What question did this study set out to answer?

The aim is to establish a three-layer ceiling framework for large language models, highlighting limitations and architectural progressions.

March 3, 20260 citationsOpen Access

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

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HQHan Qin

Key Points

The aim is to establish a three-layer ceiling framework for large language models, highlighting limitations and architectural progressions.
Proposed a conceptual framework of three layers: parameters, architecture, and multimodality.
Discussed the implications of each layer in terms of rationalization, irrationalization, and imaginarization.
Analyzed the limitations of linearity within current language models and their architectures.
Identified diminishing returns when stacking parameters within existing architectures.
Showed that changing architecture addresses some structural gaps but retains one-dimensional constraints.
Discussed how multimodality introduces new perceptual dimensions yet is constrained by physical limits of digital hardware.

Abstract

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

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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

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