How Does Your Prompt Get Responses: A Study of Distance Measuring Algorithms

This paper presents a comprehensive analysis of various distance measuring algorithms used to generate responses for prompts in modern information retrieval systems. The study explores the transition from traditional keyword-based methods such as BM25 to advanced context-aware techniques including CrossEncoders and Dense Bi-Encoders. We examine multiple similarity and distance metrics including Euclidean distance, Manhattan distance, Jaccard similarity, Pearson correlation, dot product, Hamming distance, Minkowski distance, and KL divergence. Additionally, the paper investigates hybrid approaches that combine sparse and dense retrieval methods to achieve optimal performance. Through comparative analysis and practical implementations, we demonstrate how these algorithms work individually and in combination to improve document retrieval, question answering, and semantic search capabilities. Our findings highlight the importance of selecting appropriate distance metrics based on specific use cases, data characteristics, and desired outcomes in natural language processing applications.