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While the vocabulary is out, here is how the words in this journey fit together, because they get used as though they were interchangeable and they are not. Each one sits inside the one before it.
Artificial intelligence is the broad ambition, machines doing things that seem to need intelligence. A hand-written chess program counts. So does a spam filter.
Machine learning is one approach to that ambition. Rather than writing the rules, let the system work them out from data. This is the shift that arrived when machines started learning from examples.
Neural networks are one technique for machine learning, layers of simple units with adjustable weights between them.
Deep learning is neural networks with many layers, which is what made image recognition work.
Large language models are one application of deep learning, aimed at text.
Each one sits inside the last, with one important exception. Large language models are deep neural networks, but older language models include hand-counted and statistical systems. Not every language model uses deep learning, and plenty of artificial intelligence involves no learning at all.