{"id":"2b8ba0c2-886e-413e-9a93-2f7f18eec2f4","arxiv_id":"2501.02026","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A prompting framework that recursively decomposes reasoning tasks and self-scores candidate thoughts is reported to improve LLM accuracy on math and letter-concatenation benchmarks, though the headline improvement is overstated relative to the presented baselines.","lead":"RDoLT is a prompting framework that breaks reasoning questions into easy, intermediate, and final stages, generates three candidate thoughts per stage, and uses the LLM itself to score and propagate the best ones. The paper claims consistent gains over existing prompting methods, but its own tables show the gain is smaller and less consistent than the abstract suggests.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never validates the four-feature self-scoring that selects every propagated thought, and its own Appendix D trace shows that scoring can be internally inconsistent; without that validation the central RDoLT mechanism is unsupported.","rationale":"The reader's weakest assumption and my concern align: RDoLT's only novel machinery is the scoring-and-selection loop, and every downstream result inherits the quality of those scores. The paper supplies no ground-truth check of the scorer, and the Appendix D worked example is a direct counterexample in two ways: a false claim about disjoint cycles receives the maximum Logical Validity score, and two intermediate thoughts making the same computation receive very different scores. This makes the score signal look arbitrary rather than a reliable selector. The absence of a quantitative KPM ablation compounds the problem: even if the empirical accuracies in Table 1 are reproducible, there is no evidence that the proposed selection mechanism, rather than the extra prompts or model stochasticity, produces the gains. The threshold sweep in §5.1 without a stated held-out split further threatens the integrity of the reported numbers. I am not claiming the empirical results are fabricated; I am claiming the evidence as written does not support the mechanism-based superiority claim. The paper has useful ingredients—clear benchmark coverage, open-source model focus, and a concrete framework description—but the central validation gap is load-bearing. Therefore the reader's REJECT verdict remains appropriate; a resubmission with a scorer-reliability probe and a proper KPM ablation could change that assessment.","tokens_in":20326,"tokens_out":9344,"duration_ms":91458,"concrete_test":"Run the exact RDoLT pipeline (same prompts, temperature=0.4) on 100 held-out problems from GSM8K and SVAMP with tau fixed on a development split before seeing test answers. For each generated thought, record the LLM's four-feature score and a ground-truth label (whether the thought's arithmetic/answer is correct). Then check (a) separation: average score of correct vs incorrect thoughts, and (b) selection benefit: accuracy of thoughts passing tau vs a random subset of the same size. If scores do not separate correct from incorrect, or if score-selected accuracy is not above random selection, the scoring mechanism is not validated and the reported gains cannot be attributed to RDoLT.","verdict_should_be":"UNCHANGED","load_bearing_attack":"All of RDoLT's downstream steps consume the four-feature scores (Eqs. 6-11), and the KPM propagates only the thoughts that pass the threshold. The paper never validates that these scores track reasoning quality. The Appendix D trace is internally inconsistent: the easy step scores a mathematically false claim—'(1,2,5,4)(2,3) is a product of disjoint cycles'—as LV=10/10 (the cycles share the element 2), and in the intermediate step T2 and T3 state the same computation '120/4=30' but receive scores 21 and 36. Thus the score signal can be arbitrary. No ablation of the scorer or KPM is reported; Figure 4 is qualitative, and the threshold tau is swept in §5.1 without a stated held-out split, so the Table 1 numbers may reflect post-hoc selection. Since the asserted advantage of RDoLT is precisely its score-driven selection and propagation, the central mechanism is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces RDoLT, a prompting framework that recursively decomposes a reasoning task into easy, intermediate, and final sub-tasks; generates multiple candidate thoughts per sub-task; scores each thought along four features (Logical Validity, Coherence, Simplicity, Adaptiveness); and propagates both selected and rejected thoughts through a Knowledge Propagation Module (KPM) to later stages. The authors evaluate RDoLT against Vanilla, CoT, CoT-SC, Least-to-Most, and Auto-CoT on GSM8K, SVAMP, MultiArith, LastLetterConcatenation, and Gaokao 2023 Math across five LLMs, claiming consistent superiority and a 6.28% gain over state-of-the-art on GSM8K with ChatGPT-4o. They also report variant analyses with different thresholds and different numbers of thoughts per step.","tokens_in":20566,"tokens_out":5984,"duration_ms":52118,"significance":"If the central claims held, the paper would offer a useful prompt-only method for improving LLM reasoning without fine-tuning. The framework's emphasis on tracking rejected thoughts and explicitly scoring intermediate steps is a reasonable research direction. However, the manuscript's own data contradict the headline claims: several cells in Table 1 show CoT or CoT-SC outperforming RDoLT, and the abstract's 6.28% gain is calculated against the Vanilla baseline rather than against the strongest prior method. The scoring mechanism is unvalidated and is directly contradicted by the Appendix D worked example, and the threshold and thought-count parameters appear to be selected post hoc. The paper does provide detailed worked examples and a reproducible evaluation setup, which is a strength, but the current evidence is insufficient to support the claimed consistent improvement.","major_comments":[{"comment":"The claim that RDoLT surpasses state-of-the-art techniques by 6.28% on GSM8K with ChatGPT-4o is not supported by Table 1. The 6.28% gap is between RDoLT (90.98) and Vanilla (84.7), whereas the strongest baseline in that row is CoT-SC (89.4), giving a 1.58% advantage. Moreover, Table 1 contains multiple rows where CoT or CoT-SC beat RDoLT: GSM8K Llama3 (CoT-SC 72.86 vs RDoLT 72.63), SVAMP Llama3 (CoT 69.54 vs RDoLT 69.23), SVAMP Gemma2-9B (Auto-CoT 64.52 vs RDoLT 64.19), MultiArith Gemma2-27B (CoT 72.73 vs RDoLT 72.49), and Gaokao Gemma2-27B (CoT 70.28 vs RDoLT 70.05). The statement that RDoLT outperforms other prompting methods in 65% of evaluated benchmarks is also inconsistent with the table, since RDoLT wins roughly 19 of 25 model-benchmark cells; the paper needs a precise aggregate metric with a defined counting rule.","section":"Abstract; Table 1"},{"comment":"The four-feature self-scoring system is the mechanism that selects all propagated thoughts, yet the paper never validates that these scores track reasoning quality. Appendix D is a direct counterexample: in the Easy step, Thought 1 receives LV=10 while asserting that (1,2,5,4)(2,3) is a product of disjoint cycles, even though the two cycles share the element 2 and are not disjoint; in the Intermediate step, Thought 2 and Thought 3 both state the same computation 120/4=30 but receive scores of 21 and 36, respectively; and in the Final step, the highest-scoring thought (T3, score 39) produces the wrong answer 2, while the correct thought (T1, score 29) is rejected. Since Eq. (11) selects thoughts based on these scores and Eq. (12) propagates them through KPM, the central selection and propagation mechanism is unsupported.","section":"§3.3, Eqs. (6)-(10); Appendix D"},{"comment":"The robustness analysis sweeps the selection threshold τ from 25 to 40 and shows that the optimal threshold varies across variants (e.g., Single-Step peaks at ≥35, while One-Shot and Multi-Requests variants peak at ≥30). No held-out split, cross-validation procedure, or prespecified rule is given for choosing τ, and it is unclear how the thresholds used to produce Table 1 were fixed. Without such a protocol, the reported accuracies may reflect post-hoc selection of a free parameter that is load-bearing for the KPM selection rule in Eq. (13).","section":"§5.1, Table 2"},{"comment":"The thought-quantity analysis is internally inconsistent and cannot justify the n=3 setting used in Table 1. The text states that generating five thoughts per step yields a 60.00% success rate, but Table 3 reports 49.75% for that same row; the 'Total Solved' values in the per-step rows (20+30+40=90) match the step columns, yet the reported success rates do not agree with any clearly defined denominator, and the denominator is never stated. The seven-thoughts row similarly reports 77 total solved and a success rate of 38.89, which is inconsistent with 77/210=36.67. Because the paper uses n=3 for all headline results, the choice of n needs a principled justification, not a flawed aggregate table.","section":"§5.2, Table 3"},{"comment":"No statistical significance testing, confidence intervals, or multiple-run variance is reported; every comparison is a single point estimate. This is particularly concerning because many RDoLT advantages are below one percentage point (e.g., GSM8K Gemma2-27B: RDoLT 76.58 vs CoT-SC 76.72; MultiArith Gemma2-27B: RDoLT 72.49 vs CoT 72.73). With such small margins and no indication of run-to-run variability or evaluation procedure, the claimed consistent superiority cannot be established.","section":"§5, Table 1"}],"minor_comments":[{"comment":"The symbol I is used for the prompt context in Eq. (5) and as an indicator function in Eq. (6); this overloaded notation should be disambiguated.","section":"§3.2, Eq. (5); §3.3, Eq. (6)"},{"comment":"There are several typos in dataset names: 'GSMK8' should be 'GSM8K', 'Multi-Arithmetic' should be 'MultiArith', and the appendix heading 'gmsk8' should be capitalized consistently.","section":"§4.1; Appendix C"},{"comment":"Abbreviations are inconsistent: 'Least2Most' is sometimes 'L2M', 'Auto CoT' is sometimes 'A-CoT', and 'CoT-SC' appears as both 'CoT-SC' and 'CoT-SC' without a single definition; the table should use one abbreviation consistently in captions and text.","section":"§4.2; Table 1"},{"comment":"In the KPM block after the Intermediate step, the 'Selected Thoughts (Easy)' line is repeated, but the actual intermediate selected thoughts are not clearly separated from the easy ones; the example should list the intermediate selected thoughts explicitly.","section":"Appendix B"}],"recommendation":"reject","confidential_remarks":"The manuscript's central claim of consistent superiority is contradicted by its own Table 1, and the self-scoring mechanism is invalidated by the Appendix D trace. The threshold-sweep analysis and the thought-quantity table contain inconsistencies that would require significant rework to address. The novelty relative to ToT/GoT is not demonstrated, and the reference list contains unprofessional entries (e.g., 'Chilled and Chilled'). While some of these issues could in principle be fixed in a major revision, the combination of a false headline claim and an unsupported core mechanism makes the current version unsuitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"RDoLT is a specific combination of three things: recursive decomposition, multi-thought generation with scoring, and a knowledge propagation module that keeps rejected thoughts in play. The authors test it across five benchmarks and five models, which is more evidence than many prompt papers include. The worked examples in the appendix are transparent. That is the good part.\n\nThe bad part is that the central mechanism is unsupported. The four-feature scoring is the load-bearing component: it selects which thoughts move forward, and the KPM consumes those scores at every step. But the paper never validates that the scores track reasoning quality. The appendix MMLU example undercuts it. The easy step gives Logical Validity 10/10 to the claim that (1,2,5,4)(2,3) is a product of disjoint cycles, which is false because both cycles share the element 2. And the intermediate step gives two identical statements, '120/4=30', scores of 21 and 36. That is not a rounding difference; it is arbitrary scoring. If the scorer can be this wrong on a simple example, the selection mechanism has no demonstrated validity.\n\nThen there are the standard issues. The abstract's 6.28% gain is over the vanilla baseline, not over state of the art. Table 1 shows CoT beating RDoLT in several cells (SVAMP/Llama3, MultiArith/Gemma2 27B, Gaokao/Gemma2 27B), which contradicts the 'consistent' framing. The threshold tau is swept in Section 5.1 with no stated held-out split, so Table 1 numbers may be post-hoc. The KPM is not ablated; Figure 4 is qualitative. These are load-bearing, not cosmetic.\n\nI don't doubt the tables are honestly reported; the problem is that the interpretation is not supported. The paper deserves a serious referee to check the numbers and force a validation of the scoring, but as it stands it should not be accepted. The most useful path would be a revised version with an ablation of the KPM, a held-out split for tau, and a ground-truth check of the scoring.","headline":"RDoLT is a plausible combination with solid experimental breadth, but the load-bearing scoring mechanism is never validated and the paper's own appendix shows it can be arbitrary, so the headline claims do not hold.","tokens_in":21098,"tokens_out":3522,"would_cite":false,"duration_ms":33789,"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":"The paper claims that a prompt-only framework, RDoLT, improves LLM reasoning by recursively decomposing tasks, scoring each thought on four features, and propagating both accepted and rejected thoughts to later stages.","keywords":["prompt engineering","recursive decomposition","chain-of-thought prompting","knowledge propagation","thought scoring","large language models","mathematical reasoning"],"falsifier":"Take a benchmark with known correct answers, run RDoLT, and compare accuracy under the real scorer against accuracy under random thought selection or selection of the lowest-scoring thought; if the real scorer does not beat both, the scoring mechanism is not carrying the reported gain.","tokens_in":20133,"feed_emoji":"🧠","tokens_out":5859,"duration_ms":51756,"temperature":0.7,"pith_summary":"RDoLT is a prompting-only framework that tries to make large language models reason better without fine-tuning. It decomposes a problem into easy, intermediate, and final sub-tasks, generates several candidate thoughts at each stage, scores them on logical validity, coherence, simplicity, and adaptiveness, and then propagates both accepted and rejected thoughts forward through a Knowledge Propagation Module. The paper claims this consistently beats chain-of-thought, self-consistency, least-to-most, and auto-CoT prompting across five benchmarks, including a 90.98% GSM8K accuracy with ChatGPT-4o. If true, a purely textual change to the prompt would yield robust accuracy gains of roughly 1.5 to 6.75 points across models and task families.","feed_headline":"Prompt-only RDoLT lifts math reasoning to 90.98% on GSM8K","feed_subtitle":"Recursive decomposition and thought scoring beat CoT baselines on five benchmarks, with no fine-tuning.","key_machinery":"The Knowledge Propagation Module (KPM) is the paper's central object: it stores both selected ('strong') and rejected ('weak') thoughts at each decomposition level and makes them available to all later levels, with regeneration when every thought is rejected. Selection is driven by a four-feature thought score, logical validity, coherence, simplicity, and adaptiveness, summed and compared against a threshold $\\tau$.","core_discovery":"The paper's central claim is that recursive, score-guided decomposition plus memory of rejected thoughts is enough to improve LLM reasoning over existing prompting methods. On GSM8K the reported RDoLT result is 90.98% with ChatGPT-4o, which the paper describes as surpassing the state of the art by 6.28 percentage points; the strongest listed baseline in its comparison table, CoT-SC, is 89.4%. The paper also reports RDoLT as the top method in 65% of the evaluated benchmark settings, with accuracy gains of 5.5 to 6.75 points on other benchmarks. The framework's distinctive mechanism is not a new model but a workflow: generate thoughts, score them on four features, select those above a threshold, and keep weak thoughts visible to later stages for re-evaluation.","pith_inferences":["Editorial inference: the strongest test of RDoLT is the reliability of its self-scorer; the appendix's MMLU example shows a highest-scoring final thought being selected while the mathematically correct answer appears in a rejected thought, so a direct check of scorer accuracy on known-answer problems would settle whether selection is helping.","Editorial inference: if the gains are real but threshold-dependent, the method could be made more robust by deriving the threshold from model confidence or adding a second scoring pass, rather than fixing it a priori.","Editorial inference: KPM's weak-thought memory resembles a short-term associative memory, so applying it to multi-step planning or code generation, where an early wrong branch can be revisited, is a natural next experiment the paper does not run."],"forward_implications":["Prompt-only deployment: if RDoLT's numbers hold, users can get 1.5 to 6.75 point accuracy gains on math and letter-concatenation tasks by changing the prompt, with no gradient updates.","Weak-thought memory matters: KPM's use of rejected thoughts implies that discarded ideas can later become relevant, so methods that discard non-majority reasoning paths may be leaving accuracy on the table.","Threshold sensitivity is a practical lever: the variant study shows optimal thresholds vary across RDoLT variants, with most peaking at 30 or 35 and all dropping at 40.","The gain is consistent but not universal: in some benchmark-model cells, such as Gemma-2 27B on MultiArith and Gaokao 2023 Math, CoT remains the better performer in the paper's tables."],"supporting_citations":[{"why":"Introduces chain-of-thought prompting, the baseline that RDoLT extends and compares against.","marker":"Wei et al. [2022]"},{"why":"Introduces self-consistency prompting, the majority-voting baseline that RDoLT's knowledge propagation is designed to improve on.","marker":"Wang et al. [2022]"},{"why":"Introduces least-to-most prompting, the progressive-complexity baseline that RDoLT contrasts with.","marker":"Zhou et al. [2022]"},{"why":"Introduces tree-of-thoughts, the structured-search baseline whose rigid branches RDoLT claims to avoid.","marker":"Yao et al. [2023a]"},{"why":"Introduces graph-of-thoughts, a flexible graph-based baseline that RDoLT positions itself against.","marker":"Besta et al. [2024a]"},{"why":"Supplies GSM8K, the primary benchmark for the headline 90.98% result.","marker":"Cobbe et al. [2021]"},{"why":"Supplies SVAMP, another load-bearing evaluation benchmark for the framework's claims.","marker":"Patel et al. [2021]"}],"fun_headline_variants":["RDoLT recursive decomposition hits 90.98% on GSM8K","Score-guided thought recursion beats CoT by 6.28% on GSM8K","Prompt-only RDoLT improves math reasoning across five benchmarks","Weak-thought memory and recursion boost LLM reasoning","RDoLT: no fine-tuning, just recursive prompts for 90.98%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Every downstream step consumes the model's own four-feature thought scores, so the framework stands or falls on whether those scores reliably pick thoughts that lead to correct answers.","fun_headline_variants_meta":{"raw":{"variants":["RDoLT recursive decomposition hits 90.98% on GSM8K","Score-guided thought recursion beats CoT by 6.28% on GSM8K","Prompt-only RDoLT improves math reasoning across five benchmarks","Weak-thought memory and recursion boost LLM reasoning","RDoLT: no fine-tuning, just recursive prompts for 90.98%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000208,"raw_usage":{"total_tokens":1401,"prompt_tokens":937,"completion_tokens":464,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":368}},"tokens_in":553,"tokens_out":464,"duration_ms":5109,"temperature":1.0,"reasoning_tokens":368,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:23:59.010953+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a benchmark with known correct answers, run RDoLT, and compare accuracy under the real scorer against accuracy under random thought selection or selection of the lowest-scoring thought; if the real scorer does not beat both, the scoring mechanism is not carrying the reported gain.","supporting_citations":[],"review_version":1}