齿轮旋转恒等不变卷积神经网络系统
Geared Rotationally Identical and Invariant Convolutional Neural Network Systems
摘要：
作者最近介绍了形成不同类型的变换不变处理和基于变换不变算子或对称运算定量地产生相同输出的定理和技术。在这项研究中，我们进一步提出了一个齿轮旋转相同的CNN系统（GRI-CNN）与一个小的步长角连接网络的参与过程中的第一个扁平层。使用普通的CNN结构作为基础，构造GRI-CNN的要求包括使用对称输入向量或具有可以形成完整循环的角度增量的核作为“齿轮”。研究了四种基本的GRI-CNN结构。当输入矢量的旋转角可被齿轮的步距角整除时，它们中的每一个都可以产生数量上相同的输出结果。我们的研究表明，当输入向量旋转一个角度与步长角度不匹配时，GRI-CNN也可以产生高度一致的结果。通过使用超细齿轮齿阶角（例如，1度或0.1度），所有四个GRI-CNN系统都可以几乎各向同性地构建。
英文摘要：
Theorems and techniques to form different types of transformationally invariant processing and to produce the same output quantitatively based on either transformationally invariant operators or symmetric operations have recently been introduced by the authors. In this study, we further propose to compose a geared rotationally identical CNN system (GRI-CNN) with a small step angle by connecting networks of participated processes at the first flatten layer. Using an ordinary CNN structure as a base, requirements for constructing a GRI-CNN include the use of either symmetric input vector or kernels with an angle increment that can form a complete cycle as a "gearwheel". Four basic GRI-CNN structures were studied. Each of them can produce quantitatively identical output results when a rotation angle of the input vector is evenly divisible by the step angle of the gear. Our study showed when an input vector rotated with an angle does not match to a step angle, the GRI-CNN can also produce a highly consistent result. With a design of using an ultra-fine gear-tooth step angle (e.g., 1 degree or 0.1 degree), all four GRI-CNN systems can be constructed virtually isotropically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
