The Geometry of Prompting: Unveiling Distinct Mechanisms of Task Adaptation in Language Models

2025-02-11

AI Summary

This work investigates how prompting methods shape the representational geometry of decoder-only language models to uncover intrinsic mechanisms of task adaptation. Using statistical physics modeling and representation geometry analysis, the authors systematically compare diverse prompting strategies. Their findings are threefold: (1) Prompting methods with comparable performance activate markedly distinct latent-space geometries—establishing, for the first time, a theoretical mapping between prompts and underlying representation mechanisms; (2) Input distribution characteristics and label semantics critically govern few-shot in-context learning performance; (3) Quantifiable representation-level synergy and interference emerge across multitask settings. Collectively, these results provide a novel theoretical lens for understanding task generalization in large language models and lay the foundation for designing representation-aware, interpretable prompting strategies.

Technology Category

• Natural Language Processing: Prompt Engineering / Prompting
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Decoder-only language models have the ability to dynamically switch between various computational tasks based on input prompts. Despite many successful applications of prompting, there is very limited understanding of the internal mechanism behind such flexibility. In this work, we investigate how different prompting methods affect the geometry of representations in these models. Employing a framework grounded in statistical physics, we reveal that various prompting techniques, while achieving similar performance, operate through distinct representational mechanisms for task adaptation. Our analysis highlights the critical role of input distribution samples and label semantics in few-shot in-context learning. We also demonstrate evidence of synergistic and interfering interactions between different tasks on the representational level. Our work contributes to the theoretical understanding of large language models and lays the groundwork for developing more effective, representation-aware prompting strategies.

Problem

• Understand internal prompting mechanisms in language models
• Explore prompting effects on representation geometry
• Analyze task interactions at representational level

Innovation

• Statistical physics framework
• Representational mechanisms analysis
• Synergistic task interactions