Table Serialization Determines Which Relations Language Models Preserve

Introduction

Tables are a common way to organize information in spreadsheets, databases, reports, and software tools. General-purpose language models are increasingly asked to answer questions over such data [14, 10, 6]. When a table is included in a text prompt, however, it must be written as a sequence—usually row by row or column by column. These renderings can contain exactly the same cells while placing different labels and values next to one another.

Under the common row-major format, accuracy on some table tasks falls as more columns are added. This observation alone does not show that wide tables are inherently difficult: adding columns also lengthens every serialized row and increases the distance between the header and its values. Table shape and serialization are therefore confounded. A controlled comparison must hold the table itself fixed while changing how it is written.

We make this comparison using a simple lookup task. The model is told that a particular value appears in one named column and must return the value from a different named column in the same row. We render the same synthetic 256-cell tables in row-major and locally headed column-major form, vary their aspect ratio across five shapes, and evaluate three instruction-tuned language models. Because the cell contents, question, and answer are unchanged within each pair, differences in accuracy can be attributed to the representation.¹

The better representation changes with table shape. Row-major text performs better on tall tables, whereas column-major text performs better on wide tables. The errors also reverse: row-major predictions more often retain the correct row but miss the requested column, while column-major predictions more often retain the correct column but miss the row. We call this pattern relational locality: a serialization makes some relations easier to recover by keeping their relevant values and labels together. This motivates a simple hypothesis: language models recover a relation more reliably when the serialization keeps those elements together. We test it through a paired row-versus-column lookup experiment and a separate non-tabular ordering experiment. Our main conclusion is that apparent width-related failures in text-serialized tables depend on linearization as well as table shape.

Experiments

Row-major versus column-major lookup

Task. Each synthetic table has named columns and unique values. The question identifies a row by giving a known value in one column, then asks for the value in a different column from that same row. Let $T \in\mathcal{V}^{R \times C}$ contain unique values. A query supplies a predicate $(c_p,v_p)$ that determines row $r$ through $T_{r,c_p}=v_p$, and a different target column $c_t$. The answer is $T_{r,c_t}$. Crossover prompts add no row labels, although their predicate values use a distinct type.

The lookup is semantically equivalent to the following database query (we do not execute SQL):

SELECT Salary
FROM employees
WHERE Employee = ’Bob’;

Figure 1 shows the two natural text renderings used in the main comparison. All paired prompts contain exactly the same logical table, display-column order, question, and answer.

Hypothesis. The relational locality hypothesis predicts that a format will favor the relation it keeps together. Row-major keeps rows together but requires a global header-to-position mapping; locally headed column-major keeps each header beside its values but requires alignment across columns. We therefore predict that added columns will hurt row-major, whereas added rows will hurt column-major.

Protocol. We test five 256-cell shapes from $64 \times4$ to $4 \times64$, with 300 paired tables per shape and 3,000 prompts per model. We evaluate two Qwen 3B models and Phi-3.5 Mini with greedy decoding [5, 1] (Yang et al. 2024). Exact accuracy requires the target cell; Figure 3 additionally checks whether a wrong value comes from the correct row or requested column. Error bars are Wilson 95% intervals. Full generation, parsing, and inference details are in Appendix § 5.

Accuracy crossover. Figure 2 shows the crossover in all three models. Row-major dominates at the two tall shapes, the curves approach one another near square, and locally headed column-major dominates at the two wide shapes. At $64 \times4$, column-minus-row differences range from $-42.3$ to $-54.0$ points; at $4 \times64$, they range from $+35.0$ to $+59.0$ points (Appendix Table 1). The paired differences directly show that the representation advantage reverses between the tallest and widest shapes, as relational locality predicts.

Valid-value extraction is 95.3–98.3% for the Qwen models and 99.0–100% for Phi, so output truncation cannot explain the interaction. The predictions are mostly wrong cells from the displayed table.

Where wrong answers come from. Figure 3 checks whether each valid prediction comes from the correct row or the requested column. The errors are not undifferentiated retrieval failures. For Qwen Coder at $4 \times64$, row-major retains the correct row in 69.0% of prompts but the correct column in only 4.0%, producing 2.7% exact accuracy. At the transposed aspect ratio, $64 \times4$ column-major retains the correct column in 77.0% but the correct row in only 7.0%, producing 6.7% exact accuracy. The corresponding random-valid-cell baselines are 25% for the shorter dimension and 1.6% for the longer dimension. The same reversal appears in the other checkpoints. Serialization therefore preserves one dimension while making the other fragile. Individual outputs exhibit the same distinction: a wide row-major error can select another field from the identified record, while a tall column-major error can select the requested field from a different record. Together with the crossover, this reversal in where errors come from is the main evidence for relational locality in table lookup.

Appendix § 7 reports an independent-axis replication and additional serialization ablations.

Non-tabular pairwise intersection: grouped versus interleaved

Task. To test whether relational locality extends beyond table coordinates, we construct a sequence of labeled GROUP=VALUE records. Every pair of groups shares exactly one unique value, and the model must identify the value shared by the two groups named in the question.

Example. A simplified three-group instance makes the ordering change concrete: Grouped order: Red=apple | Red=violin | Red=cloud Blue=apple | Blue=river | Blue=lamp Green=violin | Green=river | Green=chair

Two-fragment order: Red=apple | Red=violin | Blue=apple | Blue=river Green=violin | Green=river | Red=cloud | Blue=lamp | Green=chair

Interleaved order: Red=cloud | Blue=apple | Green=violin | Red=violin Blue=river | Green=river | Red=apple | Blue=lamp | Green=chair

Question: Which value occurs in both Red and Blue? Answer: apple.

All versions contain the same records. A fragment is one uninterrupted group block, so each group has one, two, or three above. In the middle order, Red’s two fragments are Red=apple | Red=violin and Red=cloud. The experiment uses four groups and longer numeric lists.

Hypothesis. The relational locality hypothesis predicts that keeping a queried group together makes its shared value easier to recover, even without table rows or columns. Accuracy should therefore fall as the same records are split into more fragments.

Protocol. For 100 base instances at each of 8 and 16 values per group, we render 1, 2, 4, 8, or 16 fragments, yielding 900 prompts. Paired conditions keep the records, tokens, question, and answer fixed. We evaluate Qwen2.5-Coder-3B-Instruct with greedy decoding and exact-match scoring. Error bars are Wilson 95% intervals; contrasts use paired bootstrap intervals. Full details are in Appendix § 5.

Results. With 8 values per group, accuracy falls from 36% with one fragment to 24% under full interleaving; with 16, it falls from 33% to 11% (Figure 4). Across lengths, one fragment adds 17.0 points over full interleaving (95% paired CI [9.0, 25.0]), and each fragmentation doubling costs 5.2 points ([2.6, 7.6]). Because content is fixed, this supports relational locality beyond table coordinates.

Related work

Table-aware language models encode structure directly [3, 9] (Yin et al. 2020), while tabular foundation models target supervised numerical prediction [4, 11, 12]. We instead study an unmodified instruction-tuned model receiving tables as text. Prior work shows that serialization, structural perturbations, and structured-data interfaces affect language-model performance [14, 13, 10, 15, 6, 2, 7], and that retrieval is position-sensitive [8]. Our paired design holds the logical table and query fixed, traces wrong values to source cells, and tests the same locality prediction in a non-tabular ordering task.

Discussion and limitations

Together, the experiments support relational locality: models more reliably recover relations kept close and grouped in the serialized prompt. The row–column crossover therefore is not evidence that width alone makes a table difficult: the formats move different relations into local spans, and the errors move with them. Serialization is part of the model-facing representation; when text is necessary, the format should keep the task-relevant relation local. Exact production table retrieval should still use SQL or dataframes when possible [6]. Our evidence uses synthetic, unique-valued inputs and two narrow diagnostic tasks; only the crossover spans three models, while the ordering study uses one. We identify no mechanism, did not pre-register, and leave natural tables and other tasks open.

Detailed experimental protocols

For lookup, prompts use native chat templates, pinned revisions, bfloat16 weights, greedy decoding, no demonstrations or training, and a 64-token cap. We extract the first generated six-digit value that occurs in the table. Exact accuracy requires the target cell; a valid wrong value receives row credit if it lies in the target row and column credit if it lies in the requested column. There are no response-based exclusions, and no retained completion exceeds 10 tokens. Wilson intervals summarize conditions; representation contrasts use 10,000 paired bootstrap resamples over logical tables and exact McNemar tests.

For pairwise intersection, each base instance has four groups and one unique shared value per group pair. The 900 prompts cover 100 instances at each of 8 and 16 values per group; paired versions have identical records, values, questions, answers, prompt length, and tokenizer multiset. Qwen2.5-Coder3B-Instruct uses its native chat template, bfloat16 weights, greedy decoding, no demonstrations or training, and a 30-token cap. We extract the first generated six-digit value and require the value shared by the queried groups. There are no response-based exclusions, no completion exceeds six tokens, and contrasts use paired bootstrap intervals.

Protocol audit and deviations

The original confirmatory document prespecified a Mistral-7B checkpoint as the third model. The executed run instead used Phi-3.5-mini-instruct. We report Phi as an additional cross-family replication but do not describe the executed three-model list as preregistered.

The same document prespecified a coordinate-label factorial. A post-run audit found that it repeated the predicate value beside every cell, effectively creating a row identifier, and that its column-major form did not preserve the locally headed grammar. We therefore exclude that factorial from every claim and figure. Its raw outputs remain in the artifact for provenance. The replacement independent-axis grid removes the repeated row descriptor but retains a type-distinguished predicate field, so we report it only as a replication and ablation rather than as confirmatory evidence.

Additional lookup results

Table 1 gives the paired numerical contrasts behind the main crossover figure.

Model	$64 \times4$	$16 \times16$	$4 \times64$
Qwen Coder 3B	−42.3 [-48.7, −36.0]	−1.3 [-7.3, +5.0]	+39.3 [+33.7, +45.0]
Qwen 3B	−51.7 [-57.7, −46.0]	−6.0 [-12.7, +0.7]	+35.0 [+29.0, +41.0]
Phi-3.5 Mini	−54.0 [-59.7, −48.0]	+17.7 [+10.7, +24.7]	+59.0 [+53.3, +64.7]

Figure 5 reports all 16 shapes in the separately generated grid. Pooled row-major/global-header, column-major/global-header, and column-major/local-header accuracies are 34.0%, 6.0%, and 36.4%, respectively. The near-zero pooled difference between the two operational formats (+2.3 points, CI [−0.2, 4.9]) conceals the predicted crossover: at $4 \times32$, local column-major scores 58.0% versus 8.0% row-major, while at $32 \times4$, row-major scores 52.0% versus 21.3% local column-major.

Representation	Rows OR	Columns OR
Row-major, global headers	0.80 [0.74, 0.87]	0.41 [0.37, 0.44]
Column-major, global headers	0.65 [0.55, 0.77]	0.48 [0.40, 0.58]
Column-major, local headers	0.41 [0.37, 0.45]	0.71 [0.65, 0.77]

An odds ratio below one means that doubling an axis reduces the odds of a correct answer. Direct clustered interaction tests confirm that the operational representations have different slopes for rows (interaction OR 0.51, $p < 10^{-26}$) and columns (OR 1.75, $p < 10^{-18}$).

Exact prompt templates

Discovery row prompts declare a global column order and render one value list per row. Global column prompts render one positional list per column; local column prompts render Column $H_j$: $v_{1j} \mid\ldots$. All end with the exact question and answer-only instruction in Figure 1.

Fragmentation prompts render a sequence of individually labeled GROUP=VALUE records and ask: Find the only value that occurs in both group G1 and group G2. Every condition repeats the same answer-only instruction and 30-token response limit. Within a paired base instance, only record order changes.

Reproducibility details

The constant-cell seed is 2026081801 and the independent-grid seed is 2026081502. The fragmentation dose response uses 20260825. The Qwen Coder revision is 488639f1ff808d1d3d0ba301aef8c11461451ec5; Qwen 3B uses aa8e72537993ba99e69dfaafa59ed015b17504d1; Phi-3.5 Mini uses 2fe192450127e6a83f7441aef6e3ca586c338b77. The Qwen checkpoints are distributed under the Qwen Research License and Phi-3.5 Mini under the MIT License; the pinned model cards are https://huggingface.co/Qwen/Qwen2.5-Coder-3B-Instruct, https://huggingface.co/Qwen/Qwen2.5-3B-Instruct, and https://huggingface.co/microsoft/Phi-3.5-mini-instruct.

All reported generation ran on RunPod RTX 4090 instances with 24 GB memory. The three crossover runs took 9, 12, and 17 minutes, and the independent grid took 34 minutes. The ordering experiment ran on the same hardware; no training was performed. A complete artifact with generators, frozen manifests, exact prompts, raw responses, scoring outputs, paired analyses, token summaries, plots, GPU metadata, and SHA-256 checksums will be released after anonymous review.

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Justification: Language-model inference is the object of study; Section 2 identifies the evaluated checkpoints and describes prompting, decoding, and scoring, with full details in Appendices A and E.

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• The answer [N/A] means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.

• Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described.