Does equivariance matter at scale?

2024/10/30 by Johann Brehmer, Brehmer, Johann, Sönke Behrends +5 · 5 voices · 20 citations
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Advanced Graph Neural Networks #Cartography #Geography #Machine Learning in Materials Science #Mathematics #Model Reduction and Neural Networks #Scale (ratio)

paper · pdf · doi:10.48550/arxiv.2410.23179

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given large datasets and sufficient compute, is it beneficial to design neural architectures for the structure and symmetries of each problem? Or is it more efficient to learn them from data? We study empirically how equivariant and non-equivariant networks scale with compute and training samples. Focusing on a benchmark problem of rigid-body interactions and on general-purpose transformer architectures, we perform a series of experiments, varying the model size, training steps, and dataset size. We find evidence for three conclusions. First, equivariance improves data efficiency, but training non-equivariant models with data augmentation can close this gap given sufficient epochs. Second, scaling with compute follows a power law, with equivariant models outperforming non-equivariant ones at each tested compute budget. Finally, the optimal allocation of a compute budget onto model size and training duration differs between equivariant and non-equivariant models.

Cited by

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• LeMat-Traj: A Scalable and Unified Dataset of Materials Trajectories for Atomistic Modeling
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• AdS-GNN -- a Conformally Equivariant Graph Neural Network
• Position: It's Time to Optimize LLMs for Self-Consistency
• Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries

Discussions

• Excellent talk by @johannbrehmer.bsky.social On “Does equivariance matter at scale?” At NeurReps workshop arxiv.org/abs/2410.23179 www.neurreps.org [bsky, 63 points, 1 comments]
• The snow is gently falling outside the window, the models are training, what could be better? Two articles cool to read: Does Equivariance matter at scale? (@johannbrehmer.bsky.social et al.) arxiv. [bsky, 42 points, 0 comments]
• Tomorrow, in the reading group, Johannes Brehmer will present his paper "Does equivariance matter at scale?" arxiv.org/abs/2410.23179 Join us on zoom at 12pm ET / 6pm CET: portal.valencelabs.com/logg [bsky, 28 points, 0 comments]
• Does physical modeling matter or should we just do data-driven stuff? I feel like this paper characterizes things perfectly: arxiv.org/abs/2410.23179. Physics-based modeling is always helpful but the [bsky, 19 points, 1 comments]
• You might not be surprised to hear that equivariance improves data efficiency. But did you expect equivariant models to also be more *compute*-efficient? Learning symmetries from data costs FLOPs! [bsky, 6 points, 1 comments]

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• Approximately Equivariant Neural Processes