Table Serialization Determines Which Relations Language Models Preserve

We study how text serialization affects table lookup in instruction-tuned language models. Our diagnostic asks the model to find the row containing a specified value under one named column, then return the value under another named column in that same row. We render the same synthetic 256-cell tables in row-major form and in column-major form with each header placed beside its values, while varying the table aspect ratio across five shapes. Across three models, the better format changes with table shape: row-major performs better on tall tables, whereas column-major performs better on wide tables. At $64\times4$, row-major leads by 42.3--54.0 percentage points; at $4\times64$, column-major leads by 35.0--59.0 points. Mapping wrong answers back to their source cells reveals a complementary error pattern: row-major tends to preserve the correct row but lose the target column, while column-major tends to preserve the correct column but lose the row. We use the term \emph{relational locality} to describe this pattern: serialization keeps one relation locally available while making the other depend on positional alignment. A separate non-tabular ordering experiment supports this interpretation. Thus, apparent width-related failures in text-serialized tables depend on linearization, not table shape alone.