{"id":"c9669f75-71c9-477d-acda-c1a9ce8e2d12","arxiv_id":"2506.03616","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A likelihood-based [PAUSE] token insertion method for fine-tuning shows small gains on GSM8K and MBPP, but the AQUA-RAT result is unreliable because the test set contains training samples.","lead":"The authors propose a fine-tuning method that inserts special [PAUSE] tokens before the tokens the model is least confident about, reporting gains of up to 4.7% on GSM8K. The idea is simple and cheap, but the evaluation is compromised by a test set that includes training samples and by a lack of repeated runs.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim is undermined by evaluation leakage: AQUA-RAT test contamination, near-duplicate examples, and nine unseeded runs cannot support 'consistently outperforms.'","rationale":"The reader's verdict is REJECT, and my analysis agrees that the evaluation is not reliable. However, my load-bearing concern differs slightly in emphasis. The reader's weakest_assumption focuses on low-likelihood positions being formatting artifacts, which Appendix B indeed substantiates and which undermines the causal mechanism. I agree with that. But the most decisive, load-bearing issue for the central claim is the documented leakage in the AQUA-RAT test set (Appendix A), because it directly invalidates one of the three headline numbers (3.23%p) and thereby the 'consistent' claim. The mechanism concern matters for the paper's interpretation, but the leakage alone is sufficient to reject. In addition, the absence of any error bars or seeds means the remaining small gains cannot be assessed. I set agreement_with_reader to 'partial' because the reader identified the mechanism weakness but did not elevate the AQUA-RAT contamination to the central position, whereas I see it as the single most load-bearing flaw. My verdict remains REJECT: the advertised empirical claim is not supported by the reported experiments. The paper does provide a reproducible pipeline sketch and a plausible hypothesis, but reproducibility of the method does not rescue the validity of the evaluation; a clean re-run could change the verdict to ACCEPT or CONDITIONAL.","tokens_in":16548,"tokens_out":1982,"duration_ms":17838,"concrete_test":"Re-run the full comparison on uncontaminated splits: use the original AQUA-RAT validation/test sets (or an explicitly disjoint held-out sample from the original training set) while training on the same split as SFT and every baseline, with at least 3 random seeds per condition, and report mean±std. If DIT's advantage over SFT on AQUA-RAT disappears or falls within noise, the headline 'consistently outperforms' fails on a second, independent check.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim is that DIT 'consistently outperforms traditional fine-tuning and previous token insertion methods' (abstract), with gains up to 4.7%p on GSM8K, 3.23%p on AQUA-RAT, and 3.4%p on MBPP (Table 1). The load-bearing assumption is that these comparisons are valid and that DIT's placement mechanism—low token log-likelihood positions—is the cause. Both legs fail.\n\nFirst, Appendix A states that AQUA-RAT's test set was supplemented by randomly extracting 2000 samples from the training set. The authors use the full ~74k sampled training set for training (Table 2 lists train=70,104), and then evaluate on a test set that includes 2,000 of those same training samples. This is direct train/test leakage. The AQUA-RAT numbers in Table 1 therefore cannot support the 3.23%p claim, nor any comparison against SFT or baselines on that dataset.\n\nSecond, on the mechanism: Appendix B reports that the low-likelihood positions found by the model are 'the start and end positions of equations and the points where sentences change.' The Appendix E examples confirm that DIT inserts [PAUSE] at formatting junctures (before '=', before '»', after '.', before '####'). So the positions are not generally 'model uncertainty about content' but structural boundaries. The causal story in §5.2–5.4—that DIT boosts probability on genuinely difficult tokens—is therefore not established. The method may still work as a structural heuristic, but the paper's claim of a 'model-based, dynamic approach rather than a heuristic one' is unsupported.\n\nThird, the evaluation has no seeds, no error bars, and no repeated runs. The reported differences are often small (e.g., Phi-3 Mini: 78.84 vs 78.62 on GSM8K, 62.46 vs 62.82 on AQUA-RAT; Llama 3: 70.71 vs 69.96 on AQUA-RAT). With no variance estimate, these differences are within plausible run-to-run noise.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Dynamic Inserting Tokens Training (DIT), a fine-tuning method that inserts a special [PAUSE] token before the M_DIT tokens with the lowest log-likelihood in each target sequence, based on a forward pass of the model. The loss on [PAUSE] tokens is excluded, so the inserted tokens act as dummy tokens that alter the context for predicting the subsequent low-confidence token. The authors compare DIT against standard SFT and three heuristic insertion baselines (Random, Append, After-All-Words) on GSM8K, AQUA-RAT, and MBPP, using Phi-2, Phi-3 Mini, and Llama 3 8B. They report accuracy/pass@1 gains up to 4.7%p on GSM8K, 3.23%p on AQUA-RAT, and 3.4%p on MBPP, and present analyses (training loss, token log-probability distributions) aimed at explaining why the inserted tokens help.","tokens_in":16943,"tokens_out":7888,"duration_ms":73362,"significance":"If the empirical claims held, the paper would make a useful and inexpensive contribution: a fine-tuning-only token-insertion strategy, requiring no pause-token pre-training and no inference-time changes, that improves reasoning on math and code benchmarks for small open models. The method is simple, reproducible (code and data links are provided), and the authors include a complexity analysis and an honest limitations section. However, the significance is reduced by (i) the invalid AQUA-RAT evaluation due to train/test leakage, (ii) the lack of statistical grounding (no error bars/multiple seeds) for small differences, and (iii) the overstatement of 'consistent' superiority given that several comparisons in Table 1 favor SFT or APPD. The mechanistic interpretation as a 'model-based, dynamic' approach is also not yet distinguished from a structural heuristic.","major_comments":[{"comment":"The AQUA-RAT evaluation is invalid due to train/test contamination. Appendix A states that the validation and test sets were 'supplemented' by randomly extracting 2,000 samples from the training set, and Table 2 shows that training used 70,104 samples. Since the 2,000 extracted samples are a subset of the training data, the test set overlaps with the training set. Consequently, all AQUA-RAT numbers in Table 1, including the claimed 3.23%p gain for Phi-2, are unreliable and cannot support any comparative claim. The experiment should be re-run on a clean split (e.g., the original withheld test set, possibly using the full 98k training data or a proper sampling scheme).","section":"Appendix A / Table 2"},{"comment":"The claimed mechanism is not established. The paper interprets low token log-likelihood as 'model uncertainty' and uses it to justify the placement of [PAUSE] tokens, but Appendix B reports that the low-likelihood positions correspond to 'the start and end positions of equations and the points where sentences change,' and the examples in Appendix E show insertions before formatting tokens such as '=', '»', '####', and after sentence boundaries. This suggests the selection rule is largely capturing structural or format-related surprises rather than content uncertainty about the reasoning itself. The causal story in §5.2–5.4 (that [PAUSE] increases the loss on genuinely difficult tokens and boosts their probability) is therefore not supported by the evidence. The authors should either provide evidence that the selected positions are not merely structural (e.g., comparing against random insertion within the same structural categories), or revise the framing to characterize DIT as a learned structural heuristic.","section":"§3.1, §3.2, Appendix B"},{"comment":"The abstract's claim that DIT 'consistently outperforms traditional fine-tuning and previous token insertion methods' is contradicted by the paper's own results. In Table 1, DIT is worse than SFT on Phi-3 Mini GSM8K (78.62 vs 78.84) and on Llama 3 AQUA-RAT (69.96 vs 70.71), and worse than APPD on Phi-3 Mini GSM8K (78.62 vs 79.45), Phi-3 Mini AQUA-RAT (62.82 vs 63.22), and Llama 3 AQUA-RAT (69.96 vs 72.18). The text in §5.1 partially acknowledges this, but the abstract and contribution bullets should be revised to reflect the mixed results (e.g., 'can improve' instead of 'consistently outperforms').","section":"Abstract and Table 1"},{"comment":"The experiments appear to be based on a single run, and no error bars or multiple seeds are reported. Several of the reported improvements are very small (e.g., Phi-3 Mini AQUA-RAT: 62.82 vs 62.46, a 0.36%p difference; Phi-3 Mini MBPP is a tie at 32.2). Without variance estimates or at least two or three seeds, these differences cannot be distinguished from training noise, which further weakens the 'consistent outperformance' claim. The authors should report means and standard deviations across seeds, or at minimum verify that the main conclusions hold under different random seeds.","section":"§5.1 / Appendix C"}],"minor_comments":[{"comment":"The abstract and Section 1 report 'up to 4.7%p' on GSM8K, while the contributions bullet in Section 1 reports 'up to 4.25%p'; these numbers should be reconciled.","section":"Abstract and Section 1"},{"comment":"In the Phi-3 Mini MBPP row, SFT and DIT both show 32.2; the bold/underline formatting should clarify whether this is a tie and how ties are handled.","section":"Table 1"},{"comment":"The abbreviation 'AAW' is introduced as 'AA W' in the bullet list; please standardize the formatting.","section":"Section 4.1"},{"comment":"The choice to exclude [PAUSE] tokens from the loss is only described in Appendix B, but the comparison with 'DIT(learnable)' in Table 3 shows a large drop (47.15 vs 56.33) that makes this design decision important; it should be motivated in the main text.","section":"Appendix B / Section 6"},{"comment":"The text states that for Llama 3 on AQUA-RAT and MBPP, DIT slightly decreases compared to SFT, but Table 1 shows DIT improves on MBPP (14.0 vs 12.6); this should be corrected.","section":"Section 5.1"},{"comment":"The references for the base models (e.g., 'Microsoft, 2023' as a blog post) are informal; please use the canonical technical reports or model cards.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision rather than rejection because the central idea is simple and potentially useful, and the main evaluation flaw (AQUA-RAT contamination) is correctable by re-running the experiments on a clean split. However, the authors must also address the overstatement of 'consistent' superiority, add statistical grounding, and either support or reframe the mechanistic claim. If the AQUA-RAT results are removed or corrected and the remaining evidence is mixed, the contribution would be substantially weaker but still potentially publishable as a negative or preliminary result."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea is genuinely new relative to the cited pause-token work: instead of random insertion during pre-training (Goyal et al.) or after every word (Herel and Mikolov), DIT inserts a [PAUSE] token before the M tokens with lowest log-likelihood during fine-tuning. The strongest piece of evidence is Appendix B, where dynamic selection beats hand-crafted rules at the same structural positions (56.33 vs 53.90 on GSM8K/Phi-2). That is a real, modest result and worth taking seriously.\n\nWhat undercuts the paper is the evaluation. The abstract says DIT \"consistently outperforms,\" but Table 1 shows it is best in only six of nine settings: it loses to SFT on GSM8K for Phi-3 Mini (78.62 vs 78.84), on AQUA-RAT for Llama 3 (69.96 vs 70.71), ties SFT on MBPP for Phi-3 Mini, and is second-best to APPD in several rows. The abstract/introduction claim of up to 4.7%p on GSM8K conflicts with the contributions bullet's 4.25%p. More importantly, there are no error bars, no seeds, and many differences are under a point, so with no variance estimate those are indistinguishable from noise.\n\nOn the AQUA-RAT split, I think the stress-test note goes too far. The wording in Appendix A is clumsy—\"supplement these sets by randomly extracting 2000 samples from the training set\"—but Table 2's numbers (70,104 train + 2,254 val + 2,254 test ≈ 74k) imply the 2000 were moved out of the 74k pool before the final split, so no overlap with the actual training set. The authors should state this explicitly, but calling it \"direct train/test leakage\" is not supported by the numbers.\n\nThe mechanism story is also soft. The low-likelihood positions turn out to be equation boundaries and sentence breaks, as the paper's own Appendix B and examples show. That undercuts the \"model uncertainty\" framing in Section 5.2–5.3. But again, DIT does beat the rule-based baselines that target exactly those structural points, so something more than the heuristic is happening; the paper just doesn't pin down what.\n\nOne more thing to check: GSM8K has no validation split in Table 2. If the \"lowest evaluation loss\" model selection is done on the test set, that is a real leak. The paper needs to clarify.\n\nNet: a testable, cheap idea with a plausible mechanism, but the reported evidence does not support the advertised claims. I would send it to a serious referee—the method deserves a clean re-run with multiple seeds, a clarified split, and toned-down language—but I would not accept it as is.","headline":"A plausible cheap fine-tuning trick that is oversold: the AQUA-RAT leakage concern is probably a misreading, but missing seeds and the 'consistent' overclaim sink the empirical case as written.","tokens_in":17526,"tokens_out":6603,"would_cite":false,"duration_ms":63946,"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":"Inserting [PAUSE] tokens before the tokens a model is least confident about, chosen by log-likelihood during fine-tuning, improves reasoning on math and code tasks across model sizes.","keywords":["Dynamic Inserting Tokens Training","pause token insertion","log-likelihood confidence","mathematical reasoning","code reasoning","fine-tuning","loss calibration","reasoning language models"],"falsifier":"A direct falsification: insert [PAUSE] tokens immediately before the M tokens with the highest log-likelihood in the same training sequences, under identical settings. If accuracy matches DIT within noise, then the paper's claim that low-confidence positions are special is false, and the gain is just from adding tokens.","tokens_in":16365,"feed_emoji":"⏸️","tokens_out":8416,"duration_ms":82350,"temperature":0.7,"pith_summary":"The paper introduces Dynamic Inserting Tokens Training (DIT), a fine-tuning method that inserts a [PAUSE] token immediately before the M tokens in a training target that have the lowest log-likelihood under the model. The authors claim this simple modification consistently beats standard supervised fine-tuning and earlier pause-token insertion strategies on GSM8K, AQUA-RAT, and MBPP, with gains up to 4.7 percentage points on GSM8K, 3.23 percentage points on AQUA-RAT, and 3.4 percentage points in pass@1 on MBPP. They interpret the result as showing that low-likelihood positions mark genuine uncertainty, and that giving the model a pause before those positions raises the training loss on hard tokens and improves the probability of previously low-confidence tokens during inference. If the claim is right, a cheap fine-tuning change can improve reasoning without pre-training on pause tokens or hand-crafted insertion rules.","feed_headline":"Pause tokens before low-confidence tokens boost reasoning by 4.7 pts","feed_subtitle":"Fine-tuning-only trick beats random or fixed pause insertion on math and code reasoning.","key_machinery":"The central object is a pause-injected training sequence: given a (prefix, target) pair, a forward pass ranks the target tokens by their next-token log-likelihood, and a hyperparameter $M_{\\mathrm{DIT}}$ controls how many of the lowest-ranked positions receive a single [PAUSE] immediately before them. The model is then fine-tuned with the usual next-token prediction loss, but the positions where the next token is [PAUSE] are excluded from the loss, so [PAUSE] acts as a dummy token that never needs to be predicted. The mechanism does its work by making hard tokens harder: inserting an unpredicted token before an already low-likelihood token raises the cross-entropy loss at that position, which is exactly the training signal the paper argues is missing in standard fine-tuning. The empirical footprint of the mechanism is that DIT has higher training loss than SFT on the same data, while the probability of the formerly lowest-probability tokens rises at inference.","core_discovery":"Across supervised fine-tuning on three reasoning datasets (GSM8K, AQUA-RAT, MBPP) and three decoder-only models (Phi-2 2.7B, Phi-3 Mini 3.8B, Llama-3-8B), the paper reports that DIT—inserting [PAUSE] tokens immediately before the M tokens with the lowest next-token log-likelihood in each target sequence, and excluding the [PAUSE] tokens from the loss—is the only insertion scheme that consistently beats plain fine-tuning. The best gains are 4.7 percentage points on GSM8K, 3.23 percentage points on AQUA-RAT, and 3.4 percentage points in pass@1 on MBPP. The paper interprets the improvement as a training-signal effect: because [PAUSE] is an unseen token, the loss at the following hard token increases, and the model is forced to learn those tokens more robustly; at inference the long tail of low log-probability tokens is shortened, meaning previously uncertain tokens become more confident. The reported results are not uniformly positive—on Llama-3 with AQUA-RAT, DIT is slightly below SFT—and the paper attributes that to instruction format and hyperparameter choices rather than to the method itself.","pith_inferences":["The authors do not test inference-time insertion; a natural extension is to insert [PAUSE] at low-confidence positions during decoding after DIT training, which could concentrate extra computation at the same hard tokens and trade tokens for accuracy at inference.","Because the insertion rule depends only on next-token log-likelihood, the same recipe could be run with other uncertainty signals, such as semantic entropy over sampled rationales, to test whether better uncertainty estimates produce better insertion points.","The focal-loss analogy suggests DIT may be part of a broader family of hard-example training techniques; if so, it should transfer to tasks where errors concentrate in a few tokens, such as instruction following or long numerical derivations, rather than being specific to the three datasets tested."],"forward_implications":["DIT shows that pause-token benefits do not require pre-training on pause tokens; a fine-tuning-only insertion scheme suffices to improve results on GSM8K, AQUA-RAT, and MBPP.","Insertion position is the active ingredient: random, append-at-end, and after-every-word insertion often hurt, while log-likelihood-selected positions improve performance.","Making [PAUSE] a true dummy token (excluded from the loss) and inserting single tokens rather than blocks is important; ablations on GSM8K/Phi-2 put the optimum at five single [PAUSE] tokens per sequence.","The gains transfer across model sizes from 2.7B to 8B and across mathematical and code reasoning, indicating the effect is not tied to one architecture or answer format.","Per training example, DIT costs roughly one extra forward pass beyond SFT, which the paper argues is a small price relative to the accuracy gain."],"supporting_citations":[{"why":"Introduces pause tokens and is the prior method DIT modifies; also supplies the append baseline and the claim that pause tokens require pre-training, which DIT challenges.","marker":"Goyal et al. (2024)"},{"why":"Supplies the after-every-word insertion baseline AAW that DIT outperforms.","marker":"Herel and Mikolov (2024)"},{"why":"Supports the premise that token log-likelihood indicates model confidence and knowledge gaps, motivating insertion positions.","marker":"Jiang et al., 2023"},{"why":"Supports the premise that low probabilities signal low confidence and uncertainty.","marker":"Kadavath et al., 2022"},{"why":"Focal loss is the analogy used to explain why increasing the loss on hard tokens helps.","marker":"Lin et al., 2017"},{"why":"Provides the GSM8K dataset and its calculator-annotation format used in the experiments.","marker":"Cobbe et al., 2021"},{"why":"Provides the AQUA-RAT dataset used for math reasoning evaluation.","marker":"Ling et al., 2017"},{"why":"Provides the MBPP dataset and pass@1 evaluation for code reasoning.","marker":"Austin et al., 2021"}],"fun_headline_variants":["Dynamic pause-token insertion boosts reasoning by up to 4.7 pts","Low-confidence pause tokens: up to 4.7pt reasoning gain","Insert [PAUSE] at low-confidence spots to boost reasoning","DIT: dynamic [PAUSE] insertion lifts math and code reasoning","Pause tokens where the model is least sure: up to 4.7pt gain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the tokens with the lowest next-token log-likelihood in the training target are exactly where the model's uncertainty hurts reasoning, rather than merely being formatting artifacts such as equation delimiters or sentence boundaries.","fun_headline_variants_meta":{"raw":{"variants":["Dynamic pause-token insertion boosts reasoning by up to 4.7 pts","Low-confidence pause tokens: up to 4.7pt reasoning gain","Insert [PAUSE] at low-confidence spots to boost reasoning","DIT: dynamic [PAUSE] insertion lifts math and code reasoning","Pause tokens where the model is least sure: up to 4.7pt gain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000696,"raw_usage":{"total_tokens":3178,"prompt_tokens":1009,"completion_tokens":2169,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":2070}},"tokens_in":625,"tokens_out":2169,"duration_ms":19428,"temperature":1.0,"reasoning_tokens":2070,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:59:04.577074+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct falsification: insert [PAUSE] tokens immediately before the M tokens with the highest log-likelihood in the same training sequences, under identical settings. If accuracy matches DIT within noise, then the paper's claim that low-confidence positions are special is false, and the gain is just from adding tokens.","supporting_citations":[],"review_version":1}