Variational Autoencoders (VAEs) and other generative models are widely employed in artificial intelligence to synthesize new data. However, current approaches rely on Euclidean geometric assumptions and statistical approximations that fail to capture the structured and emergent nature of data generation. This paper introduces the Convergent Fusion Paradigm (CFP) theory, a novel geometric framework that redefines data generation by integrating dimensional expansion accompanied by qualitative transformation. By modifying the latent space geometry to interact with emergent high-dimensional structures, CFP theory addresses key challenges such as identifiability issues and unintended artifacts like hallucinations in Large Language Models (LLMs). CFP theory is based on two key conceptual hypotheses that redefine how generative models structure relationships between data and algorithms. Through the lens of CFP theory, we critically examine existing metric-learning approaches. CFP theory advances this perspective by introducing time-reversed metric embeddings and structural convergence mechanisms, leading to a novel geometric approach that better accounts for data generation as a structured epistemic process. Beyond its computational implications, CFP theory provides philosophical insights into the ontological underpinnings of data generation. By offering a systematic framework for high-dimensional learning dynamics, CFP theory contributes to establishing a theoretical foundation for understanding the data-relationship structures in AI. Finally, future research in CFP theory will be led to its implications for fully realizing qualitative transformations, introducing the potential of Hilbert space in generative modeling.

翻译：变分自编码器（VAE）及其他生成模型在人工智能领域被广泛用于合成新数据。然而，现有方法依赖于欧几里得几何假设与统计近似，未能捕捉数据生成的结构化与涌现特性。本文提出收敛融合范式（CFP）理论，这是一种新颖的几何框架，通过整合伴随质性变换的维度扩展，重新定义了数据生成过程。通过修改潜在空间几何以与涌现的高维结构交互，CFP理论解决了可识别性难题以及大型语言模型（LLMs）中幻觉等非预期伪影等关键挑战。CFP理论基于两个核心概念假设，重新定义了生成模型如何构建数据与算法之间的关系。借助CFP理论的视角，我们对现有度量学习方法进行了批判性审视。CFP理论通过引入时间反演度量嵌入与结构收敛机制推进了这一视角，形成了一种新颖的几何方法，能更好地将数据生成解释为结构化的认知过程。除计算意义外，CFP理论还为数据生成的本体论基础提供了哲学洞见。通过为高维学习动力学提供系统化框架，CFP理论有助于建立理解人工智能中数据关系结构的理论基础。最后，CFP理论的未来研究将导向其实现完全质性转化的应用前景，并探索希尔伯特空间在生成建模中的潜力。