{"id":"84f745c2-3df4-4df7-8580-5dfe555e179b","arxiv_id":"2501.00779","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"REM combines an autoencoder, a mixture-of-experts spread predictor, and latent-space gradient search for multiplex influence maximization, reporting gains over six baselines.","lead":"This paper proposes REM, a machine learning system that picks influential seed users in multiplex social networks by embedding candidate seed sets in a continuous space, estimating their spread with a mixture of graph neural networks, and searching that space with gradient steps. The authors report higher influence spread and faster inference than six baselines on five real-world networks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Tables 1 and 2 internally contradict the abstract: on Cora-ML and Celegans at small budgets, ISF, KSN, and MIM-Reasoner outspread REM; 'consistently outperforms' is not supported.","rationale":"The reader's verdict is REJECT, and my analysis supports that verdict, so I recommend UNCHANGED. My load-bearing concern differs from the reader's stated weakest assumption: the reader focuses on PMoE surrogate fidelity as the key vulnerability, while I see the paper's own reported tables as the more direct and decisive problem. The empirical claim of consistent superiority is the abstract's central assertion, and Tables 1 and 2 contain multiple settings where traditional baselines (ISF, KSN) and the learning baseline MIM-Reasoner achieve higher influence spread than REM. Because these are internal results, not external objections, the discrepancy is immediately verifiable from the manuscript itself. If the numbers are correct, the headline claim is false; if they are typos or artifacts, the empirical section is unreliable. Either way, the conclusion that REM 'surpasses state-of-the-art methods' is unsupported. The theoretical issues (Lemma 1 and Theorem 3) are also serious and would need to be fixed in any revision, but they are secondary here: even a perfect surrogate would not rescue a paper whose own evidence contradicts its main claim. No significant objection is raised beyond this; the paper's core idea could be salvageable with corrected experiments, error bars, and clarified claims limited to regimes where the evidence is favorable.","tokens_in":21614,"tokens_out":6039,"duration_ms":55327,"concrete_test":"Reproduce the Cora-ML and Celegans rows of Tables 1 and 2 using the public REM repository and the reported settings (weighted-cascade IC with p_uv = 1/d_in(v), LT threshold 0.5, 100 Monte Carlo simulations, budget 1%, 5%, 10%, 20%). Run REM, ISF, KSN, and MIM-Reasoner with their stated hyperparameters. If the reproduced numbers match the paper, then the 'consistently outperforms' claim is false as printed; if they do not match, the empirical section is unreliable. Either outcome invalidates the headline claim as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim is that REM surpasses state-of-the-art methods in influence spread. The paper's own evidence for this claim, Tables 1 and 2, directly contradict it. Under IC (Table 1), REM is below ISF, KSN, and MIM-Reasoner at 1%, 5%, and 10% budgets on Cora-ML (e.g., 347.34 vs. 398.34 for ISF at 1%; 765.48 vs. 778.62 at 5%; 965.04 vs. 979.87 at 10%), and below ISF at 1% and 5% on Celegans (1445.16 vs. 1465.86; 2278.07 vs. 2298.01). Under LT (Table 2), REM is below ISF, KSN, and MIM-Reasoner at all four budgets on Cora-ML (e.g., 1281 vs. 1392 at 10%; 2141 vs. 2145 at 20%) and below ISF at 1% on Celegans (1514 vs. 1530). These are not marginal differences on a single setting; they appear systematically on the smaller datasets and low-budget regimes. The abstract claims consistent superiority, yet the reported numbers show the opposite in these cases. This is an internal inconsistency, not a disagreement with outside consensus, so it does not require external experiments to establish. Either the table values are accurate and the claim is false as written, or the tables are erroneous, in which case the empirical reporting cannot be trusted. The theoretical weaknesses identified by the reader (circular proof of Theorem 3, invalid monotonicity argument in Lemma 1) compound the problem, but the self-contradictory empirical evidence alone is decisive for the paper's primary claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes REM, a learning-based framework for multiplex influence maximization (MIM). REM uses a VAE called Seed2Vec to embed seed sets into a continuous latent space, a Propagation Mixture of Experts (PMoE) composed of GNN experts to estimate influence spread, and an exploration objective (Eq. 11) that jointly maximizes latent entropy and PMoE-predicted spread. The generated samples are stored in a priority replay memory, and the top-k samples according to PMoE are combined with the original data to retrain the models. The paper claims that REM surpasses state-of-the-art methods in influence spread, scalability, and inference time, and it reports experiments on five multiplex networks under IC and LT diffusion models. The framework and the experimental setup are clearly described, but the central claims are not supported: the reported tables contradict the claimed consistent superiority, and the main theoretical guarantee (Theorem 3) rests on an invalid monotonicity lemma and a circular proof.","tokens_in":22004,"tokens_out":5965,"duration_ms":53438,"significance":"Multiplex influence maximization is an important problem, and the paper addresses it with a plausible architecture that combines latent-space optimization, a mixture-of-experts spread estimator, and experience replay. The experimental section is extensive in scope (five datasets, two diffusion models, seven baselines, and two ablations), and the authors state that code and datasets are available on GitHub. If the framework were correct and the claims properly qualified, it could be a useful contribution to the learning-based IM literature. However, the significance is substantially reduced because the paper's own tables contradict the abstract's claim of consistent superiority, and the theoretical justification for optimizing in latent space is not established. The self-referential use of PMoE as both the optimization objective and the replay-quality selector further raises correctness concerns that the paper does not resolve.","major_comments":[{"comment":"The abstract and Section 'Quantitative Analysis' state that REM consistently outperforms other methods, but Tables 1 and 2 contain multiple cells where REM is strictly worse than baselines. In Table 1 (IC), ISF outperforms REM on Cora-ML at 1%, 5%, and 10% budgets (398.34 vs. 347.34; 778.62 vs. 765.48; 979.87 vs. 965.04) and on Celegans at 1% and 5% (1465.86 vs. 1445.16; 2298.01 vs. 2278.07), while MIM-Reasoner beats REM on Cora-ML at 1% (398.22 vs. 347.34). In Table 2 (LT), ISF, KSN, and MIM-Reasoner all beat REM on Cora-ML at every budget (e.g., 381 vs. 376 at 1% and 2145 vs. 2141 at 20%), and ISF beats REM on Celegans at 1% (1530 vs. 1514). These are not isolated or marginal differences; they appear systematically on smaller datasets and low-budget regimes. This is an internal inconsistency between the paper's stated claim and its reported evidence, and it undermines the central empirical contribution.","section":"Quantitative Analysis, Tables 1 and 2"},{"comment":"The proof of Lemma 1 is invalid. The proof asserts that 'softmax ... is non-decreasing', which is false: softmax is not component-wise monotone, because increasing one logit decreases the normalized probability of another. Even if each expert e_i were monotone in the seed set, the PMoE output in Eq. (9) is a convex combination with weights R_i(x) that themselves depend on x, so monotonicity of the combination does not follow. Additionally, the statement 'x(i) > x(j)' for binary vectors is undefined. Since Lemma 1 is invoked as the basis for the safety of optimizing the PMoE surrogate, this is a load-bearing gap in the theoretical argument.","section":"Appendix C1, Lemma 1"},{"comment":"Theorem 3's proof is circular. It asserts that because reconstruction error is minimized, latent representations 'preserve the essential properties' of the original seed sets, and therefore if P on latent representations is ordered, the same ordering holds in the original space. This is exactly the claim of the theorem. Minimizing average MSE over a training set does not imply pairwise ordering preservation for arbitrary unseen latent pairs and their decoded seed sets; no formal argument is provided. Since Theorem 3 is the stated justification for the central method-level claim that 'the optimal seed set that maximizes influence can be found by optimizing z', the inference procedure lacks a valid correctness guarantee.","section":"Seed Node Set Inference and Appendix C3, Theorem 3"},{"comment":"The exploration objective in Eq. (11) uses the PMoE estimator P as a reward for generating new seed sets, and Algorithm 1 (lines 10-14) selects the top-k replay samples according to P and then retrains both Seed2Vec and PMoE on the combined dataset. This creates a self-referential loop in which P serves as both the optimization target and the quality selector for its own training data. The paper provides no argument, beyond the unproven Theorem 3, that systematic errors in P are corrected rather than amplified. This is a fundamental methodological concern because it affects the validity of the reported improvements and the reliability of the final seed set returned by Algorithm 2.","section":"Latent Seed Set Exploration and Algorithm 1, Eq. (11)"},{"comment":"The inference-time claim is only partially supported by Table 3. At 10,000 nodes REM is slower than MIM-Reasoner (8.873s vs. 7.948s), and the text's statement that REM has 'on average, 10% faster inference time than the second-fastest MIM-Reasoner' is not backed by reported variance or any statistical test. Since inference time is one of the three claimed advantages in the abstract, the evidence for this part of the central claim is overstated.","section":"Scalability Analysis, Table 3"}],"minor_comments":[{"comment":"The phrase 'is a crucial as it can greatly diminish' is grammatically incomplete and should read 'is a crucial factor' or similar.","section":"Abstract"},{"comment":"There are typos in 'Propagtaion' and 'ultilizes' that should be corrected.","section":"Conclusion and Appendix A"},{"comment":"The number of PMoE experts is listed as 8 in Table 4 but as 20 in the text of Appendix D1; this inconsistency needs to be resolved.","section":"Appendix D1, Table 4"},{"comment":"Appendix D1 states that Proximal Policy Optimization (PPO) is employed for policy training, but Algorithm 1 and Eq. (11) describe gradient descent on the latent variable z; the connection between PPO and the described algorithm is unexplained.","section":"Appendix D1 vs. Algorithm 1"},{"comment":"The reference to Stark et al. (2006) appears twice in identical form in the reference list and should be deduplicated.","section":"References"},{"comment":"The header 'GCCOMB' is a typo for GCOMB.","section":"Table 3"},{"comment":"The notation Fθ = Eψ ◦ Dϕ and the subsequent expression ˆx = Dϕ(Eψ(x)) are inconsistent with functional composition order; the intended order should be clarified.","section":"Eq. (4)"},{"comment":"The statement 'arg max_z H(Dϕ(z)) ∝ arg max_x H(x)' is not a well-defined proportionality between set-valued argmaxes; a formal definition of the relationship is needed.","section":"Appendix C2, Lemma 2"},{"comment":"The sentence 'According to Theorem 3, the optimal seed set that maximizes influence can be found by optimizing z' overstates the theorem, which only claims an ordering preservation between latent and original spaces, not that the latent optimum corresponds to the global optimum of influence spread.","section":"Seed Node Set Inference"}],"recommendation":"reject","confidential_remarks":"For the editor: the paper's two load-bearing pillars both fail. The empirical tables contradict the abstract's claim of consistent superiority, and the main theoretical guarantee is a circular proof built on an invalid monotonicity lemma. The self-referential training loop adds a further correctness risk that the paper does not address. In my view, these issues are decisive and would require a substantially reworked experimental analysis and a new theoretical foundation to be salvageable; I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the paper is not a dud: the assembly of a VAE latent space for seed sets, a noisy top-m mixture-of-experts spread estimator, and gradient-based latent exploration is a reasonable system for multiplex influence maximization, and the authors test it on five real datasets including two large Twitter networks. If the numbers were trustworthy, this would be a solid engineering contribution to the learning-based IM subfield. Second, the numbers are not trustworthy, and the theory meant to underwrite them is invalid. The abstract claims REM 'consistently outperforms' state-of-the-art methods, but Tables 1 and 2 show ISF, KSN, and MIM-Reasoner beating REM on Cora-ML under LT at every budget, and ISF beating REM on Celegans under IC at 1% and 5%. That is not a marginal disagreement; it is a direct internal contradiction. There are also no error bars, the initial dataset X0 is never specified, and the expert count is 8 in the main text appendix table and 20 in the supplementary hyperparameter section, while the method is described as PPO-based only in the appendix even though the actual algorithm is gradient descent on z.\n\nThe theory is worse. Lemma 1's proof of monotonicity relies on the assertion that softmax is non-decreasing, which is false component-wise, and it also drops the dependence of the experts on x in Eq. 19. Lemma 2's 'proof' just asserts that reconstructed and original entropies are nearly equal and calls that a proportionality of arg max. Theorem 3 then assumes both lemmas and also applies the PMoE P to a distribution pϕ(z), which is ill-typed. So the guarantee that optimizing z is safe does not exist.\n\nWhat is genuinely new: the specific framework and the large-scale experiments are not in the cited literature, and the paper does engage with the right prior work. The idea of using a learned surrogate inside a latent-space search for MIM is worth exploring, and the scalability results in Table 3 are at least plausible for a learning-based method.\n\nWho is this for? A researcher working on learning-based influence maximization might mine the system design, but they should not cite the performance claims. As a referee, I would send it back for major revision: fix the theorems or remove them, reconcile the tables with the claims, add error bars and dataset details. But as submitted, the central claim is unsupported. My call: reject, but with a path to revision.","headline":"Plausible system, invalid theory, and tables that contradict the abstract: this MIM paper needs major revision before its claims can be taken seriously.","tokens_in":22589,"tokens_out":2976,"would_cite":false,"duration_ms":29682,"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":"REM claims multiplex influence maximization reduces to optimizing a continuous latent seed vector, beating six baselines on five real networks.","keywords":["multiplex influence maximization","influence spread","seed set optimization","reinforcement learning","variational autoencoder","mixture of experts","graph neural networks"],"falsifier":"Run Algorithm 1's exploration on a multiplex network, record the latent samples $z$, and compare PMoE's predicted spread $P(D_\\phi(z))$ with Monte Carlo spread $\\delta(D_\\phi(z))$ computed by Eq. (2); if the rank correlation is so low that the top-$k$ replay samples are not top-$k$ in true spread, or if replacing PMoE with true Monte Carlo spread as the selection and gradient score produces higher final influence, the central claim collapses.","tokens_in":21347,"feed_emoji":"📣","tokens_out":11442,"duration_ms":97203,"temperature":0.7,"pith_summary":"The paper claims that Multiplex Influence Maximization (MIM)—choosing a small seed set whose expected spread is largest in a multi-layer social network with heterogeneous diffusion models—can be solved by a fully learning-based pipeline that beats both combinatorial-optimization algorithms and prior deep/reinforcement-learning methods. The claim is empirical as well as architectural: on five real-world multiplex networks, under both Independent Cascade and Linear Threshold models, REM reports higher influence spread, better scalability, and faster inference than six baselines, with the largest margins on the biggest networks. The significance is practical: MIM is NP-hard, and traditional greedy methods time out or exhaust memory on million-node graphs, while earlier learning methods depend on expensive simulation or on high-quality training samples. REM attacks both bottlenecks by embedding seed sets in a continuous latent space and by replacing simulation with a learned mixture-of-experts spread estimator.","feed_headline":"A learned seed-picker tops six rivals on multiplex influence","feed_subtitle":"REM fuses a latent seed generator with an expert spread estimator to beat six baselines on five networks.","key_machinery":"The load-bearing object is the Propagation Mixture of Experts (PMoE) spread estimator $P(x, G; \\xi)$: several GNN experts of different depths, with noisy top-$m$ routing, whose routed outputs are merged and normalized into a predicted infection count. PMoE does triple duty: it is the exploration objective in Eq. (11), the ranking score for the priority replay memory, and the objective for final gradient-ascent inference. Its companion is Seed2Vec, the VAE that maps discrete seed sets to a continuous latent space so that gradient methods can be applied at all. The theoretical glue is Theorem 3 (Influence Estimation Consistency), which is what authorizes replacing true spread with PMoE's predicted spread when optimizing $z$.","core_discovery":"The central discovery, stated in the paper's Theorem 3, is that the discrete MIM search can be moved into a continuous latent space without changing the answer: once the VAE reconstruction error is minimized and the PMoE estimator is monotone, ordering seed sets by PMoE's predicted spread on latent codes is the same as ordering them by true spread in the original space, so the optimal seed set can be recovered by gradient ascent on the latent vector $z$. Around that identity, REM builds a loop: Seed2Vec encodes seed sets into a Gaussian latent space; an RL-style exploration objective pushes $z$ toward high-entropy, high-predicted-spread regions; the decoded candidates are ranked by PMoE, the top $k$ are replayed through a priority memory, and the model retrains on the augmented dataset. The paper's empirical assertion is that this loop, across Tables 1 to 3, yields the best reported spread and the shortest inference times among the compared methods.","pith_inferences":["A reader could test the framework's ceiling by replacing PMoE with Monte Carlo spread as the ranking score in the replay buffer: if true-spread replay yields better final seed sets, then REM's gains come from the surrogate's accuracy rather than from the exploration loop itself.","Because the paper's case study shows GAT experts beat GCN experts, the framework is modular: any future graph encoder could be dropped into the expert slots without changing the latent exploration, so REM's performance should track progress in graph representation learning.","The paper does not test whether PMoE's rankings survive when a deployment network follows a diffusion model different from the two used in training; in that setting the reported inference-time advantage could come at an unknown accuracy cost."],"forward_implications":["If REM is correct, inference-time seed selection no longer needs Monte Carlo simulation, which is what lets it handle graphs as large as the 1.9-million-node ParisAttack network where two greedy baselines run out of memory.","The same trained PMoE estimator serves every budget tested (1%, 5%, 10%, 20%) and both diffusion models, so one training pass covers a family of MIM instances rather than a single tuning.","The ablations imply the two added components are doing the work: dropping the RL exploration loop (REM-NonRL) and dropping the mixture-of-experts estimator (REM-NonMixture) both reduce final spread, so the reported gains are tied to those mechanisms.","If Theorem 3 holds in practice, then gradient ascent on the latent code $z$ is a valid substitute for discrete combinatorial search in MIM, not only on the tested networks."],"supporting_citations":[{"why":"Supplies the VAE formulation (ELBO, reparameterization trick) that Seed2Vec uses to map discrete seed sets into a continuous Gaussian latent space.","marker":"Kingma and Welling 2013"},{"why":"Provides the noisy top-m routing mechanism that PMoE adapts to route each seed set to the most relevant GNN experts.","marker":"Shazeer et al. 2017"},{"why":"Defines multiplex influence maximization with heterogeneous diffusion models and the overlapping-activation property; its ISF and KSN algorithms are primary combinatorial baselines.","marker":"Kuhnle et al. 2018"},{"why":"MIM-Reasoner is the main multiplex reinforcement-learning counterpart that REM must beat.","marker":"Do et al. 2024"},{"why":"DeepIM is the generative single-network IM state of the art that REM extends to multiplex settings and compares against.","marker":"Ling et al. 2023"},{"why":"GCOMB provides the learning-based combinatorial-optimization baseline for budget-constrained seed selection on large graphs.","marker":"Manchanda et al. 2020"},{"why":"Prioritized experience replay is the basis for REM's priority replay memory, which stores and reweights generated seed sets by predicted spread.","marker":"Schaul et al. 2015"},{"why":"Establishes the IC and LT diffusion models, submodularity, and the NP-hardness framing that define the MIM objective and the greedy approximation guarantee.","marker":"Kempe et al. 2003"}],"fun_headline_variants":["Reinforced expert loop picks seeds faster than six rivals","Latent-space trick finds best seeds in multiplex networks","REM: RL-trained seed selector beats six on influence spread","Mixture-of-experts seed picker wins on five networks","Optimal seeds via latent-space gradient ascent in REM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the PMoE spread predictor keeps its ranking faithful for latent seed sets it has never seen, so the seed sets it scores highest are also the ones with the largest true Monte Carlo spread.","fun_headline_variants_meta":{"raw":{"variants":["Reinforced expert loop picks seeds faster than six rivals","Latent-space trick finds best seeds in multiplex networks","REM: RL-trained seed selector beats six on influence spread","Mixture-of-experts seed picker wins on five networks","Optimal seeds via latent-space gradient ascent in REM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000274,"raw_usage":{"total_tokens":1628,"prompt_tokens":924,"completion_tokens":704,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":624}},"tokens_in":540,"tokens_out":704,"duration_ms":6704,"temperature":1.0,"reasoning_tokens":624,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:44:23.170049+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1's exploration on a multiplex network, record the latent samples $z$, and compare PMoE's predicted spread $P(D_\\phi(z))$ with Monte Carlo spread $\\delta(D_\\phi(z))$ computed by Eq. (2); if the rank correlation is so low that the top-$k$ replay samples are not top-$k$ in true spread, or if replacing PMoE with true Monte Carlo spread as the selection and gradient score produces higher final influence, the central claim collapses.","supporting_citations":[],"review_version":1}