arXiv cs.AI· Marco Giunti, Fabrizia Giulia Garavaglia·· 14 小时前AI 评分18
从 Transformer 到协调变换的形式语义
From the Transformer to a Formal Semantics of Coordinated Transformations
AI 导读
研究者为参数化变换的协调系统建立了一套形式语义，以 Transformer 为典型起点但抽象掉其具体数学实现。该框架引入“变换概念”，将参数化变换的数值作用与属性层面的映射相协调，并区分系统的代数-语义共核与架构特有的功能组织。框架已应用于注意力头和残差连接，给出仅依赖共核与局部功能组织的语义解释，可推广到标准 Transformer 之外。
正文 · 原文
Abstract:We develop a formal semantics for a general class of coordinated systems of parameterized transformations, taking the Transformer as a paradigmatic starting point but abstracting from its particular mathematical instantiation. Representational vectors receive both extensional reference and ordered intensional interpretations, while parameter structures acquire relative, second-level interpretations that determine how argument properties are preserved, replaced, or combined. This yields the notion of a transforming concept: a parameterized transformation whose numerical action is coordinated with a corresponding property-level map. We then distinguish the common algebraic-semantic core of these systems from their architecture-specific functional organization, allowing different mathematical instantiations and mechanical realizations of the same abstract system type. The framework is applied to attention heads and residual connections, providing semantic explanations that depend only on the shared algebraic-semantic core and their local functional organization and therefore generalize beyond the standard Transformer. These analyses also reveal the modularity of the framework: complex architectures can be decomposed into simpler semantically coordinated subsystems whose organization may recur across different abstract system types.
| Comments: | v1: 28 pages, 9 sections, this version incorporates revisions made after the first round of peer review |
| Subjects: | Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Logic in Computer Science (cs.LO) |
| Cite as: | arXiv:2610.39735 [cs.AI] |
| (or arXiv:2610.39735v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.39735 arXiv-issued DOI via DataCite |
Submission history
From: Marco Giunti [view email]
[v1]
Thu, 29 Oct 2026 10:00:08 UTC (31 KB)
来源：arXiv cs.AI · arxiv.org