摘要
在许多机器学习任务中，希望模型的预测在输入变换时以等变的方式进行变换。卷积神经网络（CNNs）通过其结构设计实现了平移等变性；然而，对于其他变换，它们则需要学习正确的映射关系。在这项工作中，我们开发了可转向滤波器卷积神经网络（Steerable Filter CNNs, SFCNNs），该网络通过设计实现了平移和旋转的联合等变性。所提出的架构采用了可转向滤波器，能够高效地计算多种方向下的响应，而不会因滤波器旋转导致插值误差。我们利用群卷积来保证等变映射。此外，我们将He的权重初始化方案推广到定义为原子滤波器线性组合的滤波器上。数值实验表明，随着采样滤波器方向数目的增加，样本复杂度得到了显著提升，并且验证了网络能够在不同方向上泛化已学模式。所提出的方法在旋转MNIST基准测试和ISBI 2012 2D电子显微镜分割挑战赛中达到了最先进的水平。
基准测试
| 基准 | 方法 | 指标 |
|---|---|---|
| breast-tumour-classification-on-pcam | Steerable G-CNN (e) | AUC: 0.963 |
| breast-tumour-classification-on-pcam | Steerable G-CNN (C8) | AUC: 0.971 |
| breast-tumour-classification-on-pcam | Steerable G-CNN (C8) | AUC: 0.969 |
| breast-tumour-classification-on-pcam | Steerable G-CNN (C12) | AUC: 0.969 |
| colorectal-gland-segmentation-on-crag | Steerable G-CNN (e) | Dice: 0.848 F1-score: 0.811 Hausdorff Distance (mm): 175.9 |
| colorectal-gland-segmentation-on-crag | Steerable G-CNN (C8) | Dice: 0.888 F1-score: 0.861 Hausdorff Distance (mm): 139.5 |
| colorectal-gland-segmentation-on-crag | Steerable G-CNN (C12) | Dice: 0.870 F1-score: 0.855 Hausdorff Distance (mm): 156.2 |
| colorectal-gland-segmentation-on-crag | Steerable G-CNN (C12) | Dice: 0.869 F1-score: 0.837 Hausdorff Distance (mm): 164.8 |
| multi-tissue-nucleus-segmentation-on-kumar | Steerable G-CNN (e) | Dice: 0.791 Hausdorff Distance (mm): 51.0 |
| multi-tissue-nucleus-segmentation-on-kumar | Steerable G-CNN (C12) | Dice: 0.818 Hausdorff Distance (mm): 54.3 |
| multi-tissue-nucleus-segmentation-on-kumar | Steerable G-CNN (C4) | Dice: 0.809 Hausdorff Distance (mm): 54.2 |
| multi-tissue-nucleus-segmentation-on-kumar | Steerable G-CNN (C12) | Dice: 0.820 Hausdorff Distance (mm): 55.8 |
| rotated-mnist-on-rotated-mnist-1 | Steerable Filter CNN | Test error: 0.714 |