Building upon the structuralist framework established in the previous work, Reasoning as Structure-Preserving Transformation, this paper further explores the possibility of a semantics-independent reasoning architecture: Self-Expanding Temporal Hypergraphs for Critical Structure Encoding. We postulate that reasoning can be represented as a dynamical system akin to cellular automata or the evolution of identical particles, fundamentally characterized by information compression and structure-preserving transformations. The primary discussions of this paper include:(1) Axiomatic Representation: Referencing the ideas of category theory, reformulate formalized mathematics, and code logic into hypergraphs, where objects are recursively defined subgraphs;(2) Structural Invariants: Concretizing the concept of "invariants"—substructures that remain stable under permissible perturbations (e.g., reordering, local replacement) in the reasoning space—and discussing the feasibility of treating them as fundamental units of reasoning;(3) Reinforcement Learning: Investigating potential ways for applying reinforcement learning (such as AlphaZero-like algorithms) within continuously growing representation spaces, especially strategies for search and structure evaluation amidst the expansion of both embedding spaces and neural networks;(4) Unification of Philosophy and Application: Reflecting on the potential relationship between intelligence and cosmic evolution, and envisioning the application prospects of this architecture in Intermediate Representation (IR) layer code reconstruction, automated theorem discovery, and enhancing LLM reasoning. This study aims to provide preliminary philosophical support for connecting mathematics, physics, and artificial intelligence.
Qiyang Shen (Fri,) studied this question.