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Formula for Sequential Sub-Problem Generation
When generating sub-problems step-by-step during a decomposition process, the formulation of each new sub-problem depends on the history of the task. The -th sub-problem, , is created by a generation function that considers the original problem along with the preceding sub-problems and their respective solutions . This relationship is represented mathematically by the equation: .
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Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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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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Formula for Sequential Sub-Problem Solving
A problem-solving system is designed to break down a large initial problem () into a series of smaller steps. The process for generating the i-th step () is described by the formula: ) where represents all the preceding steps and their solutions. What does this formula imply about the system's approach to breaking down the problem?
Analyzing Problem Decomposition Strategies
A problem-solving process is defined by the formula ), where is the i-th sub-problem, is the original problem, and represents the set of all preceding sub-problems and their answers. This formula implies that all sub-problems can be determined and generated in a single step before any of them are solved.