Incorporating group symmetry directly into the learning process has proved to
be an effective guideline for model design. By producing features that are
guaranteed to transform covariantly to the group actions on the inputs,
group-equivariant convolutional neural networks (G-CNNs) achieve significantly
improved generalization performance in learning tasks with intrinsic symmetry.
General theory and practical implementation of G-CNNs have been studied for
planar images under either rotation or scaling transformation, but only
individually. We present, in this paper, a roto-scale-translation equivariant
CNN (RST-CNN), that is guaranteed to achieve equivariance jointly over these
three groups via coupled group convolutions. Moreover, as symmetry
transformations in reality are rarely perfect and typically subject to input
deformation, we provide a stability analysis of the equivariance of
representation to input distortion, which motivates the truncated expansion of
the convolutional filters under (pre-fixed) low-frequency spatial modes. The
resulting model provably achieves deformation-robust RST equivariance, i.e.,
the RST symmetry is still "approximately" preserved when the transformation is
"contaminated" by a nuisance data deformation, a property that is especially
important for out-of-distribution generalization. Numerical experiments on
MNIST, Fashion-MNIST, and STL-10 demonstrate that the proposed model yields
remarkable gains over prior arts, especially in the small data regime where
both rotation and scaling variations are present within the data.

该研究提出了一种基于耦合群卷积的旋转、缩放和平移等变卷积神经网络 RST-CNN，该网络通过稳定性分析可证明具有变形鲁棒性，能在旋转、缩放和平移等输入畸变的情况下保持等变性，从而在 MNIST、Fashion-MNIST 和 STL-10 数据集上实现了显著提升。

变形鲁棒的旋转 - 缩放 - 平移等变卷积神经网络

Deformation Robust Roto-Scale-Translation Equivariant CNNs

Mainstream video analytics uses a pre-trained DNN model with an assumption
that inference input and training data follow the same probability
distribution. However, this assumption does not always hold in the wild:
autonomous vehicles may capture video with varying brightness; unstable
wireless bandwidth calls for adaptive bitrate streaming of video; and,
inference servers may serve inputs from heterogeneous IoT devices/cameras. In
such situations, the level of input distortion changes rapidly, thus reshaping
the probability distribution of the input.
We present GearNN, an adaptive inference architecture that accommodates
heterogeneous DNN inputs. GearNN employs an optimization algorithm to identify
a small set of "distortion-sensitive" DNN parameters, given a memory budget.
Based on the distortion level of the input, GearNN then adapts only the
distortion-sensitive parameters, while reusing the rest of constant parameters
across all input qualities. In our evaluation of DNN inference with dynamic
input distortions, GearNN improves the accuracy (mIoU) by an average of 18.12%
over a DNN trained with the undistorted dataset and 4.84% over stability
training from Google, with only 1.8% extra memory overhead.

GearNN 是一种自适应的推理体系结构，它优化了少量的 “失真敏感” DNN 参数，根据输入的失真水平适应性地调整，从而提高了动态输入失真下 DNN 推理的准确性。