Machine Learning Fundamentals · 免费预览

索引、广播与求导

访问某个轴、组合两个形状不同的张量，以及对标量目标函数求导，是后续每个模块都依赖的三项基本功。

1. Reading an axis

Reading an axis

2. Two rules of broadcasting

Two rules of broadcasting

3. Differentiating an objective

Differentiating an objective

4. What broadcasting does to shapes

Tensor a\mathbf{a} has shape (3,1)(3, 1) and tensor b\mathbf{b} has shape (1,2)(1, 2). The expression a+b\mathbf{a} + \mathbf{b} is evaluated. What is the shape of the result, and what fills its entries?

5. The derivative at the minimum

The loss ℓ(w)=12(w−5)2\ell(w) = \frac{1}{2}(w - 5)^2 has derivative ℓ′(w)=w−5\ell'(w) = w - 5. At the parameter value w=5w = 5, the derivative equals ____.

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