迈向表格推理的柏拉图表示：一种排列不变检索的基础
Towards Platonic Representation for Table Reasoning: A Foundation for Permutation-Invariant Retrieval
AI总结：
本文提出柏拉图表示假设，主张表格推理需要内在排列不变的潜在空间，通过分析和实验揭示了现有模型在布局变化下的脆弱性，并提出结构感知的表格推理编码器。
摘要：
历史上的表格表示学习（TRL）方法大多采用了自然语言处理（NLP）的序列范式。我们认为这种线性化表格会丢弃其本质的几何和关系结构，导致表示对布局排列不敏感。本文介绍了表格的柏拉图表示假设（PRH），认为表格推理的语义稳健潜在空间必须本质上是排列不变的。为了验证这一假设，我们首先回顾了表格推理任务，突显了普遍存在的序列偏差问题。然后我们提出一个正式框架来诊断这一偏差，引入了基于中心核对齐（CKA）的两个原则性指标：（i）PI，衡量嵌入漂移在完全结构破坏下的情况，以及（ii）rho，一个基于斯皮尔曼的指标，追踪潜在结构向标准形式收敛的情况。我们的实证分析量化了现代大语言模型（LLMs）的一个预期缺陷：即使轻微的布局排列也会导致其表格嵌入产生显著且不成比例的语义变化。这暴露了检索增强生成（RAG）系统的一个根本性漏洞，即表格检索变得对布局相关的噪声敏感，而不是语义内容。为此，我们提出了一个新颖的结构感知TRL编码器架构，明确强制执行单元格标题对齐的认知原则。该模型在几何稳定性方面表现出色，并向PI理想迈进。我们的工作既对线性化表格编码器进行了基础批判，也为语义稳定、排列不变的检索提供了理论基础，为信息系统的表格推理指明了新方向。
英文摘要：
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.
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