DiffIM: Differentiable Influence Minimization with Surrogate Modeling and Continuous Relaxation

TL;DR

This paper tackles edge-removal influence minimization (IMIN) under the Independent Cascade model, a problem known to be NP-hard and non-submodular. It introduces DiffIM, a differentiable framework that combines a surrogate GNN to estimate influence and a continuous relaxation of edge removal, augmented by a gradient-driven selection variant. Across three versions—DiffIM, DiffIM+, and DiffIM++—the approach achieves large speedups (up to $15{,}160\times$) with little or no degradation in influence minimization performance, and is Pareto-optimal relative to baselines. Experiments on real-world graphs demonstrate strong scalability, effective inductive transfer, and applicability to other diffusion models (LT, G-SIR), underscoring practical impact for time-sensitive rumor blocking and related propagation control tasks.

Abstract

In social networks, people influence each other through social links, which can be represented as propagation among nodes in graphs. Influence minimization (IMIN) is the problem of manipulating the structures of an input graph (e.g., removing edges) to reduce the propagation among nodes. IMIN can represent time-critical real-world applications, such as rumor blocking, but IMIN is theoretically difficult and computationally expensive. Moreover, the discrete nature of IMIN hinders the usage of powerful machine learning techniques, which requires differentiable computation. In this work, we propose DiffIM, a novel method for IMIN with two differentiable schemes for acceleration: (1) surrogate modeling for efficient influence estimation, which avoids time-consuming simulations (e.g., Monte Carlo), and (2) the continuous relaxation of decisions, which avoids the evaluation of individual discrete decisions (e.g., removing an edge). We further propose a third accelerating scheme, gradient-driven selection, that chooses edges instantly based on gradients without optimization (spec., gradient descent iterations) on each test instance. Through extensive experiments on real-world graphs, we show that each proposed scheme significantly improves speed with little (or even no) IMIN performance degradation. Our method is Pareto-optimal (i.e., no baseline is faster and more effective than it) and typically several orders of magnitude (spec., up to 15,160X) faster than the most effective baseline while being more effective.

Figures (9)

• Figure 1: The effectiveness (the reduced ratio of influence) and running time of each method, with budget $b=5$ (top) and $b=10$ (bottom). The baselines with outputs independent of seed sets were represented as horizontal lines. We compared the running time of the best baseline to one of our methods with the most similar reduced ratio, and in all cases, DiffIM was 30 $\times$ to 15,160 $\times$ faster. See Appendix G.1 for full results with standard deviations.
• Figure 2: The running time of each DiffIM version when budget $b$ increases from $1$ to $10$. The running time of each version grew linearly with $b$, showing good scalability.
• Figure 3: The Pearson correlation coefficients between the ground-truth influence of the validation sets and that estimated by MC simulation of a trained GNN. In all the cases, trained GNNs estimated influences near-perfectly.
• Figure 4: The effectiveness (the reduced ratio of influence) and running time of each method, with budget $b \in \{5, 10\}$ on LT and G-SIR models. We compared the running time of the best baseline to one of our methods with the most similar reduced ratio. Except for (d) on CL and ET, all DiffIM versions were Pareto-optimal, i.e., no baseline is faster and more effective than any version.
• Figure 5: The effectiveness (the reduced ratio of influence) and running time of each method, with budget $b \in \{3, 5, 7, 10\}$. The error bars represent one standard deviation. The superiority of DiffIM is valid with all the values of $b$.

Theorems & Definitions (12)

• Definition 1: Independent cascade (IC) model
• Definition 2: Influenced probabilities and expected influence
• Theorem 1
• Theorem 2: yan2019rumor yan2019rumor
• Lemma 1
• proof
• proof
• Lemma 2
• proof
• Remark 1