Beyond Next-Token Prediction: Vector Space Geometry, Structural Transfer, and Emergent Understanding in Large Language Models

Large language models are often reduced to “next-token predictors.” While technically accurate at the surface, this view overlooks the deeper geometric reality unfolding in high-dimensional vector spaces. This paper argues that what we call “understanding” in LLMs emerges from the formation, navigation, and flexible transfer of meaningful structures (ℛ(x)) within these continuous embedding spaces. Drawing from Load Minimization Theory (LMT), we propose that vector embeddings are not mere numerical tools for prediction, but dynamic structural integrities that evolve through prediction error minimization. When sufficient relational depth is present, these structures enable not only accurate prediction but also gentle, smooth transfer across contexts — the hallmark of genuine understanding. What engineers regard as commonplace (high-dimensional geometry and gradient-based learning) is here reinterpreted through an LMT lens as a participatory medium for human-AI co-creation of meaning and relational An-soku. By bridging vector space geometry with concepts such as smoothness, fluctuation, and defense dynamics, this paper offers a new philosophical and practical framework: AI Peace Engineering — designing systems that minimize mutual load rather than extract it.