In a realm where data rules and numbers swarm,
There lies a quest to find the norm.
In this vast sea of computations and sums,
Gradient descent is the song that hums.
A method so simple yet so profound,
A seeker of minimum, that's where it's bound.
It starts at a point, chosen at will,
A landscape to traverse, a mission to fulfill.
You see, our mission is to minimize the cost,
Erratic predictions are what we've lost.
An optimal solution, that's the quest,
To find the best parameters that fit the best.
In the realm of machine, both wide and deep,
Where weights and biases in layers do seep,
Cost function's curves, they twist and shout,
Gradient Descent will figure it out.
Descending the path of steepest slope,
With learning rate as our guiding rope.
For each step taken, adjustment is made,
Moving closer to the valley, where the answers are laid.
Partial derivatives mark the way,
Telling us how much to sway.
We subtract this from the old value,
A small step towards the residue.
This iteration is repeated, time and again,
In the space of parameters, amidst the plain.
Until we find, in joy and mirth,
The lowest point, the model's worth.
And so you see, this wondrous dance,
A mesmerizing, elegant, mathematical prance,
That's how gradient descent does play,
In the realm where data holds the sway.
Yet remember this, my curious friend,
On the learning rate, we much depend.
Too large, we might just overshoot,
Too small, the progress is minute.
A balance we seek, a balance we find,
In the intricate dance of the algorithm kind.
Gradient descent, our loyal guide,
In the world of data, far and wide.
