假设你正在训练一个神经网络。其中一个神经元具有输入向量 [12, 35, -80, -0.4, 21]、权重 [0.1, -0.6, 0.2, -0.01, 2]、偏置 0.45 和 ReLu 激活函数。以下哪一个是 ReLu 激活函数的输出值？

Suppose you are training a neural network. One of the neurons has an input vector [12, 35, -80, -0.4, 21], weights [0.1, -0.6, 0.2, -0.01, 2], bias 0.45, and a ReLu activation function. Which value is the output of the ReLu activation function?

Question

假设你正在训练一个神经网络。其中一个神经元具有输入向量 [12, 35, -80, -0.4, 21]、权重 [0.1, -0.6, 0.2, -0.01, 2]、偏置 0.45 和 ReLu 激活函数。以下哪一个是 ReLu 激活函数的输出值？

Suppose you are training a neural network. One of the neurons has an input vector [12, 35, -80, -0.4, 21], weights [0.1, -0.6, 0.2, -0.01, 2], bias 0.45, and a ReLu activation function. Which value is the output of the ReLu activation function?

BlackTom AI · Accepted Answer

在这个问题中，我们需要先计算神经元的线性组合再应用 ReLU 激活。
第一步，计算加权和：对每个输入与对应权重相乘后求和。
12 × 0.1 = 1.2；
35 × (-0.6) = -21；
-80 × 0.2 = -16；
-0.4 × (-0.01) = 0.004；
21 × 2 = 42。
将这些项相加：1.2 - 21 - 16 + 0.004 + 42 = 6.204。
第二步，加入偏置：6.204 + 0.45 = 6.654。
第三步，应用 ReLU：ReLU(x) 等于 x 与 0 的较大值，所以 ReLU(6.654) = 6.654。
现在逐个选项分析：
-0.54：这是负数且远小于实际的线性组合结果，显然不是 ReLU 的输出。
0：只有当 z ≤ 0 时 ReLU 才输出 0，而在本题中 z = 6.654，远大于 0，因此不是输出。
1：这是一个小的正数，与实际计算的 6.654 相差很大，不能成立。
6.654：与计算得到的 ReLU 输出完全一致，因此是正确选项。

2025FallB-X-CSE571-78760 期末考试 Final Exam

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