We propose the use of group convolutional neural network architectures
(GCNNs) equivariant to the 2D Euclidean group, $E(2)$, for the task of galaxy
morphology classification by utilizing symmetries of the data present in galaxy
images as an inductive bias in the architecture. We conduct robustness studies
by introducing artificial perturbations via Poisson noise insertion and
one-pixel adversarial attacks to simulate the effects of limited observational
capabilities. We train, validate, and test GCNNs equivariant to discrete
subgroups of $E(2)$ - the cyclic and dihedral groups of order $N$ - on the
Galaxy10 DECals dataset and find that GCNNs achieve higher classification
accuracy and are consistently more robust than their non-equivariant
counterparts, with an architecture equivariant to the group $D_{16}$ achieving
a $95.52 \pm 0.18\%$ test-set accuracy. We also find that the model loses
$<6\%$ accuracy on a $50\%$-noise dataset and all GCNNs are less susceptible to
one-pixel perturbations than an identically constructed CNN. Our code is
publicly available at this https URL

使用群卷积神经网络 (GCNNs) 基于数据的对称性对星系形态分类任务进行研究，通过引入人为扰动和模拟观测能力的限制来进行鲁棒性研究，发现 GCNN 在分类准确性和鲁棒性方面优于非等变的对应模型。

用于鲁棒星系形态分类的 E (2) 等变神经网络

E(2) Equivariant Neural Networks for Robust Galaxy Morphology  Classification

3D Convolutional Neural Networks are sensitive to transformations applied to
their input. This is a problem because a voxelized version of a 3D object, and
its rotated clone, will look unrelated to each other after passing through to
the last layer of a network. Instead, an idealized model would preserve a
meaningful representation of the voxelized object, while explaining the
pose-difference between the two inputs. An equivariant representation vector
has two components: the invariant identity part, and a discernable encoding of
the transformation. Models that can't explain pose-differences risk "diluting"
the representation, in pursuit of optimizing a classification or regression
loss function.
We introduce a Group Convolutional Neural Network with linear equivariance to
translations and right angle rotations in three dimensions. We call this
network CubeNet, reflecting its cube-like symmetry. By construction, this
network helps preserve a 3D shape's global and local signature, as it is
transformed through successive layers. We apply this network to a variety of 3D
inference problems, achieving state-of-the-art on the ModelNet10 classification
challenge, and comparable performance on the ISBI 2012 Connectome Segmentation
Benchmark. To the best of our knowledge, this is the first 3D rotation
equivariant CNN for voxel representations.

介绍了一种 3D 旋转等变 CNN (CubeNet)，该网络通过保留 3D 形状的全局和局部特征，有助于维护体素化对象的有意义表示，并能解释输入之间的姿态差异。应用于各种 3D 推断问题中，在 ModelNet10 分类挑战赛上实现了最先进的性能，并在 ISBI 2012 Connectome 分割基准测试中实现了可比性能。