Causal Geometry of Batch Size and Generalisation

Zhongtian Sun, Anoushka Harit, Pietro Lio

Keywords: Causal Inference, Hypergraphs, Ricci Curvature, Gradient Noise

TL;DR: We show that batch size affects generalisation not only through noise and sharpness but also via curvature, and introduce HGCNet, the first causal–geometric framework to disentangle these pathways in graphs and text.

Abstract: Batch size strongly influences optimisation, but its causal role in non-Euclidean learning remains unexplored. We propose \textbf{HGCNet}, a causal geometric framework that treats batch size as an intervention within a hypergraph based Deep Structural Causal Model. Our method disentangles stochastic pathways (gradient noise, sharpness, complexity) from a geometric pathway via Ollivier-Ricci curvature, and introduces a curvature-aware regulariser to ensure stability. Experiments on graph and text benchmarks show $2$--$4\%$ accuracy gains over strong baselines, offering the first causal explanation of how batch size shapes generalisation beyond vision.

Submission Number: 50