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, 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.

Submission Number: 50