{"id":"58210578-edd4-4289-9903-799bc6e9094b","arxiv_id":"2412.16838","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"LLM error detectors favor conventional solution formats; generating an adaptive reference solution before grading mitigates this conformity bias on a 200-example GSM8K subset.","lead":"This paper shows that LLM-based error detectors for math word problems perform worse on valid but non-standard solutions, a bias the authors call conformity bias. They propose a framework called Ask-Before-Detection that generates an adaptive reference solution before grading, which reduces this bias on 200 example problems.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unvalidated auto-labels on the 800 erroneous alternative solutions, not solution diversity per se, are the load-bearing risk; label noise could manufacture both the D′ gap and AskBD's apparent benefit.","rationale":"","tokens_in":13481,"tokens_out":4284,"duration_ms":42033,"concrete_test":"","verdict_should_be":"UNCHANGED","load_bearing_attack":"","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies automatic error detection (AED) for math word problem (MWP) solutions and claims that LLM-based error detectors exhibit a 'conformity bias': they perform noticeably worse on valid alternative solutions than on the conventional solution for the same problem. To construct alternative solutions, the authors propose the Automatic Solution Permutation (ASP) pipeline, which extracts a solution expression, permutes it, and asks an LLM to explain the permuted expression as a new step-by-step solution. They then inject four types of errors to create a labeled detection dataset from 200 GSM8K questions. Based on a preliminary study, the paper proposes AskBD (Ask-Before-Detection), which generates an adaptive reference solution before grading, and evaluates it on 10 LLMs under naive, chain-of-thought (CoT), and combined prompting conditions. The main reported findings are that a consistent D versus D′ gap exists across models and that AskBD mitigates the gap, especially for advanced models and when combined with CoT.","tokens_in":13447,"tokens_out":9839,"duration_ms":80745,"significance":"If the data-construction pipeline is valid, the phenomenon the paper identifies is important for educational NLP and for the fair evaluation of LLM-based grading: it points to a realistic failure mode in which correct student work is rejected because it does not match a canonical solution format. The paper is honest in several respects: it reports results for 10 models spanning base and advanced tiers, it explicitly acknowledges that base models gain little from AskBD, and the framework does not fit parameters to the test set. The proposed AskBD framework is simple and potentially useful, and the finding that a reference solution must align with the student's reasoning is a valuable design insight. The main uncertainty is data validity: the alternative solutions and error labels are machine-generated and lightly human-filtered, and the reported effect sizes are not accompanied by uncertainty quantification.","major_comments":[{"comment":"The entire conformity-bias measurement depends on D′, but the manuscript does not demonstrate that the 200 alternative solutions are valid or that the injected errors are representative. The text reports only that one graduate student 'reviews the quality' of three GPT-4o-generated candidates and selects the best; there is no rubric, second annotation, inter-annotator agreement, or check that the selected alternatives are error-free at the step level. The scripted error-injection procedure is also not validated against real student errors for the alternative-solution format. If some 'correct' alternative solutions contain subtle errors, the D−D′ gap and the apparent benefit of AskBD in Tables 1 and 4 could be artifacts of the generation pipeline rather than properties of the detectors. I request an expert validation of all 200 alternative solutions and a sample of the 800 erroneous ones, with agreement rates and an error analysis.","section":"Section 2.1 and Section 2.2"},{"comment":"The abstract's claim that AskBD 'effectively mitigates bias and improves performance' is not supported for the base models. In Table 4, comparing M2 with M0, the bias gap Δ (= D−D′) improves only for Gemini-1.5-Flash among the five base models; it worsens for GPT-4o-mini (−8.8 to −11.0), Claude-3.5-Haiku (−3.5 to −6.7), Llama-3.1-8B (+0.7 to +0.1), and Qwen2.5-7B (−8.4 to −9.5). The paper should either restrict the mitigation claim to advanced models or provide an explanation/adaptation for why AskBD fails for base models. The RQ3 discussion has the same issue: M3 versus M1 worsens the gap for base Claude (−2.6 to −4.8), base Qwen (−5.0 to −6.0), and advanced GPT-4o (−4.1 to −4.9), so the 'highly compatible' conclusion is too strong.","section":"Abstract and Section 4.2, Table 4"},{"comment":"The paper reports only 3-seed means without standard deviations, confidence intervals, or significance tests. Several key comparisons are within a few points (e.g., advanced GPT-4o gap reduction from −9.5 to −9.1; base Llama Δ from +0.7 to +0.1), and with 200 examples these are likely within noise. I request bootstrap confidence intervals or paired tests (e.g., McNemar over the 1,000 solution instances) for the accuracy and Δ comparisons; the language of 'consistent', 'significant', and 'effectively' should be calibrated to the actual uncertainty.","section":"Section 4.1 and Table 4"},{"comment":"The AskBD method cannot be reproduced from the paper. The algorithm names P_cqe, P_ssi, P_sqr, and P_reg, but the actual prompt texts are not provided; Appendices D and E contain only the naive and CoT detection prompts (Figures 5 and 6). Please include all four AskBD prompts, ideally with the exact placeholders, in the appendix or a public repository.","section":"Section 3 and Algorithm 1"},{"comment":"The likelihood analysis uses the average likelihood of open-source models as a 'pseudo-indicator' for closed-source models (GPT-4o, Claude, Gemini) because their likelihoods are unavailable. The grouping and the conclusion that conformity bias 'is caused by decreased understanding' therefore are not directly measured for the closed models. Please either obtain or approximate per-model likelihoods in a way that is clearly reported, or present the open-model result as the supported claim and the closed-model connection as a hypothesis.","section":"Section 2.3.2"}],"minor_comments":[{"comment":"The caption says 'gpa' instead of 'gap', and it defines Δ = D − D′ while Tables 1-3 use Δ = D′ − D; please unify the sign convention across all tables.","section":"Table 4 caption"},{"comment":"The Claude-3.5 advanced D value is 59.9, while the corresponding M0 value in Table 4 is 59.0; one of these is a typo and should be corrected.","section":"Table 1"},{"comment":"The in-text citation 'Srivastava et al., 2024; ?' contains a literal '?' placeholder; the reference entry also appears incomplete.","section":"Section 5.2 and References"},{"comment":"There are several typographical inconsistencies: 'consderation' (Section 2.3.3), 'AskDB' (Section 4.2), 'AskBG' (Figure 4 caption), and 'advance' used as an adjective in Table 1.","section":"Throughout"},{"comment":"Figure 3c is referenced in the text ('we plot the likelihood score distribution comparisons'), but no distribution plot is described or shown in the provided manuscript text; please ensure the plot is included and discuss what it shows.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for a CS/CL venue and the phenomenon is potentially valuable. The main risks are the 200-example scale and the single-annotator, machine-generated data pipeline. If the authors can provide the requested expert validation and uncertainty quantification, the central claim would be much stronger. I also recommend that the editors ask the authors to check the consistency of the numbers between Tables 1 and 4, and to provide the AskBD prompts in the final version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead this one if your work touches automated grading or LLM robustness to surface form. The paper claims that LLM-based error detectors for math word problems perform worse on correct but non-standard solutions, and that asking the model to generate a reference solution before grading (AskBD) shrinks that gap. I think the phenomenon is real, but the current evidence is not strong enough to take the measured numbers at face value.\n\nWhat is genuinely new: the ASP pipeline that permutes the underlying arithmetic expression to produce alternative solutions that differ in structure, not just wording. That is a neat way to avoid the paraphrase failure mode. The likelihood analysis linking detector accuracy to solution likelihood is consistent with known behavior, and the finding that using the conventional solution as a reference amplifies the gap while using the matching solution reduces it makes real sense. The AskBD framework is a practical extension of Daheim et al.'s reference-based grading, and for the advanced models the results are consistent: gaps shrink and overall accuracy goes up.\n\nThe soft spots are load-bearing. First, the 800 erroneous alternative solutions are generated by scripted error injection with no human validation of the labels. The injection method was designed for conventional solutions; alternative step structures can have different dependencies, and a random step-level error can easily create follow-on issues that make the gold label ambiguous or wrong. If those labels are noisy, the D' accuracy numbers are unreliable, and the measured conformity gap could be partly an artifact of the data pipeline rather than detector bias. Second, the whole dataset is 200 GSM8K seeds, with one graduate student selecting the alternatives and no inter-annotator agreement, and no release of data or code. Third, there are no significance tests or error bars beyond three-seed means, and for base-scale models AskBD either does little or slightly worsens the gap; the claim of mitigation holds mainly for the large models. The paper's own limitation section is honest about the small scale, but it does not address the label validation issue.\n\nThe central claim is plausible—detectors favor higher-likelihood, more conventional text—and the mitigation is cheap and sensible. I would not desk-reject this, but I would send it to review with the expectation that the authors validate a sample of the erroneous labels, release the dataset, and add even basic statistical comparison. A reader working on grading systems or LLM robustness gets value from the framing and the finding; just don't rely on the numbers.\n\nRecommendation: send to peer review, conditional on major revision.","headline":"Conformity bias in LLM grading is a real risk and AskBD is a sensible fix, but the evidence sits on 200 synthetic examples with unvalidated error labels.","tokens_in":13977,"tokens_out":4699,"would_cite":false,"duration_ms":44043,"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":"LLM-powered error detectors grade conventional math solutions more accurately than equally valid alternative ones; the Ask-Before-Detection framework narrows this gap by generating a reference solution tailored to the student's approach.","keywords":["conformity bias","math word problems","automatic error detection","large language models","reference solution generation","chain-of-thought prompting","GSM8K","solution permutation"],"falsifier":"Run the same error-detection prompts on authentic student-written solutions to the same 200 math word problems, with errors labeled by independent human graders, and measure the conventional-versus-alternative gap. If the gap vanishes or reverses on real solutions, the conformity bias and AskBD's reported benefit are artifacts of the synthetic generation pipeline rather than properties of the detectors.","tokens_in":13308,"feed_emoji":"🧮","tokens_out":9198,"duration_ms":58669,"temperature":0.7,"pith_summary":"This paper argues that LLM-powered error detectors for math word problems are biased against non-standard but correct solutions. The authors name this effect conformity bias, show that it tracks the model's token likelihood for a solution, and propose a framework, Ask-Before-Detection (AskBD), that generates a reference solution tailored to the student's approach before grading. On 200 GSM8K problems, AskBD reduces the conventional-versus-alternative accuracy gap and improves overall error detection, especially when paired with chain-of-thought prompting. The motivation is that automatic grading should accept any reasonable solution, not just the textbook format.","feed_headline":"LLM graders favor textbook math answers; AskBD narrows the gap","feed_subtitle":"Generating a tailored reference before grading improved LLM error detection on 200 GSM8K problems.","key_machinery":"AskBD is a four-stage pipeline: a Condition and Question Extractor (CQE) pulls the known facts and the actual question from the problem statement; a Solution Step Inquirer (SSI) rewrites the student's solution into a list of step-level questions, appending the original question; a Step Question Responder (SQR) answers those questions into a reference solution; and a Reference-Enhanced Grader (REG) grades the original solution against that generated reference. The load-bearing mechanism is the adaptive reference: using the student's own reasoning to generate the reference, rather than a fixed conventional answer, avoids the mismatch that amplifies bias when a single reference is forced onto an alternative approach. The paper also shows that likelihood scores correlate with detection accuracy, motivating reference generation as a cheaper alternative to fine-tuning.","core_discovery":"The central claim is that current LLM-based error detectors exhibit a pronounced conformity bias on math word problems: when the same problem is solved in a non-standard but mathematically valid way, detection accuracy drops by several points across open- and closed-source models. The paper further claims that this bias is explained by likelihood: alternative solutions receive lower average token log-likelihood, and lower-likelihood solutions are graded less accurately. Because fine-tuning is expensive and uncertain, the paper introduces AskBD, which adaptively constructs a reference solution from the question's conditions and the student's own step conclusions before asking the model to grade. Adding this reference narrows the gap and, in advanced models, improves absolute detection accuracy; combining AskBD with chain-of-thought prompting gives the best performance. The authors position this as the first systematic study of conformity bias in LLM-powered error detection for math solutions.","pith_inferences":["AskBD's reference generation is prompt-only and model-agnostic, so the same recipe could transfer to other subjects where multiple solution strategies exist, such as physics or programming, without retraining.","The likelihood-based explanation predicts that any intervention raising a model's likelihood for alternative solutions, such as few-shot examples of valid non-standard reasoning, should shrink the same bias.","Because the alternative solutions were generated by a single model and filtered by one human, a study on authentic student work would separate genuine conformity bias from artifacts of the generation pipeline."],"forward_implications":["AskBD reduces the performance gap between conventional and alternative solutions for advanced LLMs.","AskBD improves overall error detection accuracy compared to naive prompting.","Combining AskBD with chain-of-thought prompting yields the best overall performance.","For base-sized models, naive AskBD is less effective, but chain-of-thought prompting works better with them and still benefits from the combination.","Uniformly using conventional solutions as references amplifies the bias, showing that the choice of reference solution matters."],"supporting_citations":[{"why":"Supplies the GSM8K dataset from which the 200 math word problems are sampled.","marker":"Cobbe et al., 2021"},{"why":"Provides the error categories and the error-injection approach used to construct the test solutions.","marker":"Li et al., 2024"},{"why":"Frames error detection in math word problems as a measure of LLM reasoning, the setup this paper extends.","marker":"Zhou et al., 2024"},{"why":"Demonstrates that introducing reference answers improves error detection, the foundation of AskBD.","marker":"Daheim et al., 2024"},{"why":"Chain-of-thought prompting, used as a baseline and as the enhancement combined with AskBD.","marker":"Wei et al., 2022a"},{"why":"Introduces an error-detection benchmark in mathematics that motivates the automatic error detection task.","marker":"Yan et al., 2024"}],"fun_headline_variants":["AskBD: Fix LLM grader bias on valid alternate math","LLM math graders gloss over valid alternatives; AskBD helps","Conformity bias in LLM math error detection? Ask before grading","Alternative math answers stump LLM graders; AskBD makes them fair"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes that the 200 alternative solutions generated by GPT-4o and selected by one graduate student are genuinely correct and representative of real student reasoning, and that the scripted error injections resemble real mistakes students make.","fun_headline_variants_meta":{"raw":{"variants":["AskBD: Fix LLM grader bias on valid alternate math","LLM math graders gloss over valid alternatives; AskBD helps","Conformity bias in LLM math error detection? Ask before grading","Alternative math answers stump LLM graders; AskBD makes them fair"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000755,"raw_usage":{"total_tokens":3314,"prompt_tokens":856,"completion_tokens":2458,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":472,"completion_tokens_details":{"reasoning_tokens":2384}},"tokens_in":472,"tokens_out":2458,"duration_ms":17805,"temperature":1.0,"reasoning_tokens":2384,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:14:18.626234+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same error-detection prompts on authentic student-written solutions to the same 200 math word problems, with errors labeled by independent human graders, and measure the conventional-versus-alternative gap. If the gap vanishes or reverses on real solutions, the conformity bias and AskBD's reported benefit are artifacts of the synthetic generation pipeline rather than properties of the detectors.","supporting_citations":[],"review_version":1}