11. Gradient derivation of perceptron

Single layer perceptron model

The second is the predicted value , Each input node is multiplied by the corresponding weight , Add up and then add up bias.

From the weight contained in each layer to the output of the activation function , This is a whole layer .
The activation function is sigmod function
wio It refers to the upper layer i Nodes are related to this layer 0 node .x10, First floor 0 Node is no. .
Because it is a single-layer single output sensor , So there is only one node in the first layer .
E yes error, That is to say loss.
t yes meansquare error.

Derivation formula

Before deriving, you need to calculate the values of all variables once to the right , This is forward propagation .


Only follow the output node O0, And the corresponding x Of j The input value of node No. is related .

The gradient information obtained is w’=w-lr▽w, Update gradient information , Update the weight of each layer of single-layer perceptron , Through continuous calculation , Finally get a suitable w, bring xw More and more close to the real value Y.

Multi output perceptron

deduction

W1ik Come on , Only right O1k Have an impact on , For the rest O10(W1i0),O11,O12 Waiting doesn't have much effect .