Compute the gradient of binary cross entropy with respect to each weight Complete the following table Feel free to round your answers to three significant digits Show your work

To compute the gradient of binary cross entropy with respect to each weight, we need to first understand the formula for binary cross entropy.

Binary cross entropy is given by the formula:

BCE = -(y * log(a) + (1-y) * log(1-a))

Where:

• BCE is the binary cross entropy loss
• y is the true label (0 or 1)
• a is the predicted probability (between 0 and 1)

Let's assume we have two weights, w1 and w2, and we want to compute the gradient of binary cross entropy with respect to these weights.

To compute the gradient, we need to calculate the partial derivatives of BCE with respect to each weight.

∂BCE/∂w1 = ∂BCE/∂a * ∂a/∂w1 ∂BCE/∂w2 = ∂BCE/∂a * ∂a/∂w2

Let's calculate each term step by step.

1. ∂BCE/∂a:

∂BCE/∂a = -(y/a - (1-y)/(1-a))

2. ∂a/∂w1:

This depends on the specific model architecture and how the weights are used. Since the question does not provide any information about the model or the weight's relationship to the predicted probability a, we cannot calculate this term without additional context.

Similarly, we cannot calculate ∂a/∂w2 without more information.

Therefore, without more information about the model architecture and the relationship between the weights and the predicted probability, we cannot complete the table for the gradient of binary cross entropy with respect to each weight