG's dynamic temporal encoding generalizes, and is used as the 'w/o TE' ablation reference.","marker":"[44]"},{"why":"Supplies the node affinity prediction task and the four tgbl-* datasets used for node-level evaluation.","marker":"[16]"},{"why":"A strong continuous-time baseline (GraphMixer) that ScaDyG outperforms, and one of the methods whose implementation library is reused for comparisons.","marker":"[5]"},{"why":"DyGFormer, the strongest continuous-time baseline in most link prediction experiments, and the library used to implement several competing baselines.","marker":"[52]"},{"why":"An exponential time encoding method for neighborhood formation that motivates the use of exponential functions in dynamic modeling.","marker":"[62]"},{"why":"The only existing decoupled temporal graph embedding method, which ScaDyG differentiates from by using adaptive rather than fixed temporal modeling.","marker":"[1]"}],"fun_headline_variants":["ScaDyG precomputes temporal messages for 60x faster graph learning","Time-aware reformulation makes dynamic graph learning 60x faster","Hypernetwork-driven aggregation scales dynamic graphs to 12 datasets","Exponential time encoding exact precomputation speeds dynamic GNNs","ScaDyG: decoupled temporal propagation matches SOTA with fewer params"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof of Proposition 1 requires the learned matrix to change its entries with the time interval Δt; if a single shared matrix must work for all intervals, the claimed equivalence between parameter-free preprocessing and composite-exponential message passing does not hold.","fun_headline_variants_meta":{"raw":{"variants":["ScaDyG precomputes temporal messages for 60x faster graph learning","Time-aware reformulation makes dynamic graph learning 60x faster","Hypernetwork-driven aggregation scales dynamic graphs to 12 datasets","Exponential time encoding exact precomputation speeds dynamic GNNs","ScaDyG: decoupled temporal propagation matches SOTA with fewer params"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1440,"prompt_tokens":984,"completion_tokens":456,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":363}},"tokens_in":600,"tokens_out":456,"duration_ms":4531,"temperature":1.0,"reasoning_tokens":363,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:49:57.179945+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a small synthetic example, fix x_v, choose distinct γ_i and nonzero coefficients a_i for a target composite exponential κ(Δt), and solve for a single matrix W1 that minimizes the approximation error of x_v ⊙ T_e(Δt) W1 versus x_v κ(Δt) W across a range of Δt values. If the minimal error is non-negligible, no fixed learned transformation can reproduce composite-exponential message passing, and the equivalence claim would require W1 to be time-dependent, exactly as the proof's construction implies.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the hypernetwork mechanism used to generate node-specific transformation matrices for message aggregation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Represents the single-exponential temporal modeling baseline that ScaDyG's dynamic temporal encoding generalizes, and is used as the 'w/o TE' ablation reference."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"An exponential time encoding method for neighborhood formation that motivates the use of exponential functions in dynamic modeling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The only existing decoupled temporal graph embedding method, which ScaDyG differentiates from by using adaptive rather than fixed temporal modeling."}],"review_version":1}