Hierarchical Factorization Structures of Computational Graphs

Author: Sergei Zubov

Affiliation: TestPress R&D Division

Abstract

We introduce a structural theory of hierarchical factorization for deterministic computational graphs. Factorization replaces interface-preserving subgraphs with block nodes while preserving external dependencies. We define factor blocks, admissible factorization steps, and iterated factorizations. The main result establishes the existence of computational towers—hierarchies of compatible graph factorizations representing the same computation.

Keywords

computational graphs, hierarchical factorization, structural decomposition, multi‑level computation, graph normalization, compositional structure