{"id":"fac05efd-f6fb-40db-9be3-93e36d70aef0","arxiv_id":"2412.20936","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":9,"one_line_summary":"cpSI-R, a temporal influence model with reactivation and reinforcement, is claimed to be monotone and submodular, but the proof assumes the properties it claims to prove.","lead":"This paper introduces cpSI-R, a model of how influence spreads in temporal social networks where nodes can drop out, return, and become more persuasive after repeated contact. It claims the model keeps seed selection tractable and beats existing influence-maximization methods on large real and synthetic networks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1 is the load-bearing step: its pointwise proof assumes 'activations are never revoked', yet cpSI-R's tau-window and reactivation dynamics admit earlier activation that expires before later edges, so the (1-1/e) guarantee is unsupported.","rationale":"The reader's weakest assumption identifies exactly the load-bearing concern: Theorem 1's proof assumes pointwise monotonicity and diminishing returns, which is what time-limited tau windows and reactivation can destroy. I found additional supporting evidence: the proof is vacuous with respect to all model parameters, Algorithm 2's return value is a final-time probability rather than a cumulative activation count, and the paper's own Lemma 1 is a concrete template for the same harmful timing effect. The experimental sections cannot rescue the claim because the dynamic update equations are never written (Algorithm 2 line 7 references them without definition), eta is tuned on the same spread curves later reported, and no code is released. The theoretical gap alone justifies rejection, so I agree with the reader's REJECT verdict and would not adjust it.","tokens_in":27874,"tokens_out":3781,"duration_ms":38856,"concrete_test":"Implement cpSI-R exactly as specified in Section 5.1 (p_uv(t) = p0*(1-e^{-alpha*k})*beta*e^{-gamma*(t-t0)}, tau-limited infectious window, reactivation only after contact with an active node) with the Algorithm 2 final-time objective. Run Monte Carlo on the Figure 1 temporal graph with p=1 on the relevant edges and small tau. Compute sigma({V1}) and sigma({V1,V3}) over at least 10^4 realizations; if the latter is less than the former, Theorem 1's monotonicity is false for the stated model. Repeat with an ever-active count to separate objective choice from model dynamics.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is Theorem 1 (Section 5.1): sigma_cpSI-R is monotone and submodular. The proof fixes a realization omega and asserts 'activations are never revoked and additional seeds only increase influence.' That premise is inconsistent with cpSI-R itself: Section 5.1 states that if t^k_uv - delta_u > tau, 'node u becomes inactive for spreading the infection until reactivated.' The paper's own Lemma 1 (Section 4) exhibits non-monotonicity under active-inactive transitions: adding V3 activates V4 early, V4's window expires before later edges, and spread drops from 6 to 4. Theorem 1's proof never rules out this timing effect; it only restates the desired inequality. The proof also never uses p0, alpha, beta, gamma, tau, or the temporal function, so it would 'prove' monotonicity for any process with that verbal premise. The implemented objective in Algorithm 2 returns |S| + sum p(i,t_r), infection probabilities at the final timestamp, not a cumulative never-revoked count, so the quantity optimized is the one Lemma 1 shows can be non-monotone. Since the (1-1/e) approximation and the novelty claim 'first temporal diffusion model retaining these properties' both rest on Theorem 1, the central contribution is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces cpSI-R, a temporal diffusion model with persistence, reactivation, and reinforcement, and claims that its influence spread function is monotone and submodular, enabling a (1-1/e) greedy approximation for influence maximization. It also proposes an adaptive temporal snapshot sampling method and a lazy-forward seed selection algorithm, reporting experiments on several temporal network datasets. The central theoretical claim is Theorem 1 in Section 5.1, and the main algorithmic contribution is the combination of sampling with lazy forward influence maximization.","tokens_in":28202,"tokens_out":2562,"duration_ms":28185,"significance":"If the central theorem were established, the paper would offer a useful addition to temporal influence maximization by providing an optimization-friendly model with active-inactive transitions. The paper also makes a strong novelty claim: that cpSI-R is the first temporal diffusion model retaining monotonicity and submodularity with recovery/reactivation. However, the proof of Theorem 1 is not a derivation; it assumes the very pointwise inequalities that need to be shown, and the implemented objective in Algorithm 2 is not the expected spread defined in Definition 6. The experimental comparison is also presented without confidence intervals or reproducibility details. The strengths of the paper are its clear motivation and the concrete counterexample in Section 4, which usefully illustrates why standard monotonicity can fail under active-inactive transitions; unfortunately, that same example undermines the proof of Theorem 1 rather than supporting it.","major_comments":[{"comment":"The proof of Theorem 1 is circular and does not engage with the model's own dynamics. It fixes a realization omega and asserts that 'activations are never revoked and additional seeds only increase influence,' but this pointwise monotonicity is exactly what needs to be proved for cpSI-R, and it is false for the active-inactive transitions described earlier in the same section. Lemma 1 in Section 4 provides a concrete temporal counterexample where adding a seed node reduces spread from 6 to 4 because early activation causes a node's tau-window to expire before later edges. The proof never uses p0, alpha, beta, gamma, tau, or the temporal interaction function, so it would apply unchanged to any process satisfying the verbal premise, which indicates that the model-specific claim has not been established. Consequently, the (1-1/e) approximation guarantee and the novelty claim that cpSI-R is the first temporal model to retain these properties rest on an unsupported theorem.","section":"Section 5.1, Theorem 1"},{"comment":"Algorithm 2 does not compute the expected spread defined in Definition 6. The function returns |S| + sum_{i in N(t)\\S(t)} p(i, t_r), which is a deterministic sum of infection probabilities at the final timestamp, not the expected number of nodes that become active during the diffusion process. The model description in Section 5.1 explicitly allows nodes to become inactive for spreading after their tau-window expires, so the final-time infection probability can be non-monotone in the seed set, as Lemma 1 demonstrates. Thus, even if Theorem 1 were correct for a cumulative spread function, the quantity actually optimized by the proposed algorithm is not protected by that theorem.","section":"Section 5.2, Algorithm 2"},{"comment":"The formal update equations of the cpSI-R model are never given. Section 5.2 refers to 'dynamic update equations' and Algorithm 2 line 7 instructs the reader to compute p(i, t_{j+1}) using those equations, but no recurrence, no state-transition rule, and no reactivation rule are specified. Without these equations, the model is not precisely defined, the proof of monotonicity/submodularity cannot be checked, and the experimental implementation is not reproducible. This is a load-bearing gap because the entire optimization framework depends on the exact stochastic process being optimized.","section":"Section 5.1 and Algorithm 2"},{"comment":"The experimental claims are difficult to assess because no confidence intervals, standard deviations, or repeated-run statistics are reported for the infection spread comparisons in Figures 5, 7, and 9. Additionally, the text states that 'All methods use the cpSI-R model for fair comparison,' which means Figure 9 compares seed selection algorithms under a single model, not the diffusion model itself; the model-vs-SIR comparisons in Figure 5 are not directly comparable to the baseline IM methods. The paper would need a more detailed experimental protocol to support the strong claim of consistent outperformance across all datasets.","section":"Section 6.3"}],"minor_comments":[{"comment":"The paper contains two different abstracts: the abstract at the top of the submitted text describes a different emphasis (persistent and reactive behaviors) from the abstract in the introduction, which mentions 'persistent and reactive behaviors' but also repeats the same claims. The duplication and inconsistency should be resolved.","section":"Abstract and Introduction"},{"comment":"Definition 6 defines expected spread as E_M[|sigma(S0, G)|], but sigma is used both as the random set and as the spread function; this overloading makes the definition ambiguous, especially given the later use of sigma_omega(S) in the proof of Theorem 1.","section":"Section 3, Definition 6"},{"comment":"The complexity statement in the toy example, 'selecting fewer snapshots based on eta reduces this to O(eta T)', appears to have the dependence on eta backwards: a higher threshold eta selects fewer snapshots, not more, so the claimed O(eta T) scaling is not justified.","section":"Section 5.2.2, toy example"},{"comment":"Algorithm 1 calls SamplingAlgorithm to set tset, but the influence calculations in CalcInfluence also call SamplingAlgorithm, so the interaction between these two calls and the role of tset in the final computation are unclear.","section":"Section 5.2, Algorithm 1"},{"comment":"The Malawi dataset row in Table 2 states 'Node and edge counts not specified' despite the text giving 142 nodes and 9,436 edges; the table and text should be reconciled.","section":"Section 6, Datasets"},{"comment":"No code or data release is mentioned, and the parameter settings for p0, alpha, beta, gamma, and tau are not reported in the experiments, which makes it impossible to reproduce the reported spread values.","section":"General"}],"recommendation":"reject","confidential_remarks":"The central theoretical result is not derived, and the implemented algorithm optimizes a different quantity than the one for which the theorem is stated. These are load-bearing issues that cannot be fixed with local edits. The paper may be salvageable if the authors redefine the model with explicit update equations, prove monotonicity/submodularity for the actual implemented objective or alternatively implement the cumulative spread objective, and provide reproducible experiments, but that would be a substantially different manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nKnow this about the paper: the cpSI-R model is a reasonable assembly of mechanisms—persistent influence, time-limited reactivation, and reinforcement—and the Jaccard/Kulczynski snapshot sampling heuristic is sensible. But the headline claim, that the spread function is monotone and submodular, is not established. The proof of Theorem 1 (Section 5.1) fixes a realization and asserts “activations are never revoked and additional seeds only increase influence.” That is the conclusion restated, not a derivation. The model itself contains a tau window after which a node becomes inactive for spreading, and the authors’ own Lemma 1 shows how this can break monotonicity: adding a seed activates a node early, the node’s window expires before later temporal edges, and spread falls from 6 to 4. The cpSI-R model has exactly that time-limited spreading behavior, and the proof never rules out the timing effect. Reactivation does not obviously help: if no active neighbor contacts the expired node in time, the downstream cascade is still lost. So the (1-1/e) greedy guarantee and the “first temporal model to retain these properties” claim rest on an unsupported, likely false, premise.\n\nWhat is genuinely new is the particular combination of persistence, reactivation, and reinforcement. The related-work discussion is competent and positioned correctly, including the group’s own prior TBCELF paper. The experiments are substantial—six datasets, including multi-million-edge networks—and the sampling idea is worth keeping. But the paper never writes the model’s formal update equations. Algorithm 2 returns final-timestamp infection probabilities, not an ever-active count, so the quantity being optimized is not the one for which the theorem is claimed. No code or data are released, and eta is tuned on the same spread curves that are then reported, so the experimental conclusions cannot be audited.\n\nThe citation pattern is fine; self-citation of TBCELF is not a concern. The math is the problem. The internal tension between Lemma 1 and Theorem 1 is never resolved, and the theorem proof is circular in a load-bearing way. I would send this to peer review rather than desk-reject, because the flaw is instructive and the sampling heuristic may be salvageable, but the likely outcome is rejection unless the model or the objective is redefined. I would not cite it in its current form. It could serve as a cautionary reading-group example of a submodularity proof that assumes what it needs to show.\n\nRecommendation: referees should be asked specifically whether sigma under cpSI-R is monotone on the Figure 1 counterexample; that question alone settles the paper.","headline":"The main theoretical claim is a restatement of the conclusion, not a proof, and the model's own tau-window dynamics allow spread to drop when seeds are added; the model idea and sampling heuristic are reasonable, but the paper's core guarantee is unsupported.","tokens_in":28719,"tokens_out":5999,"would_cite":false,"duration_ms":58014,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that its temporal diffusion model cpSI-R, which allows nodes to deactivate, reactivate, and be reinforced by repeated contact, has a monotone and submodular spread function, so greedy seed selection keeps its…","keywords":["influence maximization","temporal networks","diffusion model","monotone submodularity","reactivation and reinforcement","temporal snapshot sampling","greedy approximation","social influence"],"falsifier":"On a three-node temporal path with $a\\to v$ at $t=2$, $v\\to w$ at $t=3$, $\\tau=1$, and infection probability $1$, compare seed sets $\\{a\\}$ and $\\{a,u\\}$ where an additional edge $u\\to v$ exists at $t=1$. With $\\{a\\}$, $v$ activates at $t=2$ and still has one time unit to infect $w$ at $t=3$; with $\\{a,u\\}$, $u$ activates $v$ at $t=1$, $v$'s spreading window expires before $t=3$, and $w$ is never infected. This gives $\\sigma_{\\mathrm{cpSI\\text{-}R}}(\\{a,u\\}) < \\sigma_{\\mathrm{cpSI\\text{-}R}}(\\{a\\})$ under a final-activation count, directly violating the claimed monotonicity.","tokens_in":27633,"feed_emoji":"📈","tokens_out":6254,"duration_ms":63853,"temperature":0.7,"pith_summary":"This paper tries to show that influence maximization on temporal networks does not have to sacrifice optimization guarantees to model realistic behavioral cycles. It introduces cpSI-R, a susceptible-infected model in which nodes spread influence for a limited window, can go inactive, and can be reactivated by contact with active nodes, with each repeated exposure raising infection probability. The paper's main theoretical claim is that expected spread under cpSI-R stays monotone and submodular, so greedy seed selection keeps its approximation bound. If true, this matters because prior temporal models with active-inactive transitions are argued to break those properties, leaving seed selection without quality guarantees. The paper also reports that its sampling-and-selection pipeline beats several temporal baselines in spread and runtime on datasets ranging from school contacts to large online networks.","feed_headline":"With reactivation, temporal seed spread still keeps greedy guarantee","feed_subtitle":"cpSI-R lets disengaged nodes rejoin and strengthens repeated contacts, so seed choice stays near-optimal on evolving networks.","key_machinery":"The central object is the cpSI-R model: each infected node $u$ can try to infect a susceptible neighbor $v$ at each temporal contact $t^k_{uv}$ with probability $p_{uv}(t^k_{uv}) = p_0(1-e^{-\\alpha k})f(t^k_{uv})$, where the temporal factor is $f(t^k_{uv}) = \\beta e^{-\\gamma(t^k_{uv}-t)}$. A node can spread influence only within a time window $\\tau$ after its latest infection attempt, becomes inactive for spreading after that window, and can be reactivated by an active node, while repeated exposures increase the infection probability through the reinforcement factor $\\alpha$. The proof of monotonicity and submodularity fixes each stochastic realization $\\omega$ and asserts that a larger seed set activates at least as many nodes in every realization, then takes expectations; the optimization pipeline is carried by a Jaccard-Kulczynski similarity score that selects structurally significant snapshots and a lazy forward replacement routine that exploits diminishing returns.","core_discovery":"The central claim is Theorem 1: for any instance of cpSI-R on a temporal graph with fixed probabilities and a temporal interaction function, the expected spread function $\\sigma_{\\mathrm{cpSI\\text{-}R}}$ is monotone and submodular. The paper argues this makes cpSI-R the first temporal diffusion model with reactivation that retains these properties, so the standard greedy algorithm for influence maximization still applies with the classic $(1-1/e)$ approximation guarantee. The same section contributes a structure-aware snapshot sampling method and a lazy forward seed-selection routine that use submodularity to avoid redundant computations.","pith_inferences":["The paper does not test this, but if the timing objection to monotonicity is real, replacing final-snapshot counts with cumulative ever-active exposure would make the spread function robust to early activation and would change seed rankings under bursty contact patterns.","A natural extension is online seeding: the Jaccard-Kulczynski change-point scores could trigger re-seeding whenever a structural shift is detected, instead of committing to one fixed seed set over the whole horizon.","The $\\tau$-window mechanism implies that seeds should be scored not by static degree but by whether their contacts arrive before the downstream node's window expires; comparing cpSI-R seed sets with temporal-centrality rankings on contact datasets would isolate this effect.","If monotonicity does fail under $\\tau$ windows, restricting cpSI-R to a persistent-active state in which any contact refreshes the window would restore submodularity without sacrificing reinforcement."],"forward_implications":["Greedy seed selection under cpSI-R inherits the $(1-1/e)$ approximation ratio, so the model can be optimized with a provable quality bound despite node deactivation and reactivation.","The snapshot sampler cuts the runtime from $O(T|E| + k\\log|V|\\,T)$ to $O(r|E| + k\\log|V|\\,r)$ with $r \\ll T$, because only structurally changed timestamps are simulated.","Since reactivation is explicit, seed sets chosen under cpSI-R can sustain spread after nodes disengage, matching repeated-exposure campaigns better than one-shot cascade models.","On the six datasets reported, the cpSI-R pipeline achieves higher infection spread and lower runtime than the dynamic degree, reverse-reachable, temporal SIR, entropy, and forward-influence baselines, with the largest margins on the biggest networks."],"supporting_citations":[{"why":"Defines influence maximization and the monotonicity-submodularity framework that guarantees greedy approximation, the setting cpSI-R extends.","marker":"[1]"},{"why":"Shows how evolving-network diffusion models with recovery or reactivation can lose monotonicity and submodularity, the barrier cpSI-R claims to overcome.","marker":"[44]"},{"why":"Provides lazy forward evaluation that the seed-selection algorithm adapts to avoid recomputing marginal gains.","marker":"[54]"},{"why":"The forward influence algorithm that serves as the direct baseline and algorithmic precursor for LazyForwardInfluence.","marker":"[64]"},{"why":"Temporal SIR-based influence maximization baseline whose estimated spread is compared against cpSI-R in the experiments.","marker":"[65]"},{"why":"Dynamic Degree Discount and Dynamic CI baselines that extend static heuristics to temporal networks and are compared in the experiments.","marker":"[61]"}],"fun_headline_variants":["Reactivation keeps temporal influence greedy-optimal","cpSI-R: reactivation with greedy guarantee in temporal nets","Reactivation in temporal networks: greedy still near-best","Modeling reactivation for near-optimal temporal seed choice","Temporal influence with reactivation still near-optimal"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof of Theorem 1 assumes that once a node is activated it stays counted as influenced forever, so adding a seed can never reduce anyone's final activation count, but cpSI-R's $\\tau$-window lets an earlier activation expire before later temporal contacts, so the assumption may fail for the implemented objective.","fun_headline_variants_meta":{"raw":{"variants":["Reactivation keeps temporal influence greedy-optimal","cpSI-R: reactivation with greedy guarantee in temporal nets","Reactivation in temporal networks: greedy still near-best","Modeling reactivation for near-optimal temporal seed choice","Temporal influence with reactivation still near-optimal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000541,"raw_usage":{"total_tokens":2587,"prompt_tokens":935,"completion_tokens":1652,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":551,"completion_tokens_details":{"reasoning_tokens":1575}},"tokens_in":551,"tokens_out":1652,"duration_ms":13917,"temperature":1.0,"reasoning_tokens":1575,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:07:33.213049+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a three-node temporal path with $a\\to v$ at $t=2$, $v\\to w$ at $t=3$, $\\tau=1$, and infection probability $1$, compare seed sets $\\{a\\}$ and $\\{a,u\\}$ where an additional edge $u\\to v$ exists at $t=1$. With $\\{a\\}$, $v$ activates at $t=2$ and still has one time unit to infect $w$ at $t=3$; with $\\{a,u\\}$, $u$ activates $v$ at $t=1$, $v$'s spreading window expires before $t=3$, and $w$ is never infected. This gives $\\sigma_{\\mathrm{cpSI\\text{-}R}}(\\{a,u\\}) < \\sigma_{\\mathrm{cpSI\\text{-}R}}(\\{a\\})$ under a final-activation count, directly violating the claimed monotonicity.","supporting_citations":[{"cited_title":"Maximizing the spread of influence through a social network,","cited_arxiv_id":null,"evidence_quote":"Defines influence maximization and the monotonicity-submodularity framework that guarantees greedy approximation, the setting cpSI-R extends."},{"cited_title":"Diffusion maximization in evolving social networks,","cited_arxiv_id":null,"evidence_quote":"Shows how evolving-network diffusion models with recovery or reactivation can lose monotonicity and submodularity, the barrier cpSI-R claims to overcome."},{"cited_title":"Cost-effective outbreak detection in networks,","cited_arxiv_id":null,"evidence_quote":"Provides lazy forward evaluation that the seed-selection algorithm adapts to avoid recomputing marginal gains."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The forward influence algorithm that serves as the direct baseline and algorithmic precursor for LazyForwardInfluence."},{"cited_title":"Influence maximization on temporal networks,","cited_arxiv_id":null,"evidence_quote":"Temporal SIR-based influence maximization baseline whose estimated spread is compared against cpSI-R in the experiments."},{"cited_title":"Extended methods for influence maximization in dynamic networks,","cited_arxiv_id":null,"evidence_quote":"Dynamic Degree Discount and Dynamic CI baselines that extend static heuristics to temporal networks and are compared in the experiments."}],"review_version":1}