让神经网络对任意形状变形保持不变，提升泛化能力。
Diffeomorphism-Equivariant Neural Networks
- 通过能量优化实现微分同胚等变性，无需重新训练
- 在分割和分类任务中对未知变形保持良好性能
- 适合需要强形变鲁棒性的医学图像分析场景
将群对称性通过等变性融入神经网络，已成为应对现代深度学习效率与数据需求的有效方法。尽管现有方法如群卷积和基于平均的方法主要关注紧致、有限或低维群的线性作用，本文探索了如何将等变性扩展至无限维群。提出一种策略，通过基于能量的规范方法，在预训练神经网络中引入微分同胚等变性。将等变性表述为优化问题，使我们能够利用已有的可微图像配准方法工具箱。在分割和分类任务上的实验结果表明，该方法实现了近似等变性，并能在不依赖大规模数据增强或重训练的情况下泛化到未见过的变换。
原文摘要 · Abstract (English)
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimensional groups with linear actions, this work explores how equivariance can be extended to infinite-dimensional groups. We propose a strategy designed to induce diffeomorphism equivariance in pre-trained neural networks via energy-based canonicalisation. Formulating equivariance as an optimisation problem allows us to access the rich toolbox of already established differentiable image registration methods. Empirical results on segmentation and classification tasks confirm that our approach achieves approximate equivariance and generalises to unseen transformations without relying on extensive data augmentation or retraining.
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