Solution: Backpropagation Shapes and Gradients

Exercise: Backpropagation Shapes and Gradients

Solution

Backpropagation applies the chain rule. Since $d\tanh(z)/dz = 1-\tanh^2(z)$, the upstream hidden gradient is multiplied elementwise by this factor.

Takeaways

• State the assumption that makes the method valid before trusting the result.
• Connect the computation back to the finance workflow, not only to the code.
• Check whether the result depends on average-case behaviour, validation design, or numerical safeguards.