Multi-Scale Feature Extraction for Spherical CNNs

球形CNN （PDO-eS2CNN[1]）的作者通过将球形信号映射到旋转群SO(3)来定义旋转等变卷积。这允许他们在球面上定义旋转等变卷积。除了旋转等方差之外，他们的网络还受益于一个增加了六个pdo（偏微分算子）的核，独立地参数化了所有二阶微分（包括交叉项），从而获得了更丰富的扩散特性集。重要的是，我们注意到这些改进与特征金字塔网络（FPN）的架构优势完全正交。因此，我们建议将特征金字塔纳入他们的方法将进一步提高最先进的性能，证明旋转等方差，并获得最佳参数效率。最先进的多尺度特征提取球面cnn的第二个改进是在最先进的目标检测模型中实现更复杂的FPN架构[2,3]。这些工作结合了自上而下和自下而上路径的重复块，他们称之为多尺度特征融合（MSFF）。通过这样做，他们学习改进的特征金字塔，这些特征金字塔是由所有尺度的语义内容通知的。另外，平面分割网络（如[4,5,6]）使用亚属性卷积实现了性能的提高。这种方法可以在多个尺度上提取特征，而不需要利用编码器网络的层次结构。我们注意到，通过计算中心顶点（即2环，3环等，见图2）上更宽邻域上的扩散特性，可以对二十面体网格上的pdo执行类似的处方。[6]的作者确定了由于图像边界效应而无法捕获远程信息的关键问题，并试图通过使用诸如全局平均池化之类的技术来解决这个问题。然而，我们注意到，由于我们的域本质上是无边缘的，这些影响不适用，因此亚历卷积可能与球形数据有一些自然的协同作用。研究计划在提议的SO(3)等变网络中实现fpn将特别具有挑战性，并且可能需要大量的实现时间，因为原作者尚未发布他们的代码。然而，他们高度相关的基于pdo的平面工作[7]已经与代码一起发布，并将阐明一些关键的实现细节。本研究的第二个途径是推广在SOTA平面架构中发现的多尺度特征提取方法。最后，我们打算通过在更广泛的数据集上进行测试来找到这些改进的最佳组合，例如QM7雾化能量预测[8]，或CAM5气候分割[9]任务。

The authors of the spherical CNN (PDO-eS2CNN [1]) define a rotation equivariant convolution by mapping spherical signals to the rotational group SO(3). This allows them to define rotationally equivariant convolutions on the sphere. In addition to rotational equivariance, their network also benefits from a kernel with an increased set of six PDOs (partial differential operators), independently parameterising all second order differentials (including cross-terms) and hence attaining a richer set of diffusion characteristics. Importantly, we note that these improvements are entirely orthogonal to the architectural benefits of a Feature Pyramid Network (FPN). Hence, we propose incorporating feature pyramids into their approach would further improve the state-of-the-art performance, demonstrate rotational equivariance, and attain optimal parameter efficiency.State-Of-The-Art Multi-Scale Feature ExtractionA second improvement to spherical CNNs would be to implement the more sophisticated FPN architectures found in state-of-the-art object detection models [2, 3]. These works incorporate repeated blocks of top-down and bottom-up pathways, in what they refer to as multi-scale feature fusion (MSFF). By doing this, they learn improved feature pyramids which are informed by semantic content at all scales. Separately, planar segmentation networks such as [4, 5, 6] achieve improved performance using atrous convolutions. This approach can extract features at multiple scales without needing to exploit the hierarchical structure of an encoder network. We note an analogous prescription can be performed with PDOs on icosahedral meshes by computing diffusion characteristics on a wider neighbourhoods on a central vertex (i.e. 2-ring, 3-ring, etc, see figure 2). The authors of [6] identify the key issues with atrousconvolutions failing to capture long range information due to image boundary effects, and attempt to address this by using techniques such as global average pooling. However, we note that since our domain is inherently edgeless these effects do not apply, and hence atrous convolutions may have some natural synergy with spherical data.Research PlanThe implementation of FPNs into the proposed SO(3)-equivariant network will be particularly challenging and could take substantial implementation time because the original authors are yet to publish their code. However, their highly related planar PDO-based work [7] has been published with code and would illuminate some of the key implementation details. The second avenue of this research concerns generalizing multi-scale feature extraction methods found in the SOTA planar architectures. Finally, we intend to find an optimal combination of these improvements through testing on a wider variety of datasets, e.g. QM7 atomization energy prediction [8], or CAM5 climate segmentation [9] tasks.