{"id":"ab9a22b0-5a54-45f4-a347-178aa1975b0b","arxiv_id":"2501.11880","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"CTWalks combines community-guided temporal walks, community-labeled anonymization, and a Neural ODE encoder to improve temporal link prediction on continuous-time dynamic graphs.","lead":"CTWalks is a new method for learning node representations in continuous-time dynamic graphs. It steers temporal walks with detected communities, enriches anonymized walk encodings with community labels, and encodes time with ODEs, reporting improved temporal link prediction on five benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 1 and Appendix D.1 disagree by 27x on Taobao and 2x on Enron; without resolving which graph was used, the reported SOTA cannot be trusted.","rationale":"The reader's verdict is CONDITIONAL, and I agree that the paper should not be accepted as-is. The reader's weakest_assumption focuses on the stability and informativeness of Louvain communities; that is a legitimate design risk, and Section 7 openly acknowledges it, but the Table 3 ablation shows community-aware sampling helps on the evaluated datasets, so it is not the most decisive unresolved point. The reader's rationale also flags the Table 1 versus Appendix D.1 discrepancy, and I find that issue more load-bearing: it directly concerns whether the reported numerical results are results on the named benchmark datasets. A 27-fold difference in Taobao edge count cannot be explained by any preprocessing step stated in Section 6.1, and without resolving it the empirical SOTA claim is not reproducible. The matrix-factorization lemma in Appendix F is also flawed because the transition matrix used in the proof is not the process realized by Algorithm 1, which restricts each walk entirely to either an intra-community or an inter-community subgraph rather than summing both transition matrices; this is a serious theoretical weakness but it does not by itself overturn the experimental rankings. I am not accusing the authors of misconduct; the discrepancy may be a typo in either table, but it must be settled before the central claim can be evaluated. The announced public repository and the consistent ablations are genuine positive evidence, which is why the appropriate disposition remains CONDITIONAL rather than a stronger rejection.","tokens_in":25415,"tokens_out":6466,"duration_ms":73145,"concrete_test":"Run the released CTWalks preprocessing code on the Taobao and Enron sources cited in Appendix D.1 and print exact node and edge counts after the stated chronological 70/15/15 split and negative sampling. Then compare: if the counts match Table 1, document the subsampling or filtering rule and rerun the baselines on that exact graph; if the counts match Appendix D.1, rerun Tables 2 and 7 for Taobao and Enron on the full graphs; if neither, trace the discrepancy through the preprocessing pipeline. The central claim stands only if the reported AUC and AP values are on the same graphs described in Table 1.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is not the method's internal design but whether the experiments actually ran on the datasets they claim. The central claim—CTWalks outperforms six strong baselines on five benchmark CTDGs—is supported only by Tables 2 and 7. Yet the dataset descriptions are mutually inconsistent. Table 1 reports Taobao with 64,703 nodes and 77,436 temporal edges, while Appendix D.1 reports 987,994 nodes and 2,099,520 temporal edges, a 27-fold difference. Enron is reported as 143 nodes / 62,617 edges in Table 1 but 184 nodes / 125,235 edges in Appendix D.1. UCI and Wikipedia match, which makes the discrepancy look like a real ambiguity rather than a systematic typo. Section 6.1 describes only sorting, chronological splitting, and negative sampling; none of these steps can turn 2,099,520 interactions into 77,436. If the Taobao results in Tables 2 and 7 were produced on a subsample or filtered graph, then the claim of SOTA on Taobao is not a claim about the standard benchmark, and the baseline comparisons need to be redone on the same data. If Table 1 is the actual graph, Appendix D.1 must be corrected and the source of the discrepancy explained. Until this is settled, the headline empirical contribution is not reproducible. The community-stability issue raised by the reader is acknowledged in Section 7 and mitigated by the Table 3 ablation; the Appendix F matrix-factorization mismatch is a theoretical flaw but does not directly invalidate the empirical rankings. The dataset identity is the single point on which the entire experimental conclusion hinges.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CTWalks, a representation-learning framework for continuous-time dynamic graphs that combines community-guided temporal walk sampling, community-enriched anonymization, and an ODE-based continuous encoding. The authors argue that the community-aware sampling removes locality bias, that the anonymization improves inductive generalization, and that the ODE encoder preserves irregular temporal dynamics. Experiments on five datasets compare CTWalks against DyRep, TGAT, TGN, CTDNE, JODIE, and CAWs in transductive and inductive temporal link prediction, with an ablation study and an additional static-graph experiment supporting the main components.","tokens_in":25630,"tokens_out":4252,"duration_ms":48007,"significance":"If the empirical claims are correct, CTWalks would provide a competitive, code-released baseline for CTDG link prediction, and the ablation study gives useful evidence that community-aware sampling and continuous integration matter. The theoretical sections are less convincing: Lemma 1 largely restates the transition restriction, and the matrix-factorization analysis in Appendix F does not match the actual sampling process. Most importantly, the dataset statistics in Table 1 and Appendix D.1 are mutually inconsistent for Taobao and Enron, so the headline state-of-the-art claim is not currently reproducible.","major_comments":[{"comment":"The dataset statistics are mutually inconsistent. Table 1 reports Taobao with 64,703 nodes and 77,436 temporal edges, while Appendix D.1 reports 987,994 nodes and 2,099,520 temporal edges; Enron is listed as 143 nodes/62,617 edges in Table 1 but 184 nodes/125,235 edges in Appendix D.1. Section 6.1 describes only chronological sorting, chronological splitting, and negative sampling, none of which can reconcile these numbers. Because Tables 2 and 7 report CTWalks as state of the art on these datasets, the reader cannot determine which graph was actually used. The authors must report the exact preprocessing pipeline, clarify which statistics are correct, and rerun or confirm all baselines on the same graph.","section":"Table 1 vs Appendix D.1"},{"comment":"The claim that CTWalks 'overcomes locality bias' is close to a restatement of the sampling restriction. The inequality in Lemma 1 is obtained by setting the first-visit probabilities of intra-community neighbors to zero and renormalizing by |Ninter(u)|; this is precisely the pruning built into Algorithm 1 for bridging nodes, not an independent theoretical property of the walk. The comparison is also against a uniform random walk on the full graph, whereas a more meaningful baseline would be a walk with the same restricted transition support. Moreover, Eq. (18) assumes that intra-community transitions can never reach nodes in other communities, which fails if the community partition is imperfect; the authors acknowledge this fragility in Section 7. Please reframe the lemma as a property of the construction or provide a comparison that does not assume the conclusion.","section":"Section 5, Lemma 1 and Eq. (16)-(21)"},{"comment":"The matrix-factorization argument does not correspond to the sampling process in Algorithm 1. In CTWalks, each walk is generated entirely within either GI or GCi depending on the root node, so no single walk mixes MC and MI. The average transition behavior is therefore a weighted mixture of separate powers of MC and MI, not the sum 1/T sum_r (M_C^r + M_I^r) used in Eq. (48). Additionally, MC + MI is not a transition matrix because its rows generally sum to more than 1. As written, Lemma 2 does not establish the claimed connection between CTWalks and matrix factorization.","section":"Appendix F, Eq. (48)-(56)"},{"comment":"The term 'parameter-free' is overstated. The sampling mechanism still depends on walk length l and number of walks per node C/R, both of which are tuned per dataset in Appendix D.3, and the ODE solver step size is manually fixed. If the intended claim is only that no direction-bias hyperparameter is introduced beyond the community partition, the text should state this qualification explicitly.","section":"Abstract, Contribution 2, and Appendix D.3"}],"minor_comments":[{"comment":"Definition 3 states that temporal walks have strictly decreasing timestamps, while the anonymized walk construction in Sec. 4.2 uses ascending timestamps t1 < t2 < ... < tl; the two conventions should be aligned.","section":"Definition 3 vs Sec. 4.2"},{"comment":"The batching analysis refers to 'Section B.1' when describing the batch-processing optimization, but the actual derivation appears in Appendix C.2; the cross-reference should be corrected.","section":"Appendix C.2"},{"comment":"Several entries in Tables 2 and 7 are difficult to read because bold and dagger markers are not consistently explained, and decimal alignment varies; please clarify the highlighting convention and format the tables uniformly.","section":"Tables 2 and 7"},{"comment":"The baseline name 'CA Ws' contains a spacing typo; it should read 'CAWs'.","section":"Appendix D.2"},{"comment":"In Eq. (7), the denominator is written as a sum over valid neighbors but it is not stated whether t' is the timestamp of the edge (v,u) and whether multiple edges between the same pair are treated separately; please clarify the indexing.","section":"Eq. (7)"},{"comment":"The static-graph experiment uses word2vec with walk length 80 and 10 walks per node, but the relationship of these settings to the temporal CTWalks configuration is not discussed; a sentence explaining the choice would improve reproducibility.","section":"Appendix E"}],"recommendation":"major_revision","confidential_remarks":"The dataset discrepancy in Table 1 versus Appendix D.1 is a reproducibility gate; if it cannot be resolved, I would not certify the empirical claims. The theoretical analysis also needs substantial reframing, since Lemma 1 and Appendix F currently describe properties that are built into the sampling definition. The novelty relative to CAWs and ODE-RNN is modest, but that is not the basis of my recommendation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: CTWalks is a plausible new method—community-guided temporal walks, community-labeled anonymization, and ODE-RNN encoding—and the ablations suggest each component earns its keep. The empirical headline is shaky, though, because Table 1 and Appendix D.1 disagree about the Taobao graph by a factor of 27.\n\nWhat is actually new: the combination of Louvain-based intra/inter-community walk restrictions with community labels in the anonymization step is not in the cited CAWs/TGN/TGAT work, and it is a sensible answer to the Figure 1 ambiguity. The ablations in Table 3 are the strongest part of the paper: removing the community walks, the community labels, or the ODE integration all cost real AUC, which is evidence the design choices matter. The authors also state a public repository, and Section 7 honestly flags the dependency on community-detection quality.\n\nSoft spots, in order of severity. First, the data identity. Table 1 lists Taobao with 64,703 nodes/77,436 edges; Appendix D.1 reports 987,994 nodes/2,099,520 edges. Enron similarly differs by 2x. Section 6.1 describes only sorting, chronological splitting, and negative sampling, none of which turns 2M interactions into 77k. If Tables 2 and 7 were produced on a subsample or filtered graph, the \"SOTA on Taobao\" claim is not about the standard benchmark and the comparisons need to be redone. This is the load-bearing issue. Second, \"parameter-free\" is overstated: Algorithm 1 takes walk length and number of walks, and D.3 grid-searches l, C, and ODE step size. Third, Appendix F's matrix-factorization lemma factors (M_C + M_I), but Algorithm 1 realizes a walk that is either intra- or inter-community depending on the starting node's type, not a sum of both; the theorem is not about the actual sampling process. Fourth, Lemma 1's inequality is largely a restatement of the construction—fine as a sanity check, not a deep theoretical result.\n\nThe community-stability concern is real but mitigated by the ablation, and Section 7 admits it, so I would not block on that. The dataset discrepancy is the reason I would not trust the current numbers.\n\nWho this is for: people working on continuous-time dynamic graph embedding who want a walk-based inductive method with mesoscopic structure. It deserves a serious referee, but the referee should demand resolution of Table 1 vs D.1, release of code with a commit hash and reproduction scripts, and either removal or correction of the Appendix F claim. I would not cite it in its current form.\n\nRecommendation: send to peer review, conditional on the authors fixing the dataset descriptions and tempering the parameter-free and matrix-factorization claims.","headline":"CTWalks is a plausible new method with informative ablations, but the 27x discrepancy in the Taobao dataset between Table 1 and Appendix D.1 makes the headline empirical claims untrustworthy until resolved.","tokens_in":26269,"tokens_out":3241,"would_cite":false,"duration_ms":32472,"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":"CTWalks claims that guiding temporal walks by community boundaries, tagging them with community labels, and encoding them with ODEs yields more accurate temporal link prediction than six established baselines.","keywords":["continuous-time dynamic graphs","temporal link prediction","temporal walks","community detection","anonymized walk encoding","neural ODE","inductive learning","parameter-free sampling"],"falsifier":"Compare CTWalks with an unrestricted temporal-walk variant on a dataset whose training-time communities are weak or whose future edges mostly join nodes from different communities; if the unrestricted variant matches or exceeds CTWalks on AUC, the community-restriction claim is falsified.","tokens_in":25047,"feed_emoji":"🔗","tokens_out":6600,"duration_ms":67864,"temperature":0.7,"pith_summary":"CTWalks is a representation-learning method for continuous-time dynamic graphs, where edges are time-stamped interactions rather than snapshots. It builds a weighted static graph from interaction counts, detects communities on it, and then samples temporal walks that stay inside a community for ordinary nodes and run between communities only through bridging nodes, so no extra parameter decides exploration versus exploitation. Each sampled walk is anonymized by position counts and tagged with the community labels of the two root nodes, and the sequence is encoded by alternating GRU-style updates with an ODE that integrates the hidden state over irregular time gaps. The paper argues that community-aware sampling breaks locality bias, that the encoding corresponds to a low-rank matrix factorization, and that the full pipeline outperforms six established baselines on temporal link prediction across five datasets, with the largest margins in inductive settings involving unseen nodes. If these results hold, CTWalks offers a way to inject mesoscopic structure into dynamic graph embeddings without hand-tuned walk parameters.","feed_headline":"Community-guided walks beat six baselines in link prediction","feed_subtitle":"Keeping walks inside or between communities plus ODE encoding lifts AUC on five benchmarks.","key_machinery":"The load-bearing object is the community-restricted temporal walk with its two-layer transition structure. A weighted temporal graph $G_w$ is formed by setting edge weights to interaction counts, then modularity optimization partitions nodes into communities; bridging nodes belong to multiple communities, while non-bridging nodes are confined to one. During sampling, a walk from a non-bridging node can only follow edges inside its community, while a walk from a bridging node can only follow edges in the inter-community subgraph, with transition probability proportional to $e^{-(t-t')}$ over valid neighbors. The anonymization step replaces node identities with position-based occurrence counts and appends the community labels of the source and target roots, restoring context that purely structural anonymization loses. The encoding alternates an instantaneous GRU update $g$ with a continuous ODE integration $f$ over each inter-event interval, so the final hidden state carries both discrete structural updates and continuous temporal evolution.","core_discovery":"On its own terms, the paper's central discovery is that community structure, treated as a mesoscopic layer between local neighborhoods and the whole graph, can be made the organizing principle for temporal walk sampling, anonymization, and continuous-time encoding. The method partitions the aggregated interaction graph into communities via modularity optimization, classifies nodes as bridging or non-bridging, restricts each walk to the appropriate intra- or inter-community subgraph, and then encodes the resulting anonymized walks with an ODE-based continuous integration step. The paper claims a theoretical lemma showing this restriction reduces locality bias relative to uniform random walks, and a second lemma showing the learned embeddings factor a shifted pointwise mutual information matrix built from intra- and inter-community transition matrices. Empirically, it reports that CTWalks achieves the best or second-best AUC and AP against six baselines on five datasets, especially for inductive link prediction with new nodes.","pith_inferences":["Beyond the paper: if community restriction is the real source of gains, CTWalks should degrade on graphs with low modularity or heavy cross-community churn; a concrete test is to compare CTWalks against an unrestricted temporal-walk variant on such graphs.","Beyond the paper: the matrix-factorization view suggests CTWalks inherits Skip-Gram with negative sampling biases, so high-degree bridging nodes may dominate the embedding; measuring predictive accuracy stratified by node degree would test this.","Beyond the paper: a lightweight version that replaces the ODE solver with a closed-form temporal kernel could isolate how much of the improvement comes from continuous integration versus community-aware sampling."],"forward_implications":["If CTWalks is correct, temporal link prediction on unseen nodes should benefit most, since anonymized positional encodings plus community labels let the model transfer across nodes with similar roles.","If CTWalks is correct, sampling no longer needs hand-tuned walk-direction hyperparameters: community membership alone decides whether a walk explores inside a community or across bridging nodes.","If CTWalks is correct, irregular interaction times can be handled without discretization or imputation, because the hidden state evolves continuously between observed events.","If CTWalks is correct, the learned embeddings admit a matrix-factorization interpretation, giving a principled account of what the community-restricted walks encode."],"supporting_citations":[{"why":"The causal anonymous walk method CTWalks builds on and is compared against; supplies the anonymized-walk baseline it must beat.","marker":"[3]"},{"why":"The temporal graph network baseline with memory and message passing that CTWalks claims to outperform.","marker":"[1]"},{"why":"The temporal attention baseline with Fourier time encoding that CTWalks claims to outperform.","marker":"[2]"},{"why":"The DyRep baseline with temporal point process training that CTWalks claims to outperform.","marker":"[43]"},{"why":"The JODIE baseline with coupled recurrent networks that CTWalks claims to outperform.","marker":"[37]"},{"why":"The continuous-time dynamic network embedding baseline built on temporal random walks that CTWalks extends and compares against.","marker":"[44]"},{"why":"Neural ODEs supply the continuous-time integration machinery used in the CTWalks encoding step.","marker":"[21]"},{"why":"The Louvain modularity optimization algorithm supplies the community partition used to guide sampling.","marker":"[39]"}],"fun_headline_variants":["Community structure helps CTWalks beat six baselines","Parameter-free community temporal walks outmatch six baselines on five datasets","Community-aware walks: parameter-free, ODE-driven, top on five benchmarks","Community-guided temporal walks beat baselines with no tuning"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the community structure computed once from the training period stays meaningful for future edges, so that forbidding walks that cross community boundaries except through bridging nodes does not remove the very patterns needed to predict which nodes will connect later.","fun_headline_variants_meta":{"raw":{"variants":["Community structure helps CTWalks beat six baselines","Parameter-free community temporal walks outmatch six baselines on five datasets","Community-aware walks: parameter-free, ODE-driven, top on five benchmarks","Community-guided temporal walks beat baselines with no tuning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00103,"raw_usage":{"total_tokens":4304,"prompt_tokens":873,"completion_tokens":3431,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":489,"completion_tokens_details":{"reasoning_tokens":3360}},"tokens_in":489,"tokens_out":3431,"duration_ms":25269,"temperature":1.0,"reasoning_tokens":3360,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T17:46:56.029364+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare CTWalks with an unrestricted temporal-walk variant on a dataset whose training-time communities are weak or whose future edges mostly join nodes from different communities; if the unrestricted variant matches or exceeds CTWalks on AUC, the community-restriction claim is falsified.","supporting_citations":[{"cited_title":"Inductive representation learning in temporal networks via causal anonymous walks,","cited_arxiv_id":null,"evidence_quote":"The causal anonymous walk method CTWalks builds on and is compared against; supplies the anonymized-walk baseline it must beat."},{"cited_title":"Temporal graph networks for deep learning on dynamic graphs,","cited_arxiv_id":null,"evidence_quote":"The temporal graph network baseline with memory and message passing that CTWalks claims to outperform."},{"cited_title":"Inductive representation learning on temporal graphs,","cited_arxiv_id":null,"evidence_quote":"The temporal attention baseline with Fourier time encoding that CTWalks claims to outperform."},{"cited_title":"Dyrep: Learning representations over dynamic graphs,","cited_arxiv_id":null,"evidence_quote":"The DyRep baseline with temporal point process training that CTWalks claims to outperform."},{"cited_title":"Predicting dy- namic embedding trajectory in temporal interaction net- works,","cited_arxiv_id":null,"evidence_quote":"The JODIE baseline with coupled recurrent networks that CTWalks claims to outperform."},{"cited_title":"Continuous-time dynamic network embed- dings,","cited_arxiv_id":null,"evidence_quote":"The continuous-time dynamic network embedding baseline built on temporal random walks that CTWalks extends and compares against."},{"cited_title":"Neural ordinary differential equations,","cited_arxiv_id":null,"evidence_quote":"Neural ODEs supply the continuous-time integration machinery used in the CTWalks encoding step."},{"cited_title":"Fast unfolding of communities in large networks,","cited_arxiv_id":null,"evidence_quote":"The Louvain modularity optimization algorithm supplies the community partition used to guide sampling."}],"review_version":1}