Evolution: A Unified Formula for Feature Operators from a High-level Perspective
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Online Operator Design in Evolutionary Optimization for Flexible Job Shop Scheduling via Large Language Models
Customized static operator design has enabled widespread application of Evolutionary Algorithms (EAs), but their search effectiveness often deteriorates as evolutionary progresses. Dynamic operator configuration approach…
PhaseEvo: Towards Unified In-Context Prompt Optimization for Large Language Models
Crafting an ideal prompt for Large Language Models (LLMs) is a challenging task that demands significant resources and expert human input. Existing work treats the optimization of prompt instruction and in-context learni…
Computational EfficiencyIn-Context LearningLearning to Transfer for Evolutionary Multitasking
Evolutionary multitasking (EMT) is an emerging approach for solving multitask optimization problems (MTOPs) and has garnered considerable research interest. The implicit EMT is a significant research branch that utilizes…
Evolutionary AlgorithmsTransfer LearningA Survey and Analysis of Evolutionary Operators for Permutations
There are many combinatorial optimization problems whose solutions are best represented by permutations. The classic traveling salesperson seeks an optimal ordering over a set of cities. Scheduling problems often seek op…
Combinatorial OptimizationEvolutionary AlgorithmsSchedulingSurveyParametric Learning of Time-Advancement Operators for Unstable Flame Evolution
This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equa…
Operator learning