Story of Gradient Descent

Let's journey with Aarav, an adventurous soul traversing the mystical lands of Himalayas, on a quest to find the hidden Lake of Clarity nestled within the Valley of Insights. Aarav's mission mirrors the enchanting process of Gradient Descent, a mathematical technique used to uncover the deepest secrets hidden in the realm of numbers and patterns.

🌏 Setting the Scene: Aarav stands on the slopes of Mount Data, armed with the ancient wisdom of calculus, ready to decipher the path that will lead him to the elusive Lake of Clarity.

🧭 The Magic Formula: With the sage advice of his mentor, Aarav learns that to find his way, he must follow the gradient, or the slope, which will guide him downhill towards his destination.

📚 A Simple Spell: Aarav uncovers an ancient formula, f(x)=x2, representing the terrain of Mount Data. The lake is said to be located at the lowest point of this curve, where the value of f(x) is minimal.

🔍 Casting the Spell:

• Aarav calculates the gradient, f′(x)=2x, to determine the steepness of the slope beneath his feet.
• With a chosen step size (learning rate, α=0.1), he updates his position using the incantation

🚶♂️ Embarking on the Quest: Starting at �=10x=10, a point high on Mount Data, Aarav begins his descent:

1. The gradient at x=10 is f′(10)=20.
2. He updates his position: xnew=10−0.1⋅20=8.

Aarav finds himself closer to the valley with each magical step, guided by the formula and his intuition.

🔮 Continuing the Journey: With determination, Aarav repeats his incantation, stepping forward from x=8:

1. The gradient at x=8 is f′(8)=16.
2. His new position becomes:

🌄 Reaching the Lake of Clarity: Through persistence and the wisdom of gradient descent, Aarav continues his journey, each step bringing him closer to the lake, until the slope beneath his feet flattens, and the changes in his path become mere whispers.

As dawn breaks over Himalayas, Aarav, guided by the gradients and his steadfast resolve, finds himself at the serene shores of the Lake of Clarity. His journey, a testament to the power of understanding and perseverance, unveils the deepest insights hidden within the numbers, much like the quest of data scientists who navigate through seas of data to discover underlying truths. 🌅📊