Polynomial differential equationDifferential algebraLiouvillian first integralGodbillon–Vey sequenceThis paper gives a classification of polynomial differential operators X =X(x,x)δ+X(x,x)δ(δ= / x). The classification is defined through an order derived from X. Let X = Xy be the associated ...
论文笔记:POLYLOSS: A POLYNOMIAL EXPANSION PERSPECTIVE OF CLASSIFICATION LOSS FUNCTIONS(ICLR 2022) 科马 学生2 人赞同了该文章 简介:polyloss灵感来自泰勒展开,把损失函数看作多项式函数线性组合来设计,作者发现,高阶部分倾向于防止出错,低阶部分倾向于得到结论。让损失倾向高阶使得不犯错但不敢预测高自信结果,让损...
但在检测上,有提升的反倒是符号相反的加权 My 2 cents 一种adaptive loss,提供了除改采样率以外的新思路(且两者并不等价),同时还能加速训练收敛,可以考虑
本文探讨了PolyLoss算法，提出了一种简单而强大的分类损失函数设计方法。PolyLoss算法通过将常用的分类损失函数（如交叉熵损失和焦点损失）分解为多项式函数的线性组合，使得损失函数设计更加灵活，能够根据特定任务和数据集进行定制。该算法基于泰勒展开，允许用户轻松调整不同多项式基的重要性，同时自然包含交叉...
摘要: This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification technique that is resistant to over-fitting.收藏...
A classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices T such that p(T) = 0. We consider matrices and operators which satisfy a different type of polynomial constraint. ...
Generalized Polynomial Chaos based Fault Detection and Classification for Nonlinear Dynamic Processes This paper deals with detection and classification of intermittent stochastic faults by combining a generalized polynomial chaos (gPC) representation with either Maximum Likelihood or Bayesian estimators. The gPC...
We show that each fraction of a two-level factorial design is characterized by the ANOVA representation of its polynomial indicator function. In particular, such a representation can be used to present the problem of finding a fraction with a given orthogonality structure as the set of solutions ...
论文: PolyLoss: A Polynomial Expansion Perspective of Classification Loss Functions 地址: arxiv.org/abs/2204.1251 说明:以下(我们/本文=作者们) 摘要 交叉熵损失和焦点损失是训练时最常见的选择用于分类问题的深度神经网络。然而,一个良好的损失函数可以采用更灵活的形式,并且针对不同的任务和数据集应该进行定制...
This gives a convenient classification of $k$-primitive families and a polynomial-time algorithm to recognize them. This also extends some results of Perron--Frobenius theory to nonnegative matrix families. 展开 关键词: nonnegative matrix primitivity Hurwitz products partition permutation polynomial ...