Evolution: A Unified Formula for Feature Operators from a High-level
  Perspective
Zhicheng Cai
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.