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Introduction to Neural Networks
Introduction to Neural Networks
Challenge: Training the Perceptron
Before proceeding with training the perceptron, keep in mind that it uses the binary cross-entropy loss function discussed earlier. The final key concept before implementing backpropagation is the formula for the derivative of this loss function with respect to the output activations, an. Below are the formulas for the loss function and its derivative:
To verify that the perceptron is training correctly, the fit()
method also prints the average loss at each epoch. This is calculated by averaging the loss over all training examples in that epoch:
Finally, the formulas for computing gradients are as follows:
The sample training data along with the corresponding labels are stored as NumPy arrays in the utils.py
file. Additionally, instances of the activation functions are also defined there:
Swipe to start coding
- Compute the following gradients:
dz
,d_weights
,d_biases
, andda_prev
in thebackward()
method of theLayer
class. - Compute the
output
of the model in thefit()
method of thePerceptron
class. - Compute
da
(dan) before the loop, which is the gradient of the loss with respect to output activations. - Compute
da
and perform backpropagation in the loop by calling the appropriate method for each of the layers.
If you implemented training correctly, given the learning rate of 0.01
, the loss should steadily decrease with each epoch.
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Challenge: Training the Perceptron
Before proceeding with training the perceptron, keep in mind that it uses the binary cross-entropy loss function discussed earlier. The final key concept before implementing backpropagation is the formula for the derivative of this loss function with respect to the output activations, an. Below are the formulas for the loss function and its derivative:
To verify that the perceptron is training correctly, the fit()
method also prints the average loss at each epoch. This is calculated by averaging the loss over all training examples in that epoch:
Finally, the formulas for computing gradients are as follows:
The sample training data along with the corresponding labels are stored as NumPy arrays in the utils.py
file. Additionally, instances of the activation functions are also defined there:
Swipe to start coding
- Compute the following gradients:
dz
,d_weights
,d_biases
, andda_prev
in thebackward()
method of theLayer
class. - Compute the
output
of the model in thefit()
method of thePerceptron
class. - Compute
da
(dan) before the loop, which is the gradient of the loss with respect to output activations. - Compute
da
and perform backpropagation in the loop by calling the appropriate method for each of the layers.
If you implemented training correctly, given the learning rate of 0.01
, the loss should steadily decrease with each epoch.
Рішення
Дякуємо за ваш відгук!