Causal Geometry of Batch Size and Generalisation

Batch size strongly influences optimisation, yet its role in non-Euclidean learning remains poorly understood. We propose \textbf{HGCNet}, a causally inspired hypergraph-based Deep Structural Causal Model that treats batch size as an intervention and organises its effects through stochastic mediators (gradient noise, sharpness, complexity) and a geometric proxy via Ollivier–Ricci curvature. Curvature is endogenous to the training recipe and, together with a curvature-aware regulariser, serves as a diagnostic of geometric stability rather than an isolated intervention. Experiments on graph and text benchmarks show consistent $2$–$4\%$ accuracy improvements over strong baselines, providing the first causally structured analysis of how batch size shapes generalisation beyond vision.