Mathematics

The Intuition of Backpropagation

An exploration of backpropagation as a dynamic application of the chain rule to minimize error in neural networks.

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The Network as a Function

f(x; W) = y

Think of a neural network as a giant, flexible machine with thousands of knobs called weights. When we feed an input in, these knobs transform it through layers until an output emerges.

Step-by-step solver

Compute Cost

Define the error between the model output and actual target values.

C(w) = \frac{1}{2}(y - y_{true})^2

Find Local Gradients

Apply the chain rule to find how the cost changes with respect to individual weights.

\frac{\partial C}{\partial w_{ij}^{(l)}} = \delta_j^{(l)} a_i^{(l-1)}

Update Weights

Apply gradient descent to adjust each weight by a small amount scaled by the learning rate.

w \leftarrow w - \eta \frac{\partial C}{\partial w}

Original question

explain to me backpropogation

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