Statistical Embeddings for Similarity, Retrieval, and Interpretable Alignment of Numeric Tabular Datasets
Authors: M. Ross Kunz, John Merickel, Keith Wilson
Organizations: 1*Idaho National Laboratory.
Abstract
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches either target predictive modeling over individual datasets, which requires a shared set of variable definitions, or lack mechanisms for interpretable cross-dataset alignment. The proposed methodology characterizes numeric tabular datasets through structured exploratory data analysis descriptors, embeds those descriptors into a shared vector space using a pretrained sentence transformer, and quantifies cross-dataset similarity via Canonical Correlation Analysis (CCA). Furthermore, a penalized formulation of CCA is applied to recover sparse, interpretable variable-level correspondences between datasets, identifying which statistical descriptors or variable-level quantities drive cross-dataset alignment without requiring shared variable names or feature conventions. Differential privacy is optionally applied to the descriptor set prior to embedding, supporting deployment in sensitive data contexts without requiring access to raw observations at time of comparison. The methodology is evaluated across 15 datasets spanning general-purpose benchmarks, materials informatics, and nuclear-grade graphite characterization. Results demonstrate a total P@1 score of 0.9, with known nearest-neighbor retrieval and cluster structure remaining robust across embedding ablations and differential privacy budgets. The proposed framework provides a principled pathway for integrating heterogeneous numeric data into retrieval-augmented generation pipelines while preserving statistical context, with direct applications to data-driven algorithm selection and simulation model initialization for unknown datasets.
Foundation models have established unified representations for natural language processing, yet this paradigm remains largely unexplored for tabular data. Existing methods face fundamental limitations: LLM-based approaches lack retrieval-compatible vector outputs, whereas text embedding models often fail to capture tabular structure and numerical semantics. To bridge this gap, we first introduce the Tabular Embedding Benchmark (TabBench), a comprehensive suite designed to evaluate the tabular understanding capability of embedding models. We then propose TabEmbed, the first generalist embedding model that unifies tabular classification and retrieval within a shared embedding space. By reformulating diverse tabular tasks as semantic matching problems, TabEmbed leverages large-scale contrastive learning with positive-aware hard negative mining to discern fine-grained structural and numerical nuances. Experimental results on TabBench demonstrate that TabEmbed significantly outperforms state-of-the-art text embedding models, establishing a new baseline for universal tabular representation learning. Code and datasets are publicly available at https://github.com/qiangminjie27/TabEmbed and https://huggingface.co/datasets/qiangminjie27/TabBench.
Tabular data is the dominant structured-data modality, and learning table representations has become a core research direction. Table-level embeddings in particular underpin a wide range of applications, including table retrieval, data lake discovery, and table classification. Despite their importance, there is still limited understanding of how different embedding approaches behave across tasks, making systematic evaluation and analysis essential. In this work, we introduce a systematic evaluation of table-level embeddings that captures several complementary properties required for downstream effectiveness. We realize this evaluation by extending TEmBed, a recently proposed testbed for tabular embeddings, whose table-level coverage is currently limited to a single retrieval task. An empirical study over the TEmBed model pool confirms that no single model excels across all tasks, demonstrating that table-level embedding quality cannot be reduced to retrieval alone.
Tabular foundation models aim to learn universal representations of tabular data that transfer across tasks and domains, enabling applications such as table retrieval, semantic search and table-based prediction. Despite the growing number of such models, it remains unclear which approach works best in practice, as existing methods are often evaluated under task-specific settings that make direct comparison difficult. To address this, we introduce TEmBed, the Tabular Embedding Test Bed, a unified benchmark for systematically evaluating tabular embeddings across four representation levels: cell, row, column, and table. Evaluating a diverse set of tabular representation learning models, we show that which model to use depends on the task and representation level. Our results offer practical guidance for selecting tabular embeddings in real-world applications and lay the groundwork for developing more general-purpose tabular representation models.