⛰️ Gradient Descent Simulator

Visualize how gradient descent finds the minimum of a function - the foundation of neural network training!

Loss Function Landscape

Parameters

0.010
3.0
3.0
w = w - α * ∂L/∂w

Iteration

0

Loss

0.00

Current X

0.00

Current Y

0.00

What is Gradient Descent?

Gradient Descent is the fundamental optimization algorithm used to train neural networks and machine learning models. It iteratively adjusts parameters to minimize a loss function by moving in the direction of steepest descent.

How It Works

Step 1: Calculate Loss
Evaluate the loss function at the current position. This tells us how "wrong" our model is.
Step 2: Compute Gradient
Calculate the gradient (partial derivatives) ∂L/∂w. This tells us which direction is "downhill".
Step 3: Update Parameters
w_new = w_old - α * gradient
Move in the opposite direction of the gradient, scaled by the learning rate.
Step 4: Repeat
Continue until convergence (gradient ≈ 0) or maximum iterations reached.

Learning Rate (α)

The learning rate controls the size of steps we take toward the minimum:
• Too Small: Slow convergence, takes forever to reach minimum
• Too Large: May overshoot the minimum or diverge completely
• Just Right: Efficient convergence to the optimal solution

Types of Gradient Descent

Batch Gradient Descent: Uses entire dataset for each update. Accurate but slow.
Stochastic Gradient Descent (SGD): Uses one sample at a time. Fast but noisy.
Mini-Batch GD: Uses small batches. Good balance between speed and accuracy.
Momentum: Adds velocity to help escape local minima and speed up convergence.
Adam: Adaptive learning rate for each parameter. Most popular in deep learning.

Challenges

Local Minima: Function may have multiple valleys. GD can get stuck in non-optimal ones.
Saddle Points: Points where gradient is zero but not a minimum.
Vanishing/Exploding Gradients: Gradients become too small or too large in deep networks.
Choosing Learning Rate: Finding the right learning rate is crucial and problem-dependent.

Real-World Applications

• Training neural networks (backpropagation uses gradient descent)
• Linear regression, logistic regression optimization
• Support vector machines
• Deep learning models (CNNs, RNNs, Transformers)
• Recommendation systems
• Computer vision models
• Natural language processing models