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arxiv: 2605.12513 · v1 · submitted 2026-03-31 · 💻 cs.SI · cs.AI

Recognition: 2 theorem links

· Lean Theorem

SP-GCRL: Influence Maximization on Incomplete Social Graphs

Haohua Niu , Yuxuan Yang , Lingfeng Zhang , Hao Li , Jiao Liang , Zongfu Luo , Luca Rossi
Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:06 UTC · model grok-4.3

classification 💻 cs.SI cs.AI
keywords influence maximizationincomplete graphsgraph contrastive learningreinforcement learningsocial networksseed selectiondiffusion modelspartial observability
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The pith

SP-GCRL learns end-to-end seed selection policies for influence maximization on incomplete social graphs using contrastive representations and a nonlinear diffusion model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops SP-GCRL to solve influence maximization when social graphs are incomplete and diffusion dynamics are non-stationary. It introduces a social-propagation-aware nonlinear diffusion function to capture reinforcement, diminishing returns, and probability changes from repeated exposure. Dual structural views and contrastive learning produce node representations that tolerate missing edges and weak ties, while a GAT-based surrogate replaces costly strategy metrics for better efficiency. DDQN then trains a policy that selects seeds directly from these representations. Experiments on real-world networks demonstrate gains over heuristic and learning baselines across budgets and topologies while preserving scalability.

Core claim

SP-GCRL achieves higher influence spread on incomplete graphs by modeling nonlinear propagation effects, learning robust node embeddings via contrastive learning on dual views, replacing expensive metrics with a GAT regression surrogate, and optimizing seed selection end-to-end with DDQN under partial observability.

What carries the argument

The social-propagation-aware nonlinear diffusion function that models reinforcement, diminishing returns, and probability drift under repeated exposure.

If this is right

  • The framework scales to large networks while improving spread across varying seed budgets and topologies.
  • Contrastive representations reduce sensitivity to missing edges and weak ties compared with standard graph methods.
  • Replacing strategy metrics with a GAT surrogate cuts computation time without sacrificing policy quality.
  • End-to-end RL training enables direct optimization of seed sets under partial graph observability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same contrastive-plus-RL structure could be tested on other partial-observation network tasks such as link prediction or rumor containment.
  • The nonlinear diffusion model might be adapted to capture opinion polarization or fatigue effects in online campaigns.
  • Because the method avoids expensive simulations during training, it could support real-time seed selection on live platforms with streaming graph updates.

Load-bearing premise

The nonlinear diffusion function correctly models how influence reinforces or diminishes with repeated exposures on real incomplete graphs.

What would settle it

A controlled experiment on a synthetic network where repeated exposures produce linear rather than nonlinear diffusion effects, in which SP-GCRL shows no consistent advantage over baselines.

Figures

Figures reproduced from arXiv: 2605.12513 by Haohua Niu, Hao Li, Jiao Liang, Lingfeng Zhang, Luca Rossi, Yuxuan Yang, Zongfu Luo.

Figure 1
Figure 1. Figure 1: The SP-GCRL framework. that nodes propagate information with fixed probabilities, making it challeng￾ing to accurately capture the nonlinear effects of social relationships on user forwarding behaviors in real-world scenarios. To address this issue, inspired by the dynamic spreading equation proposed by [22], this study develops a nonlin￾ear propagation model that incorporates social relationships and the … view at source ↗
Figure 2
Figure 2. Figure 2: For different choices of function parameters, the propagation probability [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fitting of the exposure–response curve on six datasets. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Speedup and error under the GAT approximation. The speedup increases monoton￾ically with graph size—from small on medium graphs (900–26K nodes) to substantial gains on large graphs (1.8M and 11.6M). Note also that the speedup obtained by the CGV ap￾proximation consistently exceeds the one obtained on SBV, with a widen￾ing gap at larger scales, suggesting more effective computational reuse and parallelism. … view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of SP-GCRL and SP-GNN on four networks. (a) SP-GCRL (b) BIDGN (c) DeepIM (d) Tou-GDD (e) S2v-DQN (f) gIM [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

Influence maximization (IM) in real platforms is challenged by incomplete, noisy social graphs and non-stationary diffusion dynamics. We propose SP-GCRL, a social-propagation-aware graph contrastive reinforcement learning framework that learns end-to-end seed selection under partial observability.We first introduce a social-propagation-aware nonlinear diffusion function to model reinforcement/diminishing effects and probability drift under repeated exposure; we then construct dual structural views and perform contrastive learning to obtain node representations robust to missing edges and weak ties, while replacing expensive strategy metrics with a GAT-based regression surrogate to improve efficiency and scalability; finally, we use DDQN to learn an end-to-end seed selection policy on top of these representations. Experiments on multiple real-world networks show that SP-GCRL achieves significant gains over heuristic and learning-based baselines across budgets and topologies, while maintaining strong large-scale scalability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes SP-GCRL, a social-propagation-aware graph contrastive reinforcement learning framework for influence maximization under incomplete graphs and non-stationary diffusion. It introduces a nonlinear diffusion function to capture reinforcement, diminishing returns, and probability drift; constructs dual structural views for contrastive learning to obtain robust node embeddings; replaces expensive metrics with a GAT regression surrogate; and trains an end-to-end DDQN policy for seed selection. Experiments on real-world networks report significant gains over heuristic and learning-based baselines across budgets while preserving scalability.

Significance. If the central performance claims hold under independent validation, the work would advance practical IM methods by integrating contrastive robustness to missing edges with RL-based policy learning and a scalable surrogate, addressing a key gap between theoretical IM and noisy real platforms. The end-to-end trainable pipeline and emphasis on large-scale applicability are strengths.

major comments (2)
  1. [§4 and §5] §4 (nonlinear diffusion function) and §5 (experimental setup): the influence-spread metric used to report final results appears to be the same social-propagation-aware nonlinear diffusion function employed both for policy training and for the GAT surrogate. This creates a risk that reported gains are artifacts of internal consistency with the assumed dynamics rather than genuine robustness to missing edges or real diffusion processes. Independent hold-out evaluation against standard IC/LT models or observed cascade data is required to substantiate the claims.
  2. [§5] §5 (experiments): no ablation results, hyperparameter tables, or sensitivity analysis on the nonlinear diffusion parameters are provided, making it impossible to determine whether the reported gains depend on careful tuning of the free parameters or generalize across reasonable settings.
minor comments (2)
  1. [§3] Notation for the dual structural views and contrastive loss could be clarified with an explicit equation reference in §3.
  2. [Abstract and §1] The abstract and introduction should explicitly state the number of networks, their sizes, and the range of budgets tested to allow immediate assessment of the scalability claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments on our manuscript. The feedback highlights important aspects of evaluation and experimental rigor that we will address in the revision. We provide point-by-point responses below.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (nonlinear diffusion function) and §5 (experimental setup): the influence-spread metric used to report final results appears to be the same social-propagation-aware nonlinear diffusion function employed both for policy training and for the GAT surrogate. This creates a risk that reported gains are artifacts of internal consistency with the assumed dynamics rather than genuine robustness to missing edges or real diffusion processes. Independent hold-out evaluation against standard IC/LT models or observed cascade data is required to substantiate the claims.

    Authors: We appreciate the referee's concern regarding potential circularity in evaluation. The nonlinear diffusion function is intentionally central to SP-GCRL because it captures reinforcement, diminishing returns, and probability drift under partial observability—dynamics that standard IC/LT models do not explicitly model. Nevertheless, we agree that independent validation strengthens the claims. In the revised manuscript, we will add hold-out experiments that evaluate the learned policies using the standard Independent Cascade (IC) model with fixed probabilities, reporting influence spread under this alternative diffusion process. We will also include comparisons against observed cascade data where available in the datasets. These additions will demonstrate that performance gains are not solely artifacts of the training dynamics. revision: yes

  2. Referee: [§5] §5 (experiments): no ablation results, hyperparameter tables, or sensitivity analysis on the nonlinear diffusion parameters are provided, making it impossible to determine whether the reported gains depend on careful tuning of the free parameters or generalize across reasonable settings.

    Authors: We agree that the absence of ablations and sensitivity analysis limits interpretability. In the revised version, we will include a dedicated ablation study section that isolates the contributions of the dual-view contrastive learning, the GAT surrogate, and the nonlinear diffusion components. We will also add a hyperparameter table listing all key values (including those for the nonlinear function) and sensitivity plots showing performance variation across reasonable ranges of the reinforcement and diminishing-return coefficients. These results will confirm that gains are stable and not due to narrow tuning. revision: yes

Circularity Check

0 steps flagged

No load-bearing circularity; custom diffusion used consistently but claims rest on empirical comparisons rather than definitional reduction

full rationale

The derivation introduces a social-propagation-aware nonlinear diffusion function, dual-view contrastive representations, GAT surrogate, and DDQN policy as distinct components. No equations or steps reduce the reported influence spread or performance gains to quantities defined by the same fitted parameters by construction. Experiments compare against external baselines on real networks, and the framework builds on standard contrastive/RL primitives without self-citation chains that force the central result. Minor risk of internal consistency with the assumed diffusion model exists but does not meet the threshold for circularity under the rules requiring explicit quoteable reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The framework introduces a custom nonlinear diffusion function whose parameters are not specified in the abstract and a GAT surrogate whose regression targets depend on simulation or data; these constitute free parameters whose values are not independently derived.

free parameters (1)
  • nonlinear diffusion parameters
    Parameters controlling reinforcement and diminishing effects in the social-propagation-aware diffusion function are required to instantiate the model but are not given explicit values or derivation in the abstract.

pith-pipeline@v0.9.0 · 5458 in / 1181 out tokens · 48384 ms · 2026-05-14T21:06:38.102110+00:00 · methodology

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Reference graph

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