Formula

Language Model Loss as Negative Expected Utility

In the context of language modeling, the loss function can be defined as the negative expectation of a utility function UU. The objective is to find the parameters θ\theta that minimize this loss. The formula is given by: L(θ)=E(x,y)D[U(x,y;θ)]\mathcal{L}(\theta) = -\mathbb{E}_{(\mathbf{x},\mathbf{y})\sim\mathcal{D}}[U(\mathbf{x},\mathbf{y};\theta)] Here, the expectation E\mathbb{E} is calculated over pairs of inputs x\mathbf{x} and outputs y\mathbf{y} sampled from a dataset or distribution D\mathcal{D}. Minimizing this loss is equivalent to maximizing the expected utility provided by the model.

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Updated 2026-05-01

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Ch.4 Alignment - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

Computing Sciences