张量点:使用Python进行深度学习 [英] Tensor dot: deep learning with python

问题描述

我目前正在阅读《 Python深度学习》 ，在该书中我不确定作者试图说什么，第42页.链接为

I am currently reading Deep Learning with Python where I am not sure what the author is trying to say on page 42. The link is here

更一般而言，您可以在高维张量之间取点积，遵循与前面针对2D情况概述的形状兼容性相同的规则:

More generally, you can take the dot product between higher-dimensional tensors, following the same rules for shape compatibility as outlined earlier for the 2D case:

(a, b, c, d) . (d,) -> (a, b, c)
(a, b, c, d) . (d, e) -> (a, b, c, e)

不确定他想在这里说什么.我确实了解矩阵乘法的工作原理，但是上面两行代码不清楚.

Not sure what he is trying to say here. I do understand how matrix multiplication works but the above two lines of code is not clear.

推荐答案

按照这种表示法，矩阵乘法是

Following this notation, matrix multiplication is

(a, b) * (b, c) -> (a, c)

当第二个矩阵是向量时，它简化为

When the second matrix is a vector, it simplifies to

(a, b) * (b, ) -> (a, )

现在，当第一个或第二个矩阵具有额外维度时，本书中的公式仅说明如何扩展此操作.重要的是，两者都必须具有匹配的尺寸(最后一个暗号==第一个暗号，而无需重塑)，张量可以沿着该尺寸相乘，从而消除了该尺寸.因此，结果形状的公式为:

Now, the formulas from the book simply explain how to extend this operation, when the first or second matrix has extra dimensions. It's important that both have a matching dimension (the last dim == the first dim, without reshaping), along which the tensors can be multiplied, eliminating this dimension. Hence, the formula for the result shape:

(a, b, c, d) * (d, e) -> (a, b, c, e)

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