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Type hello, world! into an LLM. To you, that string is already meaningful: two familiar words, a comma, a space, and an exclamation mark. To the ne...

Take a simple completion: “Alice gave Bob the book because wanted it.” Suppose the model assigns a high target logit $y$ to the correct next token....

A robot is about to push a puck across a table. There is a target marked a little farther away, and beyond it, the edge. A gentle push might leave ...

Suppose you want to train a model with a matrix optimizer such as Muon. The optimizer does not think of a weight matrix as a bag of independent num...

A plugin registers commands, subscribes to events, allocates resources, and changes shared state. Loading is easy because the host can start execut...

Imagine an LLM solving a math problem. It samples a full reasoning trace, you run a verifier, and the verifier returns a number: perhaps 0 for a co...

Imagine training a robot arm from a replay buffer that contains plenty of examples of ordinary motions—move left, move right, lower the gripper—but...

A diagram-rich generated explanation from the public library.

A diagram-rich generated explanation from the public library.

A diagram-rich generated explanation from the public library.

A diagram-rich generated explanation from the public library.

Backend Engineering from first principles