artificial-intelligence - 偏差在神经网络中的作用(Role of Bias in Neural Networks)

Question

I'm aware of the Gradient Descent and the Back-propagation Theorem.

(我知道梯度下降和反向传播定理。)

What I don't get is: When is using a bias important and how do you use it?

(我没有得到的是：什么时候使用偏见很重要，你如何使用它？)

For example, when mapping the AND function, when I use 2 inputs and 1 output, it does not give the correct weights, however, when I use 3 inputs (1 of which is a bias), it gives the correct weights.

(例如，当映射AND功能时，当我使用2个输入和1个输出时，它不会给出正确的权重，但是，当我使用3个输入（其中1个是偏置）时，它会给出正确的权重。)

  ask by Karan translate from so

Answer 1

I think that biases are almost always helpful.

(我认为偏见几乎总是有用的。)

In effect, a bias value allows you to shift the activation function to the left or right , which may be critical for successful learning.

(实际上， 偏差值允许您将激活功能向左或向右移动 ，这对于成功学习可能是至关重要的。)

It might help to look at a simple example.

(看一个简单的例子可能会有所帮助。)

Consider this 1-input, 1-output network that has no bias:

(考虑这个没有偏差的1输入，1输出网络：)

The output of the network is computed by multiplying the input (x) by the weight (w ₀ ) and passing the result through some kind of activation function (eg a sigmoid function.)

(通过将输入（x）乘以权重（w ₀ ）并将结果通过某种激活函数（例如，sigmoid函数）来计算网络的输出。)

Here is the function that this network computes, for various values of w ₀ :

(对于w _0的各种值，这是该网络计算的函数：)

Changing the weight w ₀ essentially changes the "steepness" of the sigmoid.

(改变重量w ₀基本上改变了S形的“陡度”。)

That's useful, but what if you wanted the network to output 0 when x is 2?

(这很有用，但如果你希望网络在x为2时输出0怎么办？)

Just changing the steepness of the sigmoid won't really work -- you want to be able to shift the entire curve to the right .

(只是改变S形的陡峭度并不会真正起作用 - 你希望能够将整条曲线向右移动 。)

That's exactly what the bias allows you to do.

(这正是偏见允许你做的事情。)

If we add a bias to that network, like so:

(如果我们向该网络添加偏见，就像这样：)

...then the output of the network becomes sig(w ₀ *x + w ₁ *1.0).

(...然后网络的输出变为sig（w ₀ * x + w ₁ * 1.0）。)

Here is what the output of the network looks like for various values of w ₁ :

(以下是w _1的各种值的网络输出：)

Having a weight of -5 for w ₁ shifts the curve to the right, which allows us to have a network that outputs 0 when x is 2.

(对于w _1，权重为-5将曲线向右移动，这允许我们在x为2时具有输出0的网络。)