Training data isn't stored in the model. The model processes that data and uses it to adjust the weights and measures of its parameters (usually several to a hundred billion or more for commercial models), which are divided among several layers, hidden sizes, and attention heads. These weights and the architecture are what are hard-coded into the model during training.

Inferencing is what happens when the model generates text from an input, and at this point the weights and measures are hard-coded so it doesn't actually retain all that information it was trained on. The context window refers to how many tokens (words or phrases) it can store in its memory at a time.

For every token that it processes, it runs a series of calculations on embedded vectors passes them through several layers in which they're considered against the context of all the other tokens in the context window. This involves matrix multiplication and is very compute-heavy. Think like 1-4GB of RAM for every billion parameters, plus several more GB of RAM for the context window. There's just no way it would be able to hold its entire training dataset in RAM at a time.

You would need to integrate retrieval-augmented generation to fetch the relevant data into the context window before generating a response, but that's not at all the same as containing all that knowledge in a stateful manner

The size of the context window is fixed in the structure of the model. LLMs are still at their core artificial neural networks, so an analogy to biology might be helpful.

Think of the input layer of the model like the retinas in your eyes. Each token in the context window, after embedding (i.e. conversion to a series of numbers, because ofc it's just all math under the hood), is fed to a certain set of input neurons, just like the rods and cones in your retina capture light and convert it to electrical signals, which are passed to neurons in your optic nerve, which connect to neurons in your visual cortex, each layer along the way processing and analyzing the signal.

The number of tokens in the context window is directly proportional to the number of neurons in the input layer of the model. To make the context window bigger, you have to add more neurons to the input layer, but that quickly results in diminishing returns without adding more neurons to the inner layers to be able to process the extra information. Ultimately, you have to make the whole model larger, which means more parameters, which means more data to store and more processing power per prompt.