Formula

Formula for Generalization Across Tasks

Generalization across tasks occurs when an instruction-fine-tuned model's average performance over all new instruction-input pairs is above a predefined threshold value, ϵ\epsilon. This condition is mathematically expressed as:

1∣D∣∑(c′,z′)∈DP(c′,z′,y′)>ϵ\frac{1}{|\mathcal{D}|} \sum_{(\mathbf{c}',\mathbf{z}') \in \mathcal{D}} \mathrm{P}(\mathbf{c}',\mathbf{z}',\mathbf{y}') > \epsilon

where D\mathcal{D} is the set of new instruction-input pairs, (c′,z′)(\mathbf{c}',\mathbf{z}') represents a specific new instruction and input from the set, and y′\mathbf{y}' is the corresponding model 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