{"id":"ef7c6106-0c27-4c0a-bc6f-103bac0420f1","arxiv_id":"2501.02152","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A table-based reasoning prompt with iterative self-verification improves GPT-4o on calendar scheduling but degrades math performance and shows no reliable gain on travel planning.","lead":"This paper introduces a prompting framework that makes large language models write their reasoning steps into a table with rows and columns, then check and update the table until it is complete. On a calendar scheduling benchmark it beats chain-of-thought prompting, but on math tasks it underperforms simple direct prompting, and its complex travel planning results are near zero.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The abstract's math claim is contradicted by Table 3; the complementarity analysis in Table 4 does not establish that Table as Thought enhances math performance, so the central claim is only clearly supported for calendar scheduling.","rationale":"The reader's identified weakest assumption, the reliability of LLM self-verification, is a real operational weakness, but it is not the most load-bearing issue for the central claim. Even an imperfect verifier could coexist with a genuinely useful structured-reasoning effect, and the paper's own ablation shows verification contributes a modest but positive gain. The more fundamental problem is that the paper's central claim promises math gains, while Table 3 directly contradicts that promise. This is an internal inconsistency, not a matter of disagreement with the field's consensus: the reported MATH500 and GSM8K accuracies are lower for Table as Thought than for direct prompting on every model and dataset. The complementarity analysis in Table 4 is insufficient because a lower-accuracy method naturally solves some questions that a higher-accuracy method misses; the reported percentages do not control for the opposite failure direction, and no union accuracy is given. The proposed concrete test would settle whether the complementarity has any practical value. TravelPlanner results are also near zero for all methods, including Table as Thought, so the central claim is supported mainly by one planning task with no reported variance. A conditional verdict remains appropriate: the paper could be strengthened by narrowing the claims to planning, reporting significance or variance, and releasing raw outputs and prompts, but as written the central claim is overstated.","tokens_in":15025,"tokens_out":5810,"duration_ms":62194,"concrete_test":"Obtain the raw per-question outputs for MATH500 and GSM8K used for Tables 3 and 4, then compute: (a) the accuracy of an oracle that uses Table as Thought's answer when Direct Prompting is wrong and Direct Prompting's answer when Table as Thought is wrong; (b) McNemar's paired test on Direct-vs-Table-as-Thought correctness outcomes; (c) the count of items where Table as Thought fails while Direct Prompting succeeds. If the oracle accuracy does not exceed Direct Prompting's standalone accuracy, or if McNemar's test is not significant, the complementarity claim in Table 4 cannot support 'strong potential' for math. Additionally, report mean and standard deviation over at least three seeds for the calendar scheduling results, since that is the only benchmark where the central claim is clearly positive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.3 and Table 3 show that Table as Thought underperforms Direct Prompting on every reported math benchmark: MATH500 64.2 vs. 75.0 (GPT-4o) and 47.8 vs. 65.4 (GPT-4o-mini); GSM8K 94.1 vs. 95.4 and 92.4 vs. 93.9. The abstract's claim of 'strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines' is therefore not supported by the headline accuracy numbers. The paper's supporting evidence is Table 4, which reports that Table as Thought solves about 20% of MATH500 questions and more than 30% of GSM8K questions that other methods miss. But this is expected for a lower-accuracy method: it can be correct on some unique items while failing many items the baseline solves. Without reporting the union accuracy of Table as Thought and the baseline, or a paired significance test such as McNemar's, Table 4 only shows that the error sets are not identical, not that the method 'enhances' performance. The paper itself concludes that adding structure in math 'leads to a performance drop.' The one consistently positive result is calendar scheduling, so the general central claim currently rests on a single task, and no variance or significance information is reported. This is more load-bearing than the unreliable self-verification loop: even if self-verification were perfect, the math accuracies in Table 3 would still contradict the abstract's promise.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15296,"tokens_out":4321,"duration_ms":42644,"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":[{"comment":"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.","section":"Abstract; §5.3, Table 3"},{"comment":"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.","section":"§5.2, Table 1"},{"comment":"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.","section":"§3, Algorithm 1; §5.3; Appendix D.1"},{"comment":"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.","section":"§5.1, Tables 2 and 6; §4.1"}],"minor_comments":[{"comment":"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.","section":"§3, Algorithm 1"},{"comment":"The caption says \"different models\" but only GPT-4o-mini is reported, and \"TraverPlanner\" is misspelled; please correct the caption.","section":"Table 1 caption"},{"comment":"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.","section":"§5.3, Table 4"},{"comment":"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.","section":"Appendix A; Limitations"}],"recommendation":"major_revision","confidential_remarks":"The paper has a valid core idea and one solid positive result, but the abstract and conclusion substantially overstate the math evidence. The math claim is contradicted by Table 3, and the complementarity argument in Table 4 is insufficient without union accuracy or paired tests. A major revision that narrows the claims to constrained planning and adds the missing statistical evidence would put the contribution on firmer ground."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nBut 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.\n\nThe 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.\n\nMethodologically, 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.\n\nBottom 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.","headline":"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.","tokens_in":15825,"tokens_out":2489,"would_cite":false,"duration_ms":22447,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["large language models","structured reasoning","table representation","planning","chain-of-thought","self-verification","schema design","mathematical reasoning"],"falsifier":"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.","tokens_in":14811,"feed_emoji":"📊","tokens_out":5991,"duration_ms":52254,"temperature":0.7,"pith_summary":"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.","feed_headline":"Putting LLM thoughts in tables lifts planning accuracy","feed_subtitle":"Organizing each reasoning step as a table row outperforms chain-of-thought on scheduling and travel planning.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Chain-of-thought prompting is the primary baseline and the sequential-structure approach the paper extends.","marker":"Wei et al., 2023"},{"why":"Tree of Thoughts is a structured reasoning baseline that organizes reasoning at the macro level.","marker":"Yao et al., 2023"},{"why":"Graph of Thoughts is another structured baseline the paper contrasts with.","marker":"Besta et al., 2024"},{"why":"Self-consistency is an unstructured multi-path method used as related work and comparison context.","marker":"Wang et al., 2023"},{"why":"Chain-of-Table is the closest table-based reasoning work, which the paper distinguishes by applying tables to non-table tasks.","marker":"Wang et al., 2024"},{"why":"TravelPlanner dataset is the complex planning benchmark whose evaluation schema is used as the given schema.","marker":"Xie et al., 2024"},{"why":"Natural Plan calendar scheduling task is the main planning evaluation.","marker":"Zheng et al., 2024"},{"why":"GSM8K dataset provides grade-school-level math word problems for evaluating mathematical reasoning.","marker":"Cobbe et al., 2021"},{"why":"MATH500 dataset provides advanced math problems for evaluating mathematical reasoning.","marker":"Lightman et al., 2023"}],"fun_headline_variants":["Table-organized LLM thought beats chain-of-thought on planning","Structured thought tables lift LLM planning accuracy","Tabular thinking helps LLMs plan, but not solve math","LLM reasoning in tables: planning wins, math trails","Table as Thought: boosting LLM planning via structured rows"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Table-organized LLM thought beats chain-of-thought on planning","Structured thought tables lift LLM planning accuracy","Tabular thinking helps LLMs plan, but not solve math","LLM reasoning in tables: planning wins, math trails","Table as Thought: boosting LLM planning via structured rows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1237,"prompt_tokens":903,"completion_tokens":334,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":253}},"tokens_in":519,"tokens_out":334,"duration_ms":4062,"temperature":1.0,"reasoning_tokens":253,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:14:20.738107+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}