Training Dynamics of Learning 3D-Rotational Equivariance
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915647985811456 |
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| author | Shen, Max W. Nowara, Ewa Maser, Michael Cho, Kyunghyun |
| author_facet | Shen, Max W. Nowara, Ewa Maser, Michael Cho, Kyunghyun |
| contents | While data augmentation is widely used to train symmetry-agnostic models, it remains unclear how quickly and effectively they learn to respect symmetries. We investigate this by deriving a principled measure of equivariance error that, for convex losses, calculates the percent of total loss attributable to imperfections in learned symmetry. We focus our empirical investigation to 3D-rotation equivariance on high-dimensional molecular tasks (flow matching, force field prediction, denoising voxels) and find that models reduce equivariance error quickly to $\leq$2\% held-out loss within 1k-10k training steps, a result robust to model and dataset size. This happens because learning 3D-rotational equivariance is an easier learning task, with a smoother and better-conditioned loss landscape, than the main prediction task. For 3D rotations, the loss penalty for non-equivariant models is small throughout training, so they may achieve lower test loss than equivariant models per GPU-hour unless the equivariant ``efficiency gap'' is narrowed. We also experimentally and theoretically investigate the relationships between relative equivariance error, learning gradients, and model parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Training Dynamics of Learning 3D-Rotational Equivariance Shen, Max W. Nowara, Ewa Maser, Michael Cho, Kyunghyun Machine Learning Biomolecules While data augmentation is widely used to train symmetry-agnostic models, it remains unclear how quickly and effectively they learn to respect symmetries. We investigate this by deriving a principled measure of equivariance error that, for convex losses, calculates the percent of total loss attributable to imperfections in learned symmetry. We focus our empirical investigation to 3D-rotation equivariance on high-dimensional molecular tasks (flow matching, force field prediction, denoising voxels) and find that models reduce equivariance error quickly to $\leq$2\% held-out loss within 1k-10k training steps, a result robust to model and dataset size. This happens because learning 3D-rotational equivariance is an easier learning task, with a smoother and better-conditioned loss landscape, than the main prediction task. For 3D rotations, the loss penalty for non-equivariant models is small throughout training, so they may achieve lower test loss than equivariant models per GPU-hour unless the equivariant ``efficiency gap'' is narrowed. We also experimentally and theoretically investigate the relationships between relative equivariance error, learning gradients, and model parameters. |
| title | Training Dynamics of Learning 3D-Rotational Equivariance |
| topic | Machine Learning Biomolecules |
| url | https://arxiv.org/abs/2512.02303 |