[Verse 1]
Picture yourself climbing down a foggy mountain slope
Blindfolded, seeking valleys where the error function's low
Each footstep calculates the steepest downward grade
Partial derivatives become your navigation aid
The cost function's landscape sprawls beneath your neural net
Alpha sets your stride length - too big and you'll regret
Overshooting minima, bouncing wall to wall
Too small and you'll be crawling, barely moving at all
[Chorus]
Gradient descent, follow the negative slope
Minimize loss, that's how algorithms cope
Backprop the errors, update every weight
Learning rate controls how fast we iterate
Gradient descent, mathematical dance
Teaching machines through calculated chance
[Verse 2]
Start with random weights scattered across parameter space
Forward pass predictions, then we calculate disgrace
Loss function measures how badly we performed
Backward propagation gets the gradients reformed
Chain rule multiplication flows from output back
Through hidden layers, every synapse feels the slack
Momentum remembers where we've traveled in the past
Helps escape plateaus and makes convergence fast
[Chorus]
Gradient descent, follow the negative slope
Minimize loss, that's how algorithms cope
Backprop the errors, update every weight
Learning rate controls how fast we iterate
Gradient descent, mathematical dance
Teaching machines through calculated chance
[Bridge]
Saddle points can trap you in their twisted geometry
Local minima deceive with false finality
Stochastic batches add noise to break the spell
Adam optimizer adapts learning rates so well
Vanishing gradients fade in networks deep
Exploding gradients make your model weep
[Verse 3]
Convergence criteria tell us when to cease
When gradients shrink small enough to signal peace
Early stopping prevents the overfitting curse
Validation loss climbing means your model's getting worse
From linear regression to transformers tall
Gradient descent optimizes through them all
[Chorus]
Gradient descent, follow the negative slope
Minimize loss, that's how algorithms cope
Backprop the errors, update every weight
Learning rate controls how fast we iterate
Gradient descent, mathematical dance
Teaching machines through calculated chance
[Outro]
Every epoch brings us closer to the goal
Optimization's heartbeat, algorithm's soul
Gradient descent