如何在感知器的批量訓練期間計算偏差

Question

我正在對單節點感知器實施批量訓練，但不知道如何更新我的偏差。

我正在更新重量如下：

對於每個批次，我在單個批次中運行以下臨時重量更新

# update weight_update where y[i] is the actual label and o1 is the predicted output and x[i] is the input
weight_update = weight_update + (self.weights + self.learning_rate * (y[i] - o1)*x[i])

然后一個完整的批次完成我更新我的 class 中的主要重量

# update main weights (self.weights) where len(x) is the number of samples
self.weights = self.weights + (weight_update / len(x))

Answer 1

我假設 (y[i] - o1)*x[i]) 是損失 function 重量的偏導數，我不確定你使用了什么，但假設你使用了 -1/2 * (y[i] - o1)^2

now let o1 = wx + b, where w is weight matrix and b is bias vector, 
also let, L = -1/2 * (y[i] - o1)^2
you have already calculated dLdw = dLd(o1) * d(o1)dw = (y[i] - o1) * x

In a summilar way calculate dLdb, 
dLdb = dLd(o1) * d(o1)db
dLd(o1) = (y[i] - o1)
d(o1)db = d/db (wx + b) = 0 + 1 = 1
so dLdb = (y[i] - o1) * 1

現在這條線，

weight_update = weight_update + (self.weights + self.learning_rate * (y[i] - o1)*x[i])  

此時無需添加權重，只需添加漸變即可

weight_update += self.learning_rate * dLdw
# similarily
bias_update += self.learning_rate * dLdb  

當一批完成后，就做

# update main weights (self.weights) and biases (self.biases)
# where len(x) is the number of samples
self.weights += (weight_update / len(x))
self.biases+= (bias_update / len(x)) 

# dont forget to set the values of weight_update, bias_update  to 0 

這是我幾天前寫的（MNIST 示例的 1 個隱藏分層網絡），您可能會發現這很有用