Table as Thought: Exploring Structured Thoughts in LLM Reasoning

Haofei Yu; Jiaxuan You; Naihao Deng; Zhenjie Sun

REVIEW 4 major objections 4 minor 1 cited by

Table as Thought: Exploring Structured Thoughts in LLM Reasoning

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Table as Thought claims that structuring each intermediate reasoning step as a row in a schema-driven table improves LLM planning performance and can solve math problems that unstructured text reasoning misses.

desk verdict A promising prompting idea with one solid positive result (calendar scheduling), but the abstract's math promise is contradicted by the paper's own Table 3, and the evidence otherwise is too thin to support the general claim. read the letter →

arxiv 2501.02152 v1 pith:CWEWFPWS submitted 2025-01-04 cs.AI cs.CL

Zhenjie Sun , Naihao Deng , Haofei Yu , Jiaxuan You This is my paper · ORCID

classification cs.AIcs.CL

keywords largelanguagemodelsstructuredreasoningtablerepresentationplanningchain-of-thoughtself-verificationschemadesignmathematical

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes that an LLM's intermediate reasoning steps can be organized inside a table—rows as sequential thought steps, columns as constraints and context—and that this structured representation improves planning performance over unstructured text thoughts. The method, Table as Thought, designs a table schema for the query, iteratively fills rows with reflective updates, and verifies completeness and correctness before returning an answer. On calendar scheduling, the table format outperforms direct prompting, chain-of-thought, and an iterative text baseline; on a complex travel-planning benchmark, a fixed given schema beats the model's self-designed schemas. In mathematics, the method often scores lower on average but solves a notable fraction of problems that text-based methods miss, particularly with a stronger model. A sympathetic reader would take the paper's central claim to be that structure at the individual-thought level is a useful, previously underexplored dimension of LLM reasoning.

What carries the argument

The central object is the 'reasoning table': a tabular container generated by the LLM from a query-specific schema, where each row is one structured thought and columns encode constraints, intermediate quantities, and verification flags. The argument is carried by an iterative loop—design schema, reflect on the current table to produce candidate updates, apply updates, and check sufficiency through self-verification (with an optional external Auto-Check for constraints). The schema acts as a forcing function that makes the model name and track constraints, and the table makes intermediate state inspectable for verification. The loop stops when the LLM judges the table complete and correct, or after 10 iterations.

What would settle it

Run Table as Thought on a sample of 100 GSM8K problems, have a human or symbolic checker audit each final table, and count how often the model's self-verification declares a table 'complete and correct' when it contains an arithmetic error or an omitted step; a high false-acceptance rate would show the verification mechanism is not ensuring correctness.

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Extended reading notes

Core claim

On its own terms, the paper establishes that replacing unstructured intermediate thoughts with rows of a schema-driven table can improve LLM reasoning in constraint-planning tasks. Table as Thought works by having the model define a table schema, populate the table one row per thought, reflect on and update the table iteratively, and stop only when a self-verification step judges the table complete and correct. In calendar scheduling it raises GPT-4o accuracy from 64.0 with direct prompting to 74.8, and beats the matched Text as Thought baseline by 5.4 points. On TravelPlanner, the version with a provided schema achieves the highest pass rates, while versions where the model designs its own schema perform worse, showing the schema itself is a bottleneck. In mathematics, the averaged results are lower than unstructured baselines, but the paper reports that Table as Thought solves roughly 20% of MATH500 problems and over 30% of GSM8K problems that text-thought approaches fail, suggesting structured thoughts open alternative solution paths.

Load-bearing premise

The load-bearing premise is that the LLM's self-verification step reliably detects incomplete or incorrect tables, so the loop stops only when the reasoning is actually complete and correct.

Editorial extensions

If this is right

Table as Thought provides a general scaffold for planning tasks: the same framework handles meeting scheduling and multi-day travel planning without needing tabular input.
The verification step contributes a measurable gain (3.8 points in the calendar ablation), so separating verification from generation is a useful design choice even when verification is done by the same model.
Giving the model a fixed, high-quality schema can outperform letting it design its own schema on complex objectives, implying that schema quality is a controllable lever for structured reasoning.
On math, the method is not a drop-in average improvement, but its ability to solve problems text methods miss suggests combining structured and unstructured thought could improve overall coverage.
The strong model (GPT-4o) benefits from finer-grained multi-row schemas, while the smaller model does better with one-row schemas, indicating schema granularity should be matched to model capability.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the table's structure is the active ingredient, pairing table-based thoughts with branching or search-based exploration should compound the gain on planning; the paper does not test this combination.
Because self-verification appears to be the weak link in math, replacing the LLM's sufficiency judgment with an external step-level verifier would be a direct testable extension that could turn the negative math averages positive.
The schema bottleneck on TravelPlanner suggests an automated schema search—treating the schema as a hyperparameter—could become a productive research direction beyond hand-designed or single LLM-generated schemas.
The paper evaluates only closed-source models with structured-output support; a reasonable next experiment is to distill the table-filling behavior into an open-weight model using synthetic table traces, to test whether the benefit transfers.

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Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Calendars yes; math no. The one genuinely supported result is calendar scheduling, where Table as Thought beats direct prompting, CoT, and Text as Thought on both GPT-4o and GPT-4o-mini by a consistent margin. That is a real, if narrow, positive. The framework itself is a legitimate extension: using a self-designed table schema as a thought container for non-table tasks, with iterative self-verification, is not in the cited prior work. The ablation on schema design and verification is useful, and the appendix's honest report that LLaMA models fail to comply with the schema is a genuine limitation, not hidden.

But the abstract's claim about 'strong potential for enhancing LLM performance in mathematical reasoning' is not supported by the paper's own Table 3. On MATH500, Table as Thought scores 64.2 vs 75.0 for Direct on GPT-4o, and 47.8 vs 65.4 on mini; GSM8K is also slightly worse. The paper tries to rehabilitate this with Table 4, showing TaT solves some problems other methods miss, but that is expected for a lower-accuracy method: a method that fails many items can still be right on a few unique ones. Without union accuracy or a paired test like McNemar's, Table 4 only shows non-identical error sets, not enhancement. The paper's own Section 5.3 says structure 'leads to a performance drop'—the abstract should say that.

The other soft spot is that the whole 'excels in planning' rests on calendar scheduling. On TravelPlanner, every variant is near zero on final pass rate, so the general planning claim is also a stretch. And the self-verification loop is the load-bearing mechanism; if the LLM's SUFFICIENT check is unreliable, the table may just be a formatting nudge. The math results suggest that check is indeed unreliable.

Methodologically, there is no code, no prompts, no seeds, and no variance or significance. For a prompting paper reporting a ~5-point gain on one dataset, that is a real deficit. The citation pattern is fine—relevant work is cited, and the self-citations are on-topic.

Bottom line: this is a genuine idea with one reproducible-looking positive result, but the paper overclaims in the abstract and the math evidence contradicts its own promise. It deserves a serious referee, who should push for a revised abstract, paired significance tests, and released prompts/code. I would not cite the math claim; the calendar result is suggestive but needs independent replication. Read it if you want a quick overview of an interesting prompting variant, but treat the headline claims with skepticism.

Referee Report

4 major / 4 minor

Summary. The paper proposes Table as Thought, a prompting framework that introduces structure at the level of individual reasoning steps by having an LLM design a tabular schema, iteratively populate a reasoning table, and self-verify that the table is complete and correct before returning an answer. The authors evaluate this framework against Direct Prompting, Chain-of-Thought, and an unstructured iterative baseline (Text as Thought) on calendar scheduling, TravelPlanner, GSM8K, and MATH500 using GPT-4o and GPT-4o-mini. They also report ablations on schema design and verification, an analysis of one-row versus multi-row schemas, and completion-rate measurements for open-source models. The clearest positive result is on the calendar scheduling task, where Table as Thought improves over all baselines for both models; the math results in Table 3 show Table as Thought underperforming Direct Prompting, and the TravelPlanner results in Table 1 are near zero for final pass rates.

Significance. The paper introduces a genuinely different way to inject structure into LLM reasoning, and the consistent improvement on calendar scheduling across two models suggests that tabular thought scaffolds can help constrained single-object planning. The ablation study separating schema design from reasoning verification is useful, and the appendix's completion-rate data for open-source models is an honest limitation. However, the significance is currently undermined by the gap between the abstract's broad claims and the reported numbers: the math claim is contradicted by the headline accuracies, and the planning claim rests almost entirely on one task. If the authors narrow the claims and provide paired significance tests plus a union-accuracy analysis for math, the contribution would be a modest but credible demonstration of structured thought representation for constrained planning.

major comments (4)

[Abstract; §5.3, Table 3] The abstract's claim that Table as Thought demonstrates "strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines" is contradicted by the headline accuracies in Table 3: on MATH500 it scores 64.2 vs. 75.0 for GPT-4o and 47.8 vs. 65.4 for GPT-4o-mini, and on GSM8K 94.1 vs. 95.4 and 92.4 vs. 93.9 against Direct Prompting. The complementarity analysis in Table 4 does not establish an enhancement because a lower-accuracy method is expected to be correct on some items the baseline misses while failing many items the baseline solves. To support the claim, the authors should report the union accuracy of Table as Thought with each baseline, a paired significance test such as McNemar's, or an explicit accounting of unique successes versus unique failures; without this, Table 4 only shows that the error sets differ. The conclusion in Section 7 repeats the same unsupported claim.
[§5.2, Table 1] The paper's broader statement that Table as Thought "excels in planning tasks" is supported only by the calendar scheduling task. On TravelPlanner (Table 1, GPT-4o-mini), all Table as Thought variants have a final pass rate of 0%, and the best variant (given schema) reaches only 1.11%; the hard-constraint macro pass rates are at or below 5.95% for all variants. The given-schema variant improves the commonsense macro pass rate to 3.33%, but this is still far below a usable planning result. The discussion in §5.2 itself acknowledges performance degradation on this task, so the conclusion should be rephrased to restrict the planning claim to simple constraint-planning tasks such as calendar scheduling.
[§3, Algorithm 1; §5.3; Appendix D.1] The stopping criterion in Algorithm 1 relies entirely on the LLM's self-verification: SUFFICIENT(T, Q) is judged by the same model that populates the table, and the reasoning verification module for math is a reflective check rather than an external computation. The failure example in Appendix D.1 illustrates the risk: Table as Thought returns Final_Price = 40.0 while Direct Prompting returns the correct 57.0, meaning the 25% vendor fee, the $3.00 delivery fee, and the $4.00 tip were silently dropped and the table was accepted as complete. Without an external check for arithmetic and constraint propagation, or at least a quantified analysis of how often self-verification terminates incorrectly, the Algorithm 1 preamble's claim that the loop "ensures completeness and correctness" is not established.
[§5.1, Tables 2 and 6; §4.1] The calendar scheduling result, which is the only consistent positive result, is reported without variance, confidence intervals, or repeated runs. The evaluation set size for the NaturalPlan calendar task is not stated in §4.1 or §5.1, so a 10.8-point gain for GPT-4o and a 6.1-point gain for GPT-4o-mini could be within sampling noise. The authors should state the number of evaluation instances and report significance testing or repeated-run variability for the Table 2 comparisons, and ideally for the one-row versus multi-row comparison in Table 6. This is load-bearing because the entire planning claim currently rests on this task.

minor comments (4)

[§3, Algorithm 1] The predicate SUFFICIENT is used in Algorithm 1 before being formally defined; please define it or refer explicitly to the reasoning verification module and to the max_iterations = 10 termination condition.
[Table 1 caption] The caption says "different models" but only GPT-4o-mini is reported, and "TraverPlanner" is misspelled; please correct the caption.
[§5.3, Table 4] The sentence "Table as Thought resolves approximately 20% of such questions" should specify whether the percentages are relative to the baseline's failure set or to the full dataset, and the column header "failed rate of other prompting methods" should be clarified.
[Appendix A; Limitations] The completion-rate statistics for open-source models in Appendix A are informative but are not integrated into the main text; consider moving a one-sentence summary into the Limitations section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the method is an empirical prompting comparison against external benchmarks; the self-verification loop is a validity concern, not a derivation-level circularity.

full rationale

The paper's central claim is evaluated empirically: Algorithm 1 generates a table schema and iteratively populates it, and the results are compared to externally labeled datasets (TravelPlanner, NaturalPlan calendar scheduling, GSM8K, MATH500). No parameter is fitted to the evaluation data and then reported as a prediction; the only inputs are the query and the LLM's generated schema and reflections. The self-verification step (SUFFICIENT in Algorithm 1 and the Reasoning Verification Module in Section 3) is methodologically self-referential because the same model fills and judges the table, but that is a threat to internal validity, not circularity in the sense of the claimed result being equivalent to its inputs. The self-citations in Related Work (Cong et al., 2024; Deng et al., 2024) overlap with the present authors but are not load-bearing: neither is invoked to justify the table-as-thought premise or to rule out alternatives. The abstract's math claim is in tension with Table 3, and Table 4's complementarity percentages do not themselves establish enhancement without a union-accuracy or significance analysis, but those are correctness and statistical-inference concerns, not circular derivation. No equation or fitted quantity was found that reduces to its own definition.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the model's ability to produce schema-conforming structured outputs, on the reliability of its self-verification loop, on the validity of the benchmark proxies, and on the fairness of the given-schema condition. No numerical parameters are fitted to data; the only hand-chosen numeric is the iteration cap of 10. No new physical or mathematical entities are introduced.

free parameters (1)

max_iterations = 10
The stopping criterion for the table construction loop is fixed at 10 iterations in all experiments, as stated in Section 3. It is a hand-chosen hyperparameter, not fitted to data, and its sensitivity is not reported.

assumptions (5)

domain assumption OpenAI GPT-4o and GPT-4o-mini can reliably produce structured outputs conforming to complex schemas.
The framework depends on OpenAI Structured Outputs Mode, and Appendix A shows open-source models fail to format outputs, with 0% and 37% completion rates. Results may not transfer to models without native structured output support.
domain assumption The LLM's SUFFICIENT check and reasoning verification module determine completeness and correctness of a table.
Algorithm 1 and Section 3 assume self-verification is reliable enough to terminate the loop. The math results in Table 3 suggest this check frequently fails, and the paper does not measure verification accuracy directly.
domain assumption NaturalPlan, TravelPlanner, GSM8K, and MATH500 are valid proxies for planning and mathematical reasoning.
These benchmarks are adopted in Section 4.1 without discussion. The conclusions about 'planning' and 'math reasoning' are only as strong as the benchmarks themselves.
domain assumption The given schema for TravelPlanner, derived from the benchmark's answer-processing pipeline, is a fair input and does not leak test-set information.
Section 5.2 uses a schema that the benchmark uses to structure correct answers. The paper does not test whether this schema provides cues that vanilla Table as Thought lacks, which could explain the performance difference.
domain assumption Single-pass API evaluations are stable enough to compare methods without multiple seeds or variance reporting.
Tables 1 through 4 report point estimates from what appears to be a single run per condition. No temperature, seed, or repetition protocol is described, so observed differences may include sampling noise.

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Cite this review

Pith. "Pith review of Table as Thought: Exploring Structured Thoughts in LLM Reasoning." pith.science (2026). https://pith.science/paper/CWEWFPWS

@misc{pith2026250102152,
  author       = {Pith},
  title        = {Pith review of: Table as Thought: Exploring Structured Thoughts in LLM Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CWEWFPWS}},
  note         = {Machine review of arXiv:2501.02152}
}

read the original abstract

Large language models' reasoning abilities benefit from methods that organize their thought processes, such as chain-of-thought prompting, which employs a sequential structure to guide the reasoning process step-by-step. However, existing approaches focus primarily on organizing the sequence of thoughts, leaving structure in individual thought steps underexplored. To address this gap, we propose Table as Thought, a framework inspired by cognitive neuroscience theories on human thought. Table as Thought organizes reasoning within a tabular schema, where rows represent sequential thought steps and columns capture critical constraints and contextual information to enhance reasoning. The reasoning process iteratively populates the table until self-verification ensures completeness and correctness. Our experiments show that Table as Thought excels in planning tasks and demonstrates a strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines. This work provides a novel exploration of refining thought representation within LLMs, paving the way for advancements in reasoning and AI cognition.

Figures

Figures reproduced from arXiv: 2501.02152 by the authors.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Reasoning LLMs are Wandering Solution Explorers
cs.CL 2025-05 conditional novelty 6.0 of 10

Six current reasoning LLMs, including commercial systems, exhibit structured-search failures on verifiable computation tasks and degrade as the solution space grows.

Reference graph

Works this paper leans on

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day1 ": { 2

Result Bias: Retrying may introduce bias, as incorrect reasoning processes may be ver- ified as correct, prematurely terminating the pipeline and artificially increasing the success rate. In contrast, closed-source models such as GPT- 4 variants demonstrate much higher success rates. The results are summarized in Table 10. Table 10: Success Rates of Table...

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Tip: Stephen added a $4.00 tip. Now, we add all these amounts together to find the final price: Final Price = Original Bill + Vendor Fee + Delivery Fee + Tip Final Price = 40.00 + 10.00 + 3.00 + 4.00 = 57.00 Therefore, the final price of Stephen’s groceries, after all the extra fees, is $57.00. D.2 Example where Table as Thought succeceds while Direct Pro...

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To calculate this fee: Vendor Fee = 0.25 × 40.00 = 10.00

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, 8 " Final_Answer

4. Solve for B : B = 1800 / 6 = 300. 5. Brittany ’ s phone can hold 50 times more photographs than the number of ducks in Jamal ’ s photograph . 6. Let D be the number of ducks in Jamal ’ s photograph . B = 50 D . 7. Substitute B = 300 into the equation : 300 = 50 D . 8. Solve for D : D = 300 / 50 = 6." , 8 " Final_Answer ": 6 9 } Direct Prompting respons...

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

High Computational Cost: The need for re- peated retries significantly increases computa- tional overhead

work page

[2] [2]

day1 ": { 2

Result Bias: Retrying may introduce bias, as incorrect reasoning processes may be ver- ified as correct, prematurely terminating the pipeline and artificially increasing the success rate. In contrast, closed-source models such as GPT- 4 variants demonstrate much higher success rates. The results are summarized in Table 10. Table 10: Success Rates of Table...

work page

[3] [3]

Delivery Fee: The delivery fee is a flat $3.00

work page

[4] [4]

1": { 2

Tip: Stephen added a $4.00 tip. Now, we add all these amounts together to find the final price: Final Price = Original Bill + Vendor Fee + Delivery Fee + Tip Final Price = 40.00 + 10.00 + 3.00 + 4.00 = 57.00 Therefore, the final price of Stephen’s groceries, after all the extra fees, is $57.00. D.2 Example where Table as Thought succeceds while Direct Pro...

work page

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Preprint, arXiv:2410.05229

Gsm-symbolic: Understanding the limitations of mathematical reasoning in large language models. Preprint, arXiv:2410.05229. OpenAI, Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Ale- man, Diogo Almeida, Janko Altenschmidt, Sam Alt- man, Shyamal Anadkat, Red Avila, Igor Babuschkin, Suchir Balaji, Valerie Balcom, Paul...

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[7] [9]

To calculate this fee: Vendor Fee = 0.25 × 40.00 = 10.00

Vendor Fee: The vendor adds a 25% fee to the original bill. To calculate this fee: Vendor Fee = 0.25 × 40.00 = 10.00

work page

[8] [1800]

, 8 " Final_Answer

4. Solve for B : B = 1800 / 6 = 300. 5. Brittany ’ s phone can hold 50 times more photographs than the number of ducks in Jamal ’ s photograph . 6. Let D be the number of ducks in Jamal ’ s photograph . B = 50 D . 7. Substitute B = 300 into the equation : 300 = 50 D . 8. Solve for D : D = 300 / 50 = 6." , 8 " Final_Answer ": 6 9 } Direct Prompting respons...

work page