The Three Ceilings of Large Language Models: From Discreteness Deepening to Dimensional Expansion / 大语言模型的三层天花板:从离散度深化到维度扩展

Full bilingual text and framework available at self-as-an-end.net — Framework reference: self-as-an-end.net/framework.html AI's ceiling is not one layer but three. Each layer's breakthrough method is the starting point of the next. This paper argues for a three-layer progressive structure: (1) Stacking parameters—isomorphic with rationalization—diminishing returns within the same architecture are unavoidable. (2) Changing architecture—isomorphic with irrationalization—fills structural gaps, but the one-dimensionality constraint of pure language remains. (3) Multimodality—isomorphic with imaginarization—adds orthogonal perceptual dimensions, but multimodality on digital hardware is simulated imaginarization; the ceiling lies at the physical limits of digital hardware. The paper argues that multimodal architecture is the third-order chisel of language, locally negating the linearity dimension of the form-meaning binding law. Bilingual Chinese-English. AI的天花板不是一层,是三层。每层天花板的突破方式恰好是下一层的起点。本文论证三层递进结构:(一)堆参数——与有理数化同构——递减效应不可避免。(二)换架构——与无理数化同构——填补结构间隙但一维性约束不变。(三)多模态——与虚数化同构——数字硬件上的多模态是模拟的虚数化,天花板在物理极限。论证多模态架构是语言的三阶凿。中英双语。 Related Identifiers Is supplement to (LLM Paper) DOI: 10.5281/zenodo.18826633 Relation: IsSupplementTo Title: The Ontological Positioning of Large Language Models References (Language Paper) DOI: 10.5281/zenodo.18823131 Relation: References Title: Language as Second-Order Chisel: A Philosophy of Language within the Self-as-an-End Framework References (Framework Paper 4) DOI: 10.5281/zenodo.18727327 Relation: References Title: The Complete Self-as-an-End Framework References (Mathematics Paper) DOI: 10.5281/zenodo.18793538 Relation: References Title: Mathematics as Second-Order Chisel (Physics as Third-Order Chisel) References (Philosophy Paper) DOI: 10.5281/zenodo.18779382 Relation: References Title: Philosophy as Subject-Activity Notes Part of the Self-as-an-End theory series. This is the second paper in the LLM sub-series, expanding the scaling law ceiling prediction from the first LLM paper into a three-layer progressive structure. Bilingual (Chinese and English) full text. Series application papers published: Philosophy application (DOI: 10.5281/zenodo.18779382) Mathematics application (DOI: 10.5281/zenodo.18793538) Language application (DOI: 10.5281/zenodo.18823131) LLM application (DOI: 10.5281/zenodo.18826633) LLM application II — this paper