Machine Learning Optimization

Optimization · Axiom Academy

REAL WORLD Machine Learning Optimization Training neural networks through the lens of optimization theory Imagine you're training a neural network to recognize handwritten digits. You have 60,000 images, millions of parameters to tune, and one goal: minimize the error between predictions and actual labels. This is optimization at massive scale. Every time a neural network learns from data, it's solving an unconstrained optimization problem. The network adjusts billions of weights to find the minimum of a loss function that measures how wrong the predictions are. This is where all the optimization theory you've learned becomes absolutely critical. Modern language models like GPT have over 100 billion parameters. Training them requires solving optimization problems in 100-billion-dimensional space. The algorithms that make this possible are direct descendants of the gradient descent methods you've studied. The loss function in machine learning measures how well your model performs. For a neural network, this might be the mean squared error or cross-entropy loss. Let's visualize what a simple loss landscape looks like with just two parameters. Notice how the optimization path navigates through the landscape. With the right learning rate, it descends smoothly toward the minimum. Too large, and it might overshoot. Too small, and progress is painfully slow.

This is the written version of the interactive lesson above. See the full Optimization course.