A Mathematical Interpretation of Autoregressive Generative Pre-Trained Transformer and Self-Supervised Learning

In this paper, we present a rigorous mathematical examination of generative pre-trained transformer (GPT) models and their autoregressive self-supervised learning mechanisms. We begin by defining natural language space knowledge space, which are two key concepts for understanding the dimensionality reduction process in GPT-based large (LLMs). By exploring projection functions inverses, establish framework analyzing generation capabilities these models. then investigate GPT representation examining its implications models’ approximation properties. Finally, discuss limitations challenges mechanisms, considering trade-offs between complexity generalization, as well incomplete inverse functions. Our findings demonstrate that possess capability to encode into low-dimensional vectors through mechanism. This comprehensive analysis provides solid foundation future advancements LLMs, promising processing tasks such translation, text summarization, question answering due improved optimization model training performance.