Towards Platonic Representation for Table Reasoning: A Foundation for Permutation-Invariant Retrieval

Computer Science > Artificial Intelligence [Submitted on 13 Apr 2026] Towards Platonic Representation for Table Reasoning: A Foundation for Permutation-Invariant Retrieval Willy Carlos Tchuitcheu, Tan Lu, Ann Dooms Historical approaches to Table Representation Learning (TRL) have largely adopted the sequential paradigms of Natural Language Processing (NLP). We argue that this linearization of tables discards their essential geometric and relational structure, creating representations that are brittle to layout permutations. This paper introduces the Platonic Representation Hypothesis (PRH) for tables, positing that a semantically robust latent space for table reasoning must be intrinsically Permutation Invariant (PI). To ground this hypothesis, we first conduct a retrospective analysis of table-reasoning tasks, highlighting the pervasive serialization bias that compromises structural integrity. We then propose a formal framework to diagnose this bias, introducing two principled metrics based on Centered Kernel Alignment (CKA): (i) PI, which measures embedding drift under complete structural derangement, and (ii) rho, a Spearman-based metric that tracks the convergence of latent structures toward a canonical form as structural information is incrementally restored. Our empirical analysis quantifies an expected flaw in modern Large Language Models (LLMs): even minor layout permutations induce significant, disproportionate semantic shifts in their table embeddings. This exposes a fundamental vulnerability in RAG systems, in which table retrieval becomes fragile to layout-dependent noise rather than to semantic content. In response, we present a novel, structure-aware TRL encoder architecture that explicitly enforces the cognitive principle of cell header alignment. This model demonstrates superior geometric stability and moves towards the PI ideal. Our work provides both a foundational critique of linearized table encoders and the theoretical scaffolding for semantically stable, permutation invariant retrieval, charting a new direction for table reasoning in information systems. Subjects: Artificial Intelligence (cs.AI) ACM classes: F.2.2, I.2.7 Cite as: arXiv:2604.12133 [cs.AI]   (or arXiv:2604.12133v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.12133 Focus to learn more Submission history From: Tchuitcheu Willy Carlos [view email] [v1] Mon, 13 Apr 2026 23:33:43 UTC (8,080 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)