Graph-Conditioned Stochastic Modeling of Twitter Information Cascades with Dual-Head Transformers for Early Virality Prediction

Information cascades in online social networks arise from stochastic interactions among user behavior, temporal activation, and graph-structured exposure. Early prediction of cascade outcomes remains difficult because only a short diffusion prefix is observable, while future propagation depends on sparse user-level transitions across a heterogeneous social network. This study develops a graph-conditioned stochastic modeling framework for early Twitter cascade prediction. Retweet cascades are formulated as history-dependent stochastic processes over a finite user vocabulary, and a causal dual-head Transformer is used to infer cascade virality and logarithmic final size from short observed prefixes. To incorporate social-network structure, user embeddings pretrained from the follow graph are introduced as external structural priors. A controlled ablation design separates the effects of random embeddings, graph-pretrained embeddings, frozen structural priors, and handcrafted feature fusion. Experiments on Higgs Twitter retweet cascades show that direct full-vocabulary next-user prediction is statistically fragile under sparse short-prefix observations, motivating macro-level cascade outcome prediction. Among the evaluated configurations, the frozen graph-pretrained Transformer achieves the strongest overall balance, reaching an AUC of 0.819, a Brier score of 0.151, and an RMSE of 0.192, while the causal Transformer without a graph prior already surpasses logistic regression and approaches Random Forest; however, gains over competitive baselines are modest and statistically significant only in selected pairwise comparisons. Calibration analysis, bootstrap confidence intervals, and paired statistical tests confirm that graph-derived user priors provide more reliable improvements than sequence modeling alone under short-prefix sparse observations. These findings indicate that graph-conditioned structural priors offer a promising complement to causal sequence modeling for early Twitter cascade prediction.