Temporal scaling in information propagation

For the study of information propagation, one fundamental problem is uncovering universal laws governing the dynamics of information propagation. This problem, from the microscopic perspective, is formulated as estimating the propagation probability that a piece of information propagates from one individual to another. Such a propagation probability generally depends on two major classes of factors: the intrinsic attractiveness of information and the interactions between individuals. Despite the fact that the temporal effect of attractiveness is widely studied, temporal laws underlying individual interactions remain unclear, causing inaccurate prediction of information propagation on evolving social networks. In this report, we empirically study the dynamics of information propagation, using the dataset from a population-scale social media website. We discover a temporal scaling in information propagation: the probability a message propagates between two individuals decays with the length of time latency since their latest interaction, obeying a power-law rule. Leveraging the scaling law, we further propose a temporal model to estimate future propagation probabilities between individuals, reducing the error rate of information propagation prediction from 6.7% to 2.6% and improving viral marketing with 9.7% incremental customers.

💡 Research Summary

The paper investigates a previously under‑explored aspect of information diffusion: how the time elapsed since the most recent interaction between two users (latency) influences the probability that a piece of information will be transmitted from one to the other. Using a publicly available dataset from Sina Weibo (the Chinese equivalent of Twitter) that contains half a million users, 1.2 million follower links, and 8 million messages, the authors construct a binary label for each potential diffusion event: δ = 1 if a follower retweets a message from a followee for the first time, and δ = 0 otherwise. For every such event they compute τ, the latency measured as the idle time since the last interaction (retweet or message) between the same pair of users.

The empirical analysis reveals two key phenomena. First, retweet events are highly bursty: many occur within short intervals separated by long idle periods. The distribution of τ for all positive events follows a power‑law, P(τ) ∝ τ⁻α, with an exponent α≈0.71, contrasting sharply with the exponential distribution expected under a static Poisson interaction model. Second, when the authors aggregate retweet versus non‑retweet outcomes across all edges and plot the conditional probability Pr(δ = 1 | τ) against τ on log‑log axes, they observe a clear linear relationship, indicating that the instantaneous diffusion probability decays as a power‑law of latency:

Pr(δ = 1) ∝ τ⁻αₑ,

where αₑ is edge‑specific. This edge‑specific exponent reflects heterogeneity in how quickly different user pairs lose influence over time.

Motivated by these findings, the authors propose the “Decay model”. For each directed edge (i → j) the model defines a base propagation probability qₑ (time‑invariant) and a decay exponent αₑ, yielding

Pr(δ = 1 | τ) = qₑ · τ⁻αₑ.

Both parameters are estimated in a Bayesian framework using maximum a posteriori (MAP) inference. The prior over αₑ is centered on the global exponent (≈0.71) discovered empirically, which helps mitigate over‑fitting when observations per edge are sparse—a common situation in real‑world networks.

The Decay model is benchmarked against four strong baselines: maximum‑likelihood estimation (MLE), expectation‑maximization (EM), a static Bernoulli model, and a static piecewise‑constant Bernoulli model (Static PC Bernoulli). Evaluation proceeds along two dimensions. First, a binary classification task predicts whether a given follower will retweet a new incoming message. The Decay model achieves an AUC of 97.4 % (up from 93.3 % for the best baseline) and reduces the misclassification error by roughly 50 %. Perplexity on held‑out data is also lowest for the Decay model, especially when the training set is limited, confirming its robustness to data scarcity.

Second, the authors assess the practical impact on viral marketing. Using the predicted diffusion probabilities, they run the CELF++ influence‑maximization algorithm to select an initial seed set for a five‑day diffusion window. The seed set derived from the Decay model activates 2,590 nodes in the observed propagation subgraph, a 9.7 % improvement over the best baseline (2,361 nodes). This demonstrates that incorporating the latency‑based decay dramatically improves the quality of seed selection and the eventual spread.

In the discussion, the authors argue that the discovered temporal scaling law provides a universal feature for diffusion modeling, complementing traditional static features such as node degree, content attributes, or demographic information. The Decay model can be extended by expressing qₑ as a function of exogenous variables (e.g., topic relevance, user activity levels), thereby integrating richer context while preserving the parsimonious decay component. Moreover, the Bayesian prior over αₑ offers a principled way to handle the extreme sparsity typical of edge‑level interaction data.

Overall, the paper makes three substantive contributions: (1) empirical evidence that diffusion probability decays with latency according to a power‑law, (2) a simple yet effective probabilistic model that captures this decay and outperforms state‑of‑the‑art baselines in both predictive accuracy and influence maximization, and (3) a demonstration that the temporal scaling insight can be leveraged for practical applications such as viral marketing, yielding measurable gains in reach. The work opens avenues for future research on higher‑order temporal dependencies, multi‑step Markov processes, and cross‑platform validation of the scaling law.