How models actually learn, from vanilla gradient descent to Adam
Machine learning looks like prediction, classification, generation, recommendation. Under the hood it is one repeated mathematical act: choose numbers, measure how bad they are, then change the numbers to make the badness smaller. That is optimization.
The numbers are the model's parameters, usually collected into one huge vector θ. The badness score is the loss, written L(θ). Training means searching through parameter space for a setting that makes that loss small. The shorthand below says exactly that: argmin returns the winning input (the θ that makes the loss smallest), not the winning score, and the star on θ⋆ marks it as that best setting.
A greenhouse irrigation panel can have thousands of tiny sprinkler zones. Each setting changes how healthy the plants become, but you only see the final crop score after the water has run. A neural network is similar: the parameters are the sprinkler settings, the loss is the crop score you want to improve, and optimization is the rule for changing many settings together.