{"id":"3467b5bf-4b09-4bca-9627-0394648ed5a4","arxiv_id":"2608.07158","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"TRicci removes about 80% of edges in temporal graphs while preserving 97.7% of full-graph ROC-AUC and cutting end-to-end runtime by 55.94% on graph-level prediction tasks.","lead":"This paper introduces TRicci, a temporal version of Forman-Ricci curvature that scores every timestamped interaction in a network and keeps only the highest-scoring 20% of edges for downstream prediction. It matters because large dynamic graphs are expensive to train on, and this offers a fast, curvature-based way to shrink them without much loss in accuracy.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing random-edge-deletion control: because all three tasks are defined by next-snapshot aggregate counts, random 20% edge retention may preserve full-graph signal without curvature, so TRicci's 97.7% figure does not yet establish that temporal curvature is the mechanism.","rationale":"I read the paper in good faith: the contribution is an edge-ranking functional and an empirical claim that high temporal curvature identifies task-relevant edges. The existing experiments are extensive and the results are consistent, but the central causal claim requires showing that curvature ordering, not merely retaining a 20% random sample, is what preserves predictive signal. The paper does not include this control. This is a more load-bearing gap than the reader's weakest assumption about validation-selected hyperparameters: even if tau=1, rho=0.8, and the high-curvature policy transferred perfectly to new tasks, the claim about curvature as a principled basis would still fail if random deletion performed equally well. The reader did flag the missing random baseline in the rationale, but the reader's stated weakest assumption was hyperparameter transfer, so my emphasis differs. I keep the verdict at CONDITIONAL in the sense that the paper can be strengthened, but the verdict itself is unchanged; the condition should now explicitly require the random-deletion control. The Section 3.2 / Proposition 3.2 formula mismatch is real, but it is a reproducibility/correctness defect that can be repaired without changing the experimental protocol, so it is not the single most load-bearing concern.","tokens_in":16112,"tokens_out":10184,"duration_ms":101614,"concrete_test":"Run the same GraphPulse pipeline on all 12 datasets and three tasks with the same Δ=7-day snapshots, rho=0.8, chronological 70/15/15 split, and identical feature extraction, but replace the TRicci ranking with uniform random edge deletion per snapshot, repeated over at least 5 seeds. Report the mean and standard deviation of RAUC. If the random baseline reaches RAUC ≥0.95 (or within about 0.02 of TRicci's 0.977), the curvature-specific mechanism is not supported and the central claim must be weakened; if random RAUC is ≤0.90, the curvature ranking adds genuine signal. Also run a degree-preserving random deletion as a secondary control to separate sampling effects from hub-retention effects.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline result (TRicci preserves 97.7±2.2% of full-graph ROC-AUC at rho=0.8) is measured against three topology-based sparsifiers, but never against uniform random edge deletion. That control is the minimal test of the central claim that high temporal curvature is a reliable edge-importance signal. The three tasks in Section 4.1 are aggregate next-snapshot statistics: whether |E_{t+1}|>|E_t|, whether |V_active_{t+1}|>|V_active_t|, and whether the top-k degree-node set turns over. Because features are extracted from the current sparse snapshot, a sparsifier that keeps 20% of edges roughly uniformly will estimate current-snapshot aggregate counts with small relative error on large snapshots and may inherit most of the full-graph predictive signal. If so, the 0.977 preservation ratio could reflect sampling fidelity rather than curvature. The comparison against TEDDY, MoG, and SEM does not settle this; none is a random control, and degree-based pruning can remove hubs that a random sample would retain. The absence of error bars in Table 2 also makes it impossible to tell whether the gap between 0.977 and the best baseline (0.894) is larger than run-to-run noise. This is a missing experimental control, not a claim of misconduct, and it is directly load-bearing: without it, the paper's central conclusion about curvature is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes TRicci, an edge-level sparsification score for directed weighted temporal graphs that combines log-smoothed endpoint activity, a temporal decay kernel, and outgoing-neighborhood competition in the style of Forman-Ricci curvature. Edges are scored independently within each snapshot, ranked, and a task-chosen curvature band (here, the high-curvature band) is retained at a deletion ratio rho; the sparse snapshots are then fed into the GraphPulse-style LSTM/GRU prediction pipeline. Experiments on nine blockchain transaction networks and three TGBL datasets across three graph-level prediction tasks report that retaining about 20% of edges preserves 97.7 +/- 2.2% of full-graph ROC-AUC on average and reduces end-to-end runtime by 55.94%.","tokens_in":16441,"tokens_out":7743,"duration_ms":70477,"significance":"If the reported preservation figures are robust, TRicci would be a useful model-independent preprocessing tool for snapshot-based graph-level prediction, with the practical virtues of being deterministic, per-snapshot local, and accompanied by released code. The paper is also honest that the score is an adaptation rather than a geometric theorem. However, the significance of the central claim---that high temporal curvature is the mechanism behind the preserved signal---is currently limited by the absence of a random-deletion control, single-run results for key comparisons, and validation-based selection of the policy parameters. These issues are fixable and do not, in my view, invalidate the methodology.","major_comments":[{"comment":"","section":"Section 3.2 and Proposition 3.2"},{"comment":"","section":"Section 4.1, Table 2"},{"comment":"","section":"Tables 2, 3, and 4"},{"comment":"","section":"Section 4.2.1, Figure 1 caption, Figure 5, Figure 6"}],"minor_comments":[{"comment":"","section":"Figure 2 caption and Appendix A, Table 5"},{"comment":"","section":"Section 4.1"},{"comment":"","section":"Section 4.2.1, Table 3"},{"comment":"","section":"Section 3.2"},{"comment":"","section":"Section 3.2"},{"comment":"","section":"Table 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a machine learning / data mining venue, and the code link is a strength. My main concern is experimental control rather than novelty: the missing random-deletion baseline and the lack of seed-level error bars are load-bearing for the central claim about curvature. The formula/proof mismatch in Section 3.2 must also be resolved. These are fixable, so I do not recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a clean, incremental extension of Forman–Ricci edge scoring to directed weighted temporal graphs, and the empirical study is broad and useful. But the headline result—97.7% ROC-AUC preservation at 80% sparsification—doesn't yet prove that temporal curvature is doing the work, because there is no random-edge-deletion baseline and the three prediction tasks are aggregate count statistics that random sampling may preserve almost as well.\n\nWhat's new: the TRicci score combines log-smoothed endpoint activity, directed outgoing neighborhoods, and an exponential time-decay penalty. That specific temporal extension isn't in the cited static Forman-Ricci, MoG, TEDDY, SEM, or dyGRASS work. The evaluation is also broad: 12 datasets, three graph-level tasks, and a comparison to three sparsifiers under the same retention budget. The runtime saving is real, and the sensitivity analysis for tau and rho is a nice touch. Code and artifacts are provided.\n\nThe soft spots are real but fixable. The missing random baseline is the most important. The tasks predict next-snapshot edge-count growth, active-node growth, and top-k degree turnover. A random 20% edge sample estimates total edge count and active-node coverage with small relative error on large snapshots, and retains high-degree nodes with high probability. So 97.7% preservation might reflect sampling fidelity rather than curvature. Comparing to TEDDY, MoG, and SEM doesn't settle it—none is a random control. Second, the penalty term in Section 3.2 uses sqrt(w_e w_e') in the sum, but Proposition 3.2's proof and the tau->infty limit use sqrt(w_e / w_e'). That's a discrepancy that affects the actual score if implemented as written. Third, Tables 3 and 4 show single runs with no per-dataset error bars; only cross-dataset std is reported. Fourth, tau=1, rho=0.8, and the high-curvature policy are chosen from the validation/sensitivity analysis, and the Figure 1 caption explicitly says a different curvature range might be better for other tasks—so the method's generality is partly self-selected.\n\nWho this is for: practitioners who need a cheap pre-processing step for dense temporal graphs, and researchers working on curvature-based graph measures. The paper deserves a serious referee; the missing random baseline and the formula inconsistency should be addressed, and the claims should be softened accordingly.\n\nMy recommendation: engage with it, but require the random-deletion control and consistency between definition and proof before it's citable as evidence for curvature-based edge importance.","headline":"A plausible temporal curvature sparsifier with a broad evaluation, but the missing random-deletion baseline and an internal formula inconsistency keep the central claim from being fully established.","tokens_in":17005,"tokens_out":3148,"would_cite":false,"duration_ms":29008,"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 temporal curvature score ranks which edges in a time-stamped network matter, allowing about 80% of edges to be deleted while retaining 97.7% of full-graph ROC-AUC on average.","keywords":["Temporal graph learning","Forman-Ricci curvature","Edge sparsification","Dynamic graph prediction","Snapshot-based temporal graphs","Transaction networks","Graph-level prediction"],"falsifier":"Run TRicci on a temporal graph whose prediction labels are engineered to depend on rare, low-competition, temporally isolated edges: if the high-curvature retention policy must delete those edges by construction, the sparsified graph's ROC-AUC should fall well below the full graph, and low-curvature retention should instead match it.","tokens_in":15868,"feed_emoji":"📉","tokens_out":7811,"duration_ms":67027,"temperature":0.7,"pith_summary":"The paper tries to establish that an edge's local temporal geometry, measured by a temporal extension of Forman–Ricci curvature, is a reliable signal of which interactions matter for graph-level prediction on dynamic networks. It introduces TRicci, a score that combines how distinctive an edge is relative to its endpoints' activity with a temporally weighted penalty from nearby competing edges, computed inside each snapshot. If the claim holds, large and dense temporal graphs can be aggressively sparsified before any downstream model is trained, retaining roughly a fifth of the edges while keeping almost all predictive accuracy and cutting end-to-end runtime.","feed_headline":"Curvature keeps 97.7% of graph power after 80% of edges go","feed_subtitle":"TRicci scores edges by support and temporal competition, cutting end-to-end runtime by 55.94% with almost no AUC loss.","key_machinery":"The load-bearing object is the Temporal Forman–Ricci curvature score $TRicci(e)$, a support-minus-competition functional over snapshot-level directed weighted temporal graphs. For an edge $e=(u,v,w_e,t_e)$, the support term is $S_e=w_e(1/s(u)+1/s(v))$ with $s(x)=\\log(1+\\sum w_{e'})$ the log-smoothed endpoint activity, and the competition term averages penalties from outgoing edges at $u$ and $v$, each weighted by a temporal kernel $K(e,e',\\tau)=\\exp(-|t_e-t_{e'}|/\\tau)$. The kernel makes temporally nearby interactions compete more strongly, so the score ranks edges by how isolated they are in both structure and time; the framework then selects a curvature band through validation and deletes the rest per snapshot.","core_discovery":"The paper's central claim is that high temporal curvature marks task-relevant edges: across nine blockchain transaction networks and three TGBL benchmarks, retaining only the highest-curvature approximately 20% of edges preserves 97.7±2.2% of the full-graph ROC-AUC on average, outperforming three sparsification baselines under the same 80% deletion budget, and reduces end-to-end training plus inference time by 55.94% on average. The curvature score is $TRicci(e)=S_e - D_e$, where $S_e$ weights the edge by log-smoothed inverse endpoint activity and $D_e$ averages temporally decayed penalties from outgoing neighboring edges around both endpoints. The paper frames the result as a Pareto-style concentration: most predictive temporal-structural information lives in the high-curvature slice of the edge set.","pith_inferences":["The paper leaves implicit that the same curvature ranking could be used as a deterministic edge-pruning schedule for continual or streaming learning, since each snapshot is scored independently and the retained set is reusable.","A testable extension is to replace the validation-chosen high-curvature bin with a learned threshold per task, which could close the remaining 2-3% AUC gap while keeping the runtime benefit.","The sensitivity trend suggests that on graphs with very different time scales, the decay parameter should be set relative to snapshot length or interaction frequency; treating one day as universal would likely underperform on hourly or yearly interaction streams.","If labels are driven by rare, temporally isolated events, the high-curvature policy is the wrong end of the ranking; a fair comparison on such tasks would need the band-selection variant the paper describes but does not evaluate."],"forward_implications":["A practitioner can delete roughly 80% of temporal edges before feature extraction and prediction with only about 2% average ROC-AUC loss, so dense dynamic graphs can be processed in a fraction of the time.","High-curvature retention is the effective default policy across activity-growth, participation-expansion, and influential-node-turnover tasks; low or intermediate curvature bins consistently lose more predictive signal.","Runtime savings are end-to-end: they include sparsification, feature processing, and prediction, and they hold on every dataset tested, averaging 55.94%.","Because selection is per snapshot, the sparse graph keeps coverage over the whole observation period instead of concentrating edges in dense windows.","The framework is model-independent: it ranks edges before training, so the same sparse representation can feed any downstream graph-level predictor."],"supporting_citations":[{"why":"Supplies the classical Forman-Ricci curvature definition whose support-minus-penalty structure TRicci adapts.","marker":"[6]"},{"why":"Provides the graph-based Forman curvature formulation that the temporal score extends.","marker":"[24]"},{"why":"Defines the GraphPulse temporal graph property prediction pipeline and supplies the nine blockchain datasets used in evaluation.","marker":"[22]"},{"why":"Provides the TGBL benchmark datasets and the discrete/continuous temporal graph framing used in the study.","marker":"[11]"},{"why":"Baseline TEDDY, a degree-based one-shot sparsifier, compared under the same edge-retention budget.","marker":"[20]"},{"why":"Baseline MoG, a mixture-of-experts graph sparsifier, compared under the same edge-retention budget.","marker":"[30]"},{"why":"Baseline SEM, a Ricci-curvature-based sparsifier for static graphs, compared under the same edge-retention budget.","marker":"[31]"},{"why":"Establishes the general graph-sparsification principle that small edge subsets can preserve structural properties, which motivates the retention setup.","marker":"[23]"}],"fun_headline_variants":["Temporal curvature keeps 97.7% ROC-AUC after trimming 80% edges","Prune 80% edges, keep 97.7% ROC-AUC, run 56% faster","Curvature-based sparsification: cut 80% edges, lose only 2.3% AUC","80% edge prune, 56% faster inference, 97.7% AUC preserved"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework assumes that the choices made on validation data—a one-day decay scale, an 80% deletion rate, and keeping only the highest-curvature edges—work on the test data and on other prediction tasks, even though the paper notes that other tasks may need a different curvature range.","fun_headline_variants_meta":{"raw":{"variants":["Temporal curvature keeps 97.7% ROC-AUC after trimming 80% edges","Prune 80% edges, keep 97.7% ROC-AUC, run 56% faster","Curvature-based sparsification: cut 80% edges, lose only 2.3% AUC","80% edge prune, 56% faster inference, 97.7% AUC preserved"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.002348,"raw_usage":{"total_tokens":9033,"prompt_tokens":919,"completion_tokens":8114,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":535,"completion_tokens_details":{"reasoning_tokens":8011}},"tokens_in":535,"tokens_out":8114,"duration_ms":53155,"temperature":1.0,"reasoning_tokens":8011,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:48:53.326037+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run TRicci on a temporal graph whose prediction labels are engineered to depend on rare, low-competition, temporally isolated edges: if the high-curvature retention policy must delete those edges by construction, the sparsified graph's ROC-AUC should fall well below the full graph, and low-curvature retention should instead match it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the classical Forman-Ricci curvature definition whose support-minus-penalty structure TRicci adapts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the graph-based Forman curvature formulation that the temporal score extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the GraphPulse temporal graph property prediction pipeline and supplies the nine blockchain datasets used in evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the TGBL benchmark datasets and the discrete/continuous temporal graph framing used in the study."},{"cited_title":"TEDDY: Trimming Edges with Degree-based Discrimination strategY","cited_arxiv_id":"2402.01261","evidence_quote":"Baseline TEDDY, a degree-based one-shot sparsifier, compared under the same edge-retention budget."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Baseline MoG, a mixture-of-experts graph sparsifier, compared under the same edge-retention budget."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Baseline SEM, a Ricci-curvature-based sparsifier for static graphs, compared under the same edge-retention budget."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the general graph-sparsification principle that small edge subsets can preserve structural properties, which motivates the retention setup."}],"review_version":1}