Formula

Formula for Generalization Within a Task

The condition for a model to demonstrate generalization within a given task for a specific instruction c\mathbf{c}^* is met if its average performance on a set of new inputs exceeds a minimum threshold ϵ\epsilon. This is expressed mathematically by the formula:

1ZzZP(c,z,y)>ϵ\frac{1}{|\mathcal{Z}|} \sum_{\mathbf{z}'\in \mathcal{Z}} \mathrm{P}(\mathbf{c}^*,\mathbf{z}',\mathbf{y}') > \epsilon

where Z\mathcal{Z} represents the set of new inputs, z\mathbf{z}' is a specific input from this set, and y\mathbf{y}' is the model's corresponding output.

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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