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Make Your Own Neural Network in Python

Weight Updates Calculated

Explore the process of calculating weight updates in neural networks using error slopes and the sigmoid function. This lesson helps you understand how small adjustments refine model weights through gradient descent, enhancing network training and accuracy over time.

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An example of calculating a weight update

The following network is one we’ve worked with before, but this time we’ve added example output values from the first hidden node oj=1o_{j=1} and the second hidden node oj=2o_{j=2}. These are just made-up numbers to illustrate the method and aren’t properly worked out by feeding signals forward from the input layer.

Update weights to reduce error in neural network
Update weights to reduce error in neural network

We want to update the weight w11w_{11} between the hidden and output layers, which currently has the value 2.02.0.

Let’s write out the error slope again:

∂E∂wjk=−(tk−ok)⋅sigmoid(∑jwjk⋅oj)(1−sigmoid(∑jwjk⋅oj))⋅oj\frac{\partial E}{\partial w_{jk}} = -(t_k - o_k)\cdot \text{sigmoid}\left(\sum_j w_{jk} \cdot o_j \right) \left(1-\text{sigmoid}\left(\sum_j w_{jk} \cdot o_j\right)\right)\cdot o_j ...