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

Abstract

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

Recent Advances in Generative Adversarial Networks for Gene Expression Data: A Comprehensive Review

“…The emergence of deep learning, a subset of machine learning, has been particularly transformative in this regard. In the domain of deep learning, a network learns from the data by adjusting its internal parameters [91][92][93][94]. In this way, the model is able to perform complex tasks such as complex games with reinforcement learning [95][96][97] and, as we have explored in this review, gene expression data analysis.…”

Addressing Data Scarcity in the Medical Domain: A GPT-Based Approach for Synthetic Data Generation and Feature Extraction

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Crafting a Museum Guide Using ChatGPT4

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