[Verse 1]
Neural network forward, data flows ahead
Input through the layers, predictions being fed
But when the output's wrong, we gotta learn somehow
Time to flip the script and teach the network now
Gradient descent waiting, weights need to adjust
Calculate the error, optimization's a must
From output back to input, signals propagate
Backprop algorithm seals the learning fate
[Chorus]
Back back back propagation
Chain rule drives the calculation
Error flows in reverse direction
Weights get their correction
Gradient flows, the network knows
How to minimize those loss function woes
Back back back propagation
Foundation of our education
[Verse 2]
Start with loss function, measure what went wrong
Partial derivatives keep the learning strong
Chain rule connects each layer to the next
Mathematical magic, no need to be perplexed
Delta at the output, flowing layer by layer
Each neuron gets its signal, weight updates never stray here
Learning rate controls how big the steps we take
One epoch at a time, better networks we make
[Chorus]
Back back back propagation
Chain rule drives the calculation
Error flows in reverse direction
Weights get their correction
Gradient flows, the network knows
How to minimize those loss function woes
Back back back propagation
Foundation of our education
[Bridge]
Forward pass for prediction
Backward pass for correction
Sigmoid, ReLU, tanh activation
All part of the equation
Vanishing gradients, exploding too
Batch normalization pulls us through
Learning rate scheduling, momentum's key
Backprop optimization, setting knowledge free
[Verse 3]
Hidden layers learning features automatically
Weights and biases adjusting systematically
Stochastic gradient descent, mini-batches flow
Adam optimizer helping convergence grow
Computational graph maps the journey clear
Automatic differentiation, derivatives appear
From perceptron simple to networks deep and wide
Backpropagation's been our faithful guide
[Chorus]
Back back back propagation
Chain rule drives the calculation
Error flows in reverse direction
Weights get their correction
Gradient flows, the network knows
How to minimize those loss function woes
Back back back propagation
Foundation of our education
[Outro]
Neural networks learning, backprop leads the way
Error backward flowing, weights update every day
From input to output, then output back to start
Backpropagation algorithm, machine learning's heart