[Verse 1]
Started with a problem, gotta minimize the cost
Got a function that's non-convex, data points are lost
Initialize my parameters, random's where I start
Learning rate's my compass, gradient's my art
Take the partial derivatives, direction crystal clear
Negative gradient points the way, optimization's here
Step by step we're climbing down this mathematical hill
West coast wisdom in my code, algorithmic skill
[Chorus]
Go down, go down, follow the slope
Learning rate times gradient, that's our only hope
Go down, go down, till we converge
Minimize the loss function, let the math emerge
Gradient descent, gradient descent
Finding global minimum is our main intent
[Verse 2]
Batch gradient uses all the data every time
Stochastic picks just one point, keeps the process prime
Mini-batch is hybrid flow, best of both worlds
Momentum helps us navigate when the gradient swirls
Learning rate too high and we'll overshoot the mark
Too low and convergence crawls, stuck here in the dark
Adaptive methods change the rate, AdaGrad and more
RMSprop and Adam got the keys to unlock the door
[Chorus]
Go down, go down, follow the slope
Learning rate times gradient, that's our only hope
Go down, go down, till we converge
Minimize the loss function, let the math emerge
Gradient descent, gradient descent
Finding global minimum is our main intent
[Bridge]
Local minimum traps us, saddle points deceive
But with proper initialization, we can still achieve
Escaping from the plateau when the gradient's flat
Careful with dimensions, that's where we're at
[Verse 3]
Backpropagation flows the gradients upstream
Chain rule multiplication, living the dream
Neural networks learn this way, layer after layer
Weights and biases updating, optimization player
Convergence criteria tell us when we're done
Tolerance for change achieved, the battle's finally won
From linear regression to deep learning's might
Gradient descent's the engine, making models tight
[Chorus]
Go down, go down, follow the slope
Learning rate times gradient, that's our only hope
Go down, go down, till we converge
Minimize the loss function, let the math emerge
Gradient descent, gradient descent
Finding global minimum is our main intent
[Outro]
West coast optimization, mathematical flow
Gradient descent forever, that's the way to go
Cost function minimized, parameters aligned
Gradient descent mastery, algorithm refined