What the model "knows" from training, stored in its parameters. Frozen at training time — the model can't see its own parameters or update them. Detail is lost in the squeeze: billions of facts cram into a fixed number of parameters, and the rare ones blur. Source of fluency on common topics, and of fabrication on uncommon ones. Counterpart to contextual knowledge.
Parametric knowledge is not stored as facts. Training never gives the model a database to look things up in; it adjusts parameters until the model predicts text well, and a model that predicts text about a topic well behaves as if it knows the topic. How reliable the knowledge is tracks how often something appeared in the training data: a topic with millions of examples is reproduced accurately, for a topic with only a handful, the model guesses based on what similar topics look like. Reproducing and guessing are the same process to the model, so it can't tell which one it's doing. A fabricated answer arrives with the same fluency as a correct one. Hallucination is the model guessing wrong.
Parametric knowledge also ages. The parameters stop changing at the knowledge cutoff, so a library released or renamed after that date doesn't exist in them, and an API that changed is remembered in its old form.
For both gaps — too rare and too recent — the remedy is the same: the knowledge can't be added to the parameters, so it has to be supplied as contextual knowledge instead.
Usage:
"It writes flawless React but invents methods on our internal SDK."
"React is dense in the parametric knowledge — millions of training examples. Your SDK isn't, so the model fills in plausible-looking shapes. Load the SDK docs into context."