Bridge to Backpropagation

Neural network structure explains the forward computation; backpropagation explains how loss assigns responsibility to parameters.

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Bridge To Backpropagation

This chapter described the structure of a neural network.

The progression was:

neuron -> weighted sum -> bias -> activation

Then:

layer -> input layer -> hidden layer -> output layer

And finally:

forward pass -> loss computation -> function composition

A neural network is a parameterized function built from layers.

The forward pass explains how output is produced.

input -> layer transformations -> output

It shows what the current parameters compute.

But it does not yet explain how to change those parameters.

The forward pass computes output; it does not by itself train the network.

Loss measures how wrong the output was.

output -> compare with target -> loss

But loss by itself still does not say exactly which parameter should change by how much.

The network may contain many weights and biases.

Loss gives the error, but training needs parameter responsibility.

Backpropagation answers the next question:

how did each parameter contribute to the loss?

Since the network is a composition of functions, changing an earlier parameter can affect later values and final loss.

Backpropagation uses that chain of dependency to compute gradients.

Backpropagation connects final loss back to internal parameters.

The next chapter begins with the training loop.

The core pattern is:

1. forward pass computes output
2. loss computation measures error
3. backward pass computes gradients
4. optimizer updates parameters

This completes the learning loop introduced in optimization.

Backpropagation explains how neural networks learn from loss.

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Training Loop