Inherent Nature of Hallucination in Large Language Models: A Foundational Analysis of Causes, Mechanisms, and Theoretical Limits

Abstract We argue that hallucination is not an anomalous bug but an intrinsic, emergent property of the current auto-regressive, Transformer-based paradigm. The analysis systematically deconstructs the root causes, categorizing them into data-centric, model-centric, and inference-centric factors. We demonstrate how flaws in training data, fundamental architectural limitations, and misaligned training objectives create a latent potential for hallucination, which is then actualized by probabilistic decoding strategies. The report integrates perspectives from computability theory, which posits the theoretical inevitability of such errors; statistical learning theory, which formally links generative errors to classification failures; and information theory, which provides a quantitative language for model uncertainty. By synthesizing these theoretical frameworks with empirical evidence from state-of-the-art research, we provide a foundational understanding of why LLMs hallucinate and outline the critical open challenges that define the frontier of AI safety and reliability research.