Evolution: A Unified Formula for Feature Operators from a High-level Perspective
This work provides a foundational framework for understanding and innovating feature operators in machine learning, potentially impacting all of ML/AI by unifying disparate approaches.
The paper tackles the problem of disparate mathematical formulations for feature operators like convolution, self-attention, and involution by proposing a unified formula called Evolution, which extracts and aggregates features using an Evolution Function and Evolution Kernel, and proves the equivalence through mathematical deduction.
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.