Actionable Interpretability via Causal Hypergraphs: Unravelling Batch Size Effects in Deep Learning

While the impact of batch size on generalisation is well studied in vision tasks, its causal mechanisms remain underexplored in graph and text domains. We introduce a hypergraph-based causal framework, HGCNet, that leverages deep structural causal models (DSCMs) to uncover how batch size influences generalisation via gradient noise, minima sharpness, and model complexity. Unlike prior approaches based on static pairwise dependencies, HGCNet employs hypergraphs to capture higher-order interactions across training dynamics. Using do-calculus, we quantify direct and mediated effects of batch size interventions, providing interpretable, causally grounded insights into optimisation. Experiments on citation networks, biomedical text, and e-commerce reviews show that HGCNet outperforms strong baselines including GCN, GAT, PI-GNN, BERT, and RoBERTa. Our analysis reveals that smaller batch sizes causally enhance generalisation through increased stochasticity and flatter minima, offering actionable interpretability to guide training strategies in deep learning. This work positions interpretability as a driver of principled architectural and optimisation choices beyond post hoc analysis.