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

2026-04-13

AI Summary

This work addresses a critical limitation in existing tabular representation learning methods, which rely on serialization and thereby disrupt the inherent geometric and relational structure of tables, resulting in layout sensitivity and semantic fragility. To overcome this, the authors propose the “Platonic Representation Hypothesis,” asserting that an ideal tabular representation should be permutation-invariant. Guided by this principle, they develop a structure-aware encoder that explicitly models alignment relationships between cells and headers. The study formally establishes permutation invariance as a foundational criterion for tabular representations, introduces a theoretical framework to diagnose serialization-induced biases, and proposes novel evaluation metrics—PI (based on Centered Kernel Alignment) and ρ (based on Spearman correlation)—to quantify invariance. Experiments reveal that mainstream large language models exhibit substantial semantic shifts under minor layout perturbations, whereas the proposed architecture significantly enhances geometric stability and better approximates the ideal permutation-invariant representation.

Technology Category

Knowledge Representation and Reasoning: ArgumentationMachine Learning: Representation LearningComputer Vision: Representation Learning for Vision

Application Category

Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsSemantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

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.

Problem

• Table Representation Learning
• Permutation Invariance
• Structural Integrity
• Layout Permutation
• Semantic Robustness

Innovation

• Permutation Invariance
• Table Representation Learning
• Platonic Representation Hypothesis
• Structure-aware Encoding
• Centered Kernel Alignment