在 中文 中使用 范数 的示例及其翻译为 英语
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在统计学中，这被称为L1范数。
范数的目标就是衡量矩阵的大小。
Cd'求解器只能优化Frobenius范数。
The‘cd' solver can only optimize the Frobenius norm.此范数也称为2-范数、向量模或欧几里德长度。
This norm is also called the 2-norm, vector magnitude, or Euclidean length.这是一个很好的例子，范数非常接近于常数：.
This is a good example where the norm is very close to constant:.这样一个数字G的范数被定义为一个整数：norm(G)=a2b2。
The norm of such a number G is defined as an integer: norm(G)= a2+ b2.例如，建议最大范数约束值在3到4之间。
For example, the maximum norm constraint is recommended with a value between 3-4.显然，范数，在这一切发生后的第二天早上，我和卢出现了…….
Evidently, Norm, Lou and I had shown up the morning after all this had happened….单位向量（unitvector）是具有单位范数（unitnorm）的向量：||x||2=1.
A unit vector is a vector with unit norm(unit length)||x||2= 1.归一化(Normalization)是缩放单个样本使其具有单位范数的过程。
Normalization is the process ofscaling individual samples to have unit norm.这个例子表明范数不是常量，但它与推力无关:.
This example shows that the norm is non-constant, but it does not correlate with the thrust:.其中，范数一般为欧几里得距离，不过亦可使用其他距离函数。
模型可以具有L1范数（LASSO）或L2（岭回归）或两者（弹性回归）。
Models can have L1 norm(LASSO) or L2(Ridge Regression) or both(elastic regression).直观上来说，向量x的范数就是衡量从原点到x的距离。
On an intuitive level, the norm of a vector x measures the distance from the origin to the point x.模型可以有L1范数(LASSO)或L2(RidgeRegression)或两者兼具。
Models can have L1 norm(LASSO) or L2(Ridge Regression) or both(elastic regression).其中一个非零分量为p(2)，因为R(:,2)是具有最大范数的R的列。
One of the nonzero components is p(2) because R(: ,2)is the column of R with largest norm.模型可以有L1范数（LASSO）或L2（岭回归，RidgeRegression）或兼具两者（弹性回归）。
Models can have L1 norm(LASSO) or L2(Ridge Regression) or both(elastic regression).希尔伯特-施密特算子的集合在范数拓扑下是闭集，当且仅当H是有限维空间。
The set of Hilbert- Schmidt operators is closed in the norm topology if, and only if, H is finite-dimensional.L2先验使用Frobenius范数，而L1先验使用L1范数。
问题是这不是实际上的範数，只是半範数，因为有除了零函数之外有（半）范数为零的函数。
The problem is that this is not really a norm, only a seminorm, because there are functions other than the zero function whose(semi)norms are zero.L2先验使用Frobenius范数，而L1先验使用按元素的(elementwise)L1范数。
The L2 prior uses the Frobenius norm, while the L1 prior uses an elementwise L1 norm.另外一个经常在机器学习中出现的范数是\(L^\infty\)范数，也被称为最大范数(maxnorm)。
One other norm that commonly arises in machine learning is the L∞ norm, also known as the max norm.这不能与半范数或伪范数相混淆，后者满足范数公理，但没有正定性。
This is not to be confused with a seminorm or pseudonorm,where the norm axioms are satisfied except for positive definiteness.梯度范数截断（Gradientnormclipping）：降低梯度消失风险的一个方法是截断其最大值(Mikolov,2012)[57]。
Gradient norm clipping One way to decrease the risk of exploding gradients is to clip their maximum value(Mikolov, 2012)[55].你可能注意到了，尽管范数历史上定义在先，人们也提出了半范数的定义，它是范数的一种非T0版本。
Although norms were historically defined first, people came up with the definition of seminorm as well, which is a sort of non-T0 version of a norm.特别地，我们将讨论一直以来在多任务学习的历史中普遍存在的两个主要思想：通过范数正则化制造各任务间的稀疏性；.
In particular, we will discuss two main ideas that have been pervasive throughout the history of multi-task learning:enforcing sparsity across tasks through norm regularization;下面章节中的所有范数都是使得上面的不等式成立的范数（这些范数通常称为能量范数）。
All norms in the following sections will be norms for which the above inequalities hold(these norms are often called an energy norm).在数学中，一个希尔伯特-施密特算子（得名于大卫·希尔伯特和埃哈德·施密特）,是希尔伯特空间H上的有界算子A，有有限的希尔伯特-施密特范数.
In mathematics, a Hilbert- Schmidt operator, named for David Hilbert and Erhard Schmidt, is a bounded operator A on a Hilbert space H with finite Hilbert-Schmidt norm.圆球可以理解为一般的希尔伯特空间范数的情况，在有限维的情况中依赖于欧氏距离；它的边界就是通常所指的单位球面。
The round ballis understood as the usual Hilbert space norm, based in the finite-dimensional case on the Euclidean distance; its boundary is what is usually meant by the unit sphere.在线性代数、泛函分析和数学的相关领域，拟范数与范数类似，它满足范数公理，除了三角不等式被替换为.
In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by.
