Formula

Formula for the Critique-Refine Cycle

The critique-refine cycle can be mathematically expressed as: yk+1=Refine(x,yk,Feedback(yk))\mathbf{y}_{k+1} = \mathrm{Refine}(\mathbf{x}, \mathbf{y}_k, \mathrm{Feedback}(\mathbf{y}_k)). In this formula, yk+1\mathbf{y}_{k+1} represents the improved solution. It is generated by the Refine()\mathrm{Refine}(\cdot) function, which prompts a Large Language Model with three inputs: the original problem x\mathbf{x}, the previous solution yk\mathbf{y}_k, and the feedback on that solution, denoted as Feedback(yk)\mathrm{Feedback}(\mathbf{y}_k). This feedback is provided by a verifier.

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Updated 2026-05-06

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Ch.5 Inference - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

Computing Sciences