PolynomialIntegral domainThe Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete descriptiondoi:10.1007/s00010-017-0477-8Marichal, Jean-Luc...
We investigate, for the case of unary function symbols, polynomial orderings on term algebras, that is reduction orderings determined by polynomial interpretations of the function symbols. Any total reduction ordering over unary function symbols can be characterised in terms of numerical invariants deter...
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...
论文笔记: ICLR 2022 | POLYLOSS: A POLYNOMIAL EXPANSION PERSPECTIVE OF CLASSIFICATION LOSS FUNCTIONS 论文: PolyLoss: A Polynomial Expansion Perspective of Classification Loss Functions 地址: https://arxiv.org/abs/2204.12511?context=cs说明:以下(我们/本文=作者们) 摘要交叉熵损失… 打工仔 PolyLoss:一种...
Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple SaddleQuadratic differential systemssemi-elemental triple saddlephase portraitsbifurcation diagramalgebraic invariantsThe study of planar quadratic differential systems is very important not only because they ...
相较于基线模型，PolyLoss实现了更好的性能。通过引入一个额外的超参数和添加一行代码，Poly-1公式能够实现对交叉熵损失和焦点损失的改进。研究人员发现，通过调整多项式系数，尤其是调整第一个多项式系数（Poly-1公式），能够显著提升模型性能，且无需大量代码变动和超参数调整。总之，PolyLoss为理解和改进...
Based on this we propose a polynomial classification scheme in which entanglement types are identified through "tangle patterns." This scheme provides a practicable way to classify states of arbitrary multipartite systems. Moreover, the use of polynomials induces a corresponding quantification of the ...
We give the exact number of topologically different separatrix configurations on the Poincar disc for complex polynomial differential equations with only centre singularities.doi:10.1080/10236198.2012.721782Feng Rongsupa/supsup*/supGordon and Breach Science Publishers SAJournal of Difference Equations & ...
Use 'PolynomialOrder',q to specify a polynomial kernel of order q. G(xj,xk)=(1+xj′xk)q You can set your own kernel function, for example, kernel, by setting 'KernelFunction','kernel'. The value kernel must have this form. function G = kernel(U,V)where: U is an m-by-p ...
把原始的 Cross Entropy Loss 和 Focal Loss 以泰勒展开的形式进行分析,发现后者是前者把系数进行水平移动后的结果。作者提出了Polyloss可以单独调节每个多项式前的系数,并且在分类和检测中适用的系数符号相反 通过对两个loss进行多项式展开 LCE=−log(Pt)=∑j=1∞1/j(1−Pt)j=(1−Pt)+1/2(1−Pt...