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Reference Flow Matching For Generative Modeling Continuous Normalizing Flows Flow Straight and Fast Preliminaries The objective of generative modeling is to learn the underlying distribution of the t

References John Lee, Introduction to Smooth Manifolds Loring Tu, An Introduction to Manifolds Victor Guillemin and Alan Pollack, Differential Topology For Chinese reader, you can refer to the websit

Basic Concepts Topology Space A topology space is a set with a collection of open sets that satisfy the following properties: 1. and . 2. if , then . 3. if , then . A topological space is denoted a

References John Lee, Introduction to Smooth Manifolds Loring Tu, An Introduction to Manifolds Victor Guillemin and Alan Pollack, Differential Topology For Chinese reader, you can refer to the websit

Introduction Generative Adversarial Networks is invented in 2014 by Ian J.Goodfellow, et. al. as a generative models, its idea derives from the game theory where two player compete against one another

Optimal Transport Problem Definition Given two probability measures and on measurable spaces and , respectively, the Optimal Transport Problem seeks to find a transport plan that minimizes the cos

Reference: A Convex-Programming Approach for Efficient Directed Densest Subgraph Discovery Efficient and Scalable Directed Densest Subgraph Discovery UDS problem Definition The Undirected Densest Su

This is a reading note on the paper “Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions” by A. ENE, Huy L. NGUYEN arxiv Knowledge prerequisite on submodular function (i

参考文献: Wikipedia - Submodular function Lecture 7: Submodular Functions, Lovász Extension and Minimization Learning with Submodular Functions: A Convex Optimization Perspective 子模函数 (Submodular Function

回归任务损失函数(Regression Losses) 均方误差(MSE, Mean Squared Error) 均方误差是回归任务中最常用的损失函数之一。它计算预测值与实际值之间差异的平方和的平均值。公式如下： 其中， 是实际值， 是预测值， 是样本数量。 MSE 的优点是对大误差有较强的惩罚作用，因为误差被平方了。这使得模型在训练时更倾向于减少大误差。 然而，MSE 对异常值非常敏感，因为