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Recursive Formula for Sub-Problem Generation
This formula provides a recursive definition for generating the i-th sub-problem, . It is expressed as: Here, the sub-problem is defined by a function that takes the original problem as context, along with the sub-problem itself and its answer . This structure implies that a valid sub-problem must satisfy this self-referential condition.
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Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Computing Sciences
Foundations of Large Language Models Course
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Recursive Formula for Sub-Problem Generation
Formula for Sequential Sub-Problem Generation
A user wants a language model to write a comprehensive travel guide for Paris. To manage this complex task, they first prompt the model to create a list of key sections to cover, such as 'Famous Landmarks,' 'Local Cuisine,' and 'Transportation Tips.' This process of breaking down the main task into a set of smaller, structured parts can be represented by the formula {p_1, ..., p_n} = G(p_0). In this scenario, what does the function G represent?
Decomposition of a Planning Task
Explaining the Problem Decomposition Formula
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A method for defining sub-problems uses the following recursive formula: In this formula, is the i-th sub-problem, is the original problem, is the answer to , and is a generation function. What is the most significant implication of this self-referential structure for defining a valid sub-problem?
Evaluating Sub-Problem Validity
Analyzing the Self-Referential Nature of Sub-Problem Generation