Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical formulas. However, these three operators all serve the same paramount purpose and bear no difference in essence. Hence we probe into the essence of various feature operators from a high-level perspective, transformed their components equivalently, and explored their mathematical expressions within higher dimensions. We raise one clear and concrete unified formula for different feature operators termed as Evolution. Evolution utilizes the Evolution Function to generate the Evolution Kernel, which extracts and aggregates the features in certain positions of the input feature map. We mathematically deduce the equivalent transformation from the traditional formulas of these feature operators to Evolution and prove the unification. In addition, we discuss the forms of Evolution Functions and the properties of generated Evolution Kernels, intending to give inspirations to the further research and innovations of powerful feature operators.

翻译：传统上，不同类型的特征算子（例如卷积、自注意力与内卷积）采用不同的方法来提取和聚合特征，其数学公式之间几乎难以发现相似性。然而，这三种算子均服务于相同的核心目的，本质上并无差异。为此，我们从高层视角探究了多种特征算子的本质，对其组成部分进行了等价变换，并在更高维度上探索了其数学表达式。我们提出了一种清晰且具体的统一公式，适用于不同特征算子，称之为Evolution。Evolution利用演化函数生成演化核，该核在输入特征图的特定位置上提取并聚合特征。我们通过数学推导，证明了这些特征算子的传统公式与Evolution之间的等价变换，进而验证了其统一性。此外，我们还探讨了演化函数的形式以及所生成演化核的特性，旨在为未来强大特征算子的研究与创新提供启发。