Causal Geometry of Batch Size and Generalisation

Zhongtian Sun, Anoushka Harit, Pietro Lio
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:529-553, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-sun26b, title = {Causal Geometry of Batch Size and Generalisation}, author = {Sun, Zhongtian and Harit, Anoushka and Lio, Pietro}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {529--553}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/sun26b/sun26b.pdf}, url = {https://proceedings.mlr.press/v282/sun26b.html}, 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.} }
Endnote
%0 Conference Paper %T Causal Geometry of Batch Size and Generalisation %A Zhongtian Sun %A Anoushka Harit %A Pietro Lio %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-sun26b %I PMLR %P 529--553 %U https://proceedings.mlr.press/v282/sun26b.html %V 282 %X 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.
APA
Sun, Z., Harit, A. & Lio, P.. (2026). Causal Geometry of Batch Size and Generalisation. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:529-553 Available from https://proceedings.mlr.press/v282/sun26b.html.

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