Weight sharing in convolutional neural networks (CNNs) ensures that their feature maps will be translation-equivariant. However, although conventional convolutions are equivariant to translation, they are not equivariant to other isometries of the input image data, such as rotation and reflection. For the classification of astronomical objects such as radio galaxies, which are expected statistically to be globally orientation invariant, this lack of dihedral equivariance means that a conventional CNN must learn explicitly to classify all rotated versions of a particular type of object individually. In this work we present the first application of group-equivariant convolutional neural networks to radio galaxy classification and explore their potential for reducing intra-class variability by preserving equivariance for the Euclidean group E(2), containing translations, rotations, and reflections. For the radio galaxy classification problem considered here, we find that classification performance is modestly improved by the use of both cyclic and dihedral models without additional hyper-parameter tuning, and that a D16 equivariant model provides the best test performance. We use the Monte Carlo Dropout method as a Bayesian approximation to recover epistemic uncertainty as a function of image orientation and show that E(2)-equivariant models are able to reduce variations in model confidence as a function of rotation.

中文翻译：

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使用群等变卷积神经网络对射电星系进行 Fanaroff-Riley 分类

卷积神经网络 (CNN) 中的权重共享确保它们的特征图是平移等变的。然而，尽管传统卷积与平移等变，但它们与输入图像数据的其他等距不等变，例如旋转和反射。对于诸如射电星系之类的天文物体的分类，这些天体在统计上被认为是全局方向不变的，这种缺乏二面体等变意味着传统的 CNN 必须明确地学习单独分类特定类型物体的所有旋转版本。在这项工作中，我们提出了组等变卷积神经网络在无线电星系分类中的首次应用，并探索了它们通过保持欧几里德群 E(2) 的等方差来减少类内可变性的潜力，包含平移、旋转和反射。对于这里考虑的射电星系分类问题，我们发现通过使用循环和二面体模型而无需额外的超参数调整，分类性能得到了适度的改进，并且 D16 等变模型提供了最佳测试性能。我们使用蒙特卡洛 Dropout 方法作为贝叶斯近似来恢复作为图像方向函数的认知不确定性，并表明 E(2) 等变模型能够减少模型置信度随旋转变化的变化。并且 D16 等变模型提供了最佳的测试性能。我们使用蒙特卡洛 Dropout 方法作为贝叶斯近似来恢复作为图像方向函数的认知不确定性，并表明 E(2) 等变模型能够减少模型置信度随旋转变化的变化。并且 D16 等变模型提供了最佳的测试性能。我们使用蒙特卡洛 Dropout 方法作为贝叶斯近似来恢复作为图像方向函数的认知不确定性，并表明 E(2) 等变模型能够减少模型置信度随旋转变化的变化。