V2EX element-wise operation

Element-wise operation

释义 Definition

element-wise operation逐元素运算 / 按元素运算。指对向量、矩阵、张量等数据结构中的每个对应位置的元素分别进行同一种运算(如加、减、乘、除、取指数、比较等),而不是进行矩阵乘法那类需要跨行列聚合的运算。常见于线性代数、数值计算与机器学习编程(如 NumPy、PyTorch、MATLAB)。

发音 Pronunciation (IPA)

/lmnt waz pren/

例句 Examples

The element-wise operation adds two arrays of the same shape.
逐元素运算会把形状相同的两个数组按对应位置相加。

In many neural networks, the activation function is applied as an element-wise operation to each entry of a tensor, while the loss may aggregate results across dimensions.
在许多神经网络中,激活函数会以逐元素运算的方式作用于张量的每个元素,而损失函数可能会在维度上进行聚合汇总。

词源 Etymology

该短语由 element(元素)+ -wise(“以……方式/按……”的后缀)+ operation(运算)组成,字面意思就是“按元素的运算”。在数学与计算机科学语境中,强调“每个位置独立处理”的计算方式,与需要整体结构参与的运算(如矩阵乘法)相对。

相关词 Related Words

文学与著作 Literary Works

  • Deep Learning(Ian Goodfellow, Yoshua Bengio, Aaron Courville)常在张量运算与激活函数语境中讨论逐元素(element-wise)计算。
  • The Matrix Cookbook(Petersen & Pedersen)在矩阵与向量的运算性质汇总中常出现逐元素(element-wise / elementwise)相关表述。
  • NumPy User Guide / Reference(NumPy 官方文档)广泛使用 “element-wise” 描述数组运算与 ufunc 的行为。
  • MATLAB Documentation(MathWorks 官方文档)用 “element-wise” 说明 .*./.^ 等按元素运算符。
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