Table Serialization Determines Which Relations Language Models Preserve

In the LLM era, many symbolic and structured problems are presented to models through 1D text serialization. Yet some such problems are natively two-dimensional: their relevant relations, such as row--column correspondence or spatial adjacency, are defined by position in a 2D layout rather than by sequential order. This raises a representational question: does preserving the same symbolic entries in a 1D sequence also preserve the relational structure needed for computation? We study this issue through the lens of serialization friction: the representational mismatch in which the same underlying task instances and entries are still present, but relations that depend on layout become implicit under 1D serialization. The study uses a controlled synthetic testbed of three tasks: matrix transpose, Conway's Game of Life, and LU decomposition. In each task, the same instances are presented either as 1D text serialization or as their native 2D layout rendered as an image. Across this testbed, 1D serialization degrades more sharply as task size grows, and errors under serialization exhibit spatially structured patterns, suggesting that this presentation choice is consequential within our testbed. To further interpret these results, we add supplementary analyses that include a within-visual probe and an additional comparison of the two input presentations under the mixed-training transpose setting. These findings suggest that, for layout-defined tasks, reducing inputs to 1D serialization is not a neutral choice of representation.

Transformer-based table retrieval systems flatten structured tables into token sequences, making retrieval sensitive to the choice of serialization even when table semantics remain unchanged. We show that semantically equivalent serializations, such as $\texttt{csv}$, $\texttt{tsv}$, $\texttt{html}$, $\texttt{markdown}$, and $\texttt{ddl}$, can produce substantially different embeddings and retrieval results across multiple benchmarks and retriever families. To address this instability, we treat serialization embedding as noisy views of a shared semantic signal and use its centroid as a canonical target representation. We show that centroid averaging suppresses format-specific variation and can recover the semantic content common to different serializations when format-induced shifts differ across tables. Empirically, centroid representations outrank individual formats in aggregate pairwise comparisons across $\texttt{MPNet}$, $\texttt{BGE-M3}$, $\texttt{ReasonIR}$, and $\texttt{SPLADE}$. We further introduce a lightweight residual bottleneck adapter on top of a frozen encoder that maps single-serialization embeddings towards centroid targets while preserving variance and enforcing covariance regularization. The adapter improves robustness for several dense retrievers, though gains are model-dependent and weaker for sparse lexical retrieval. These results identify serialization sensitivity as a major source of retrieval variance and show the promise of post hoc geometric correction for serialization-invariant table retrieval.

Real-world tables are often heterogeneous, combining numerical features with free-form string columns. Table foundation models (TFMs) excel on numerical tables but require strings to be encoded numerically, while large language models (LLMs) hold semantic knowledge but are not designed for tabular predictions. Most existing bridges use LLMs as plug-in encoders for cell strings, yet how to extract representations effectively for tabular learning remains underexplored. We show that the interface between LLMs and tables matter as much as the LLM itself. Applied cell-wise, larger LLMs do not give better features. With our interface, the same LLMs improve steadily with size. TILE (Table-Interfaced LLM Embeddings) combines four ingredients: row serialization to provide cross-column context, intermediate-layer extraction to avoid layers specialized for next-token prediction, columnar pooling to remove mean pooling's length bias, and by-pass features to route numbers and categories past the LLM. Paired with TFMs, TILE sets a new state of the art for tables with strings. Across 100 datasets, it beats the strongest baseline on 89% of splits, with gains across 7 LLMs and 10 tabular learners, and ranks first on the 108-dataset STRABLE benchmark.