calculus

Posts tagged “calculus”

2 posts found

Oct 8, 2025131 min readfoundation

Multi-Layer Perceptrons: How Neural Networks Bend Space to See

Why does a 3-layer network solve problems a 1000-neuron single layer cannot? Understanding forward propagation, the exponential efficiency of depth, and how simple operations compose into hierarchical reasoning.

forward-propagation mlp multi-layer-perceptron machine-learning fundamentals intermediate calculus optimization

Sep 30, 2025110 min readfoundation

Gradient Descent: Theory, Mathematics, and Implementation

Why does walking downhill in parameter space solve everything from linear regression to GPT? A rigorous treatment of gradient descent: convergence theory, variants and the challenges of real-world optimization.

optimization gradient-descent machine-learning fundamentals intermediate calculus linear-regression