{"id":"4d13fede-ca15-402b-935b-a0714b5cc669","arxiv_id":"2504.21773","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A two-stage fine-tuning method that separates answer learning from confidence learning improves confidence calibration for LLMs answering multiple questions in a single prompt.","lead":"This paper teaches large language models to answer several questions in one prompt and to mark each answer \"I am sure\" or \"I am unsure\". The method improves how well stated confidence matches actual correctness, which matters for reliable multi-question AI assistants.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The confidence stage is trained on ground-truth answers with labels from the base model before fine-tuning, but deployed on generated answers after fine-tuning; the reported AP/ECE gains are not shown to survive this train/serve mismatch.","rationale":"The reader's conditional verdict rests on the same train/serve mismatch I identify; my read does not move it. I considered other candidate concerns: the abstract's 'up to 25%' vs Section 3.4's 'up to 15%' over baselines is a reporting inconsistency, and the accuracy numbers behind the 'up to 45.8%' claim are not tabulated. Those affect the magnitude of the reported gains but not the internal logic of the method. The load-bearing issue is that confidence supervision is derived from the base model's correctness on gold answers, while confidence is deployed on the fine-tuned model's own generated answers. Without a control that varies the answer source (gold vs generated) and the label source (base vs step-1 model), the AP/ECE numbers in Table 1 could be an artifact of the training distribution rather than evidence of a calibrated knowledge boundary. This is exactly the kind of assumption a two-stage calibration method must test before the central claim is accepted.","tokens_in":16967,"tokens_out":6183,"duration_ms":64937,"concrete_test":"On the existing test sets, decode MAC-Tuning answers, then run the confidence stage twice per prompt: once with the deployed prompt containing the model's own generated answers and once with the training-condition prompt containing ground-truth answers. Report AP and ECE for both conditions. If the gold-answer condition is materially better (e.g., more than 2 AP points), the reported calibration depends on the ground-truth answer distribution and does not transfer to generated answers. In the same experiment, recompute the 'I am sure'/'I am unsure' labels using the step-1 fine-tuned model's own predictions on the training questions and measure agreement with the original base-model labels; low agreement would show the knowledge-boundary labels are stale, so the Eq. (2) objective is fitted to outdated targets.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that two-stage SFT yields reliable per-question confidence in the multi-problem setting. The confidence training signal is constructed in Section 2.1 Step 2 by comparing the base model's outputs with ground truth, and the confidence model is trained (Eq. 2) on prompts whose answer field is the ground-truth answer (Appendix A.3). At inference the same prompt is filled with the model's own post-fine-tuning generations, and AP/ECE are computed against those generations. Two untested shifts are hidden here. First, the labels 'I am sure'/'I am unsure' describe the knowledge boundary of the original LLaMA3, not of the model after the answer-tuning step; Section 3.4 reports accuracy gains of up to 45.8%, so the boundary can move substantially. Second, the confidence model never sees generated answers during training, so any mapping it learned from gold answers may not transfer to its own outputs. If either shift is large, the low ECE and high AP in Table 1 could reflect the training distribution rather than a calibrated deployed model. Neither the paper nor the appendices report a control experiment with generated answers in the confidence prompt, or with labels re-derived from the step-1 model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces MAC-Tuning, a two-stage supervised fine-tuning method for confidence estimation in multi-problem QA, where a single prompt contains several questions. Stage 1 fine-tunes the base model on multi-question answer pairs; stage 2 fine-tunes the resulting model to output per-question \"I am sure\"/\"I am unsure\" labels, with labels derived from whether the base model answered each question correctly. Experiments compare MAC-Tuning with QA-Only, Single-QA, and Merge-AC baselines on CoQA, ParaRel, GSM, MMLU, MTI-Bench, and SQA using LLaMA3-8B, Qwen2-7B, Llama-3.2-3B, and Phi-3.5-mini, reporting AP, ECE, and accuracy. The authors report large AP gains and low ECE, plus a human evaluation on 100 ParaRel examples.","tokens_in":17171,"tokens_out":6969,"duration_ms":63758,"significance":"If the reported gains hold, the method is a simple and practical recipe for obtaining per-question confidence signals in multi-problem prompts, a setting of growing practical importance. The paper is among the first to address confidence calibration specifically in multi-problem reasoning, and the breadth of base models and datasets is a strength. The human evaluation is a valuable complement to automatic metrics. However, the central quantitative claims currently rest on several unverified assumptions and missing supporting tables; the core idea is plausible and testable, so the paper warrants major revision rather than rejection. The release of code is promised but not yet accessible.","major_comments":[{"comment":"The confidence stage is trained on prompts in which the Answer field is the ground-truth answer (Appendix A.3) and labels are assigned from the base model's correctness (Section 2.1, Step 2), but at inference the same prompt is filled with the step-1 model's own generated answers, and AP/ECE are computed against those generations. The paper reports accuracy gains of up to 45.8% after step 1, so the base model's knowledge boundary is not the boundary of the model being evaluated. Because neither the distribution shift from gold to generated answers nor the shift in the underlying correctness boundary is tested, the reported calibration numbers may reflect the training distribution rather than the deployed model's confidence. Please add a control experiment that either (a) trains the confidence stage on generated answers with labels re-derived from the step-1 model, or (b) evaluates the current model on gold-answer prompts, and report AP/ECE for both conditions.","section":"Section 2.1, Eq. (2), Appendix A.3"},{"comment":"The abstract claims 'up to 25%' AP gain over baselines, but Section 3.4 first states 'up to a 15% improvement' and later states 'up to 25% ... compared with Merge-AC'. These are different claims: 25% is relative only to the Merge-AC ablation, not to the best baseline, and 15% appears to be an absolute percentage-point gain over the base model on CoQA. Please state precisely which comparison supports the headline and ensure the abstract and main text are consistent.","section":"Abstract vs. Section 3.4"},{"comment":"Accuracy is claimed to improve by up to 45.8% (average 23.7%) in Section 3.4 and by at least 10.0% (average 26.8%) in Section 3.6, but no table reports accuracy for the main experiments; Figure 3 shows only selected n-sweep results. Additionally, no standard errors or multiple seeds are reported anywhere, so it is impossible to tell whether the AP/ECE differences in Table 1 (e.g., CoQA AP 69.8 vs. 67.4) are significant. Please add an accuracy table and variance estimates.","section":"Section 3.4 and Section 3.6"},{"comment":"The out-of-domain claim that 'MAC-Tuning still outperforms the base model' is not supported by the table, which contains only MAC-Tuning rows. Please include the vanilla model's AP/ECE/accuracy on the same OOD evaluation, or state explicitly that the comparison is against the in-domain baselines in Table 1.","section":"Table 3"},{"comment":"On SQA, Phi-3.5-mini's AP drops from 96.6 (Vanilla) to 52.3 (MAC-Tuning), a large regression that contradicts the text's claim of consistent AP gains and is not discussed. Please explain this result or qualify the claim.","section":"Table 7"},{"comment":"The computation of AP and ECE depends on a 'certain prediction probability' that is described only as 'the weighted average of certain prediction probability and uncertain prediction probability.' Without a precise procedure for converting the textual 'I am sure'/'I am unsure' outputs into probabilities, the headline metrics are not reproducible. Please specify token-level probability extraction or an equivalent operationalization.","section":"Appendix A.5"}],"minor_comments":[{"comment":"In Table 6, MAC-Tuning's ECE is identically 33.5 for all four datasets; this is likely a copy/paste error and should be corrected.","section":"Table 6"},{"comment":"The human evaluation uses 100 examples and a single annotator; please report the selection procedure, confidence intervals, and ideally inter-annotator agreement, and frame the result as supporting rather than definitive.","section":"Section 3.10"},{"comment":"The implementation section does not state whether the two stages use separate training epochs or whether the same hyperparameters are used for all datasets; please clarify.","section":"Appendix A.6"},{"comment":"Cheng et al. (2023a) and (2023b) appear to be the same technical report; please merge or disambiguate the references.","section":"References"},{"comment":"The phrase 'we release our code and resource at MAC-Tuning' does not include a URL; please provide an accessible repository link.","section":"General"},{"comment":"The term 'knowledge boundary' is used for a behavioral correctness proxy; please define it explicitly to avoid conflating parametric knowledge with supervised accuracy on the training set.","section":"Section 2.1"}],"recommendation":"major_revision","confidential_remarks":"The central idea is plausible and the two-stage recipe is simple, but the paper currently over-claims relative to what is actually tabulated: the largest gains are against the Merge-AC ablation, accuracy numbers are asserted without tables, and the training/inference distribution mismatch in the confidence stage is untested. The SQA Phi-3.5 regression and the identical ECE entries in Table 6 suggest the experimental tables need careful checking before the manuscript is suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a plausible incremental contribution—two-stage SFT for multi-problem QA where the model first learns answers, then learns to say \"I am sure/unsure\" per question. The idea is simple and the human evaluation is a real plus. But the reported magnitudes are not yet trustworthy: no error bars, an abstract/section discrepancy, and one table that directly contradicts the AP claim. The train/serve mismatch is also real and untested.\n\nWhat's new: previous work (R-tuning) handles single-problem \"I don't know\"; batch prompting and MTI-Bench look at multi-problem answering but not confidence calibration. MAC-Tuning is the first to combine both, and the separation of answer learning from confidence learning is a sensible recipe. Results are consistent across LLaMA3-8B, Qwen2-7B, Llama-3.2-3B and Phi-3.5-mini, and the out-of-domain transfer experiment (train on SQA, test on others) suggests the behavior generalizes. The human evaluation with blinded annotator shows a 48-point accuracy gap between \"sure\" and \"unsure\" outputs, which is strong evidence that the confidence signal is not just an artifact of the metric.\n\nSoft spots:\n1. No seeds, no error bars. AP differences of a few points could be noise.\n2. Abstract says \"up to 25%\" AP; Section 3.4 says \"up to 15%\" vs baselines and 25% vs Merge-AC. The headline claim is the best-case ablation, not the average.\n3. Table 7 shows Phi-3.5 on SQA: Vanilla AP 96.6, MAC-Tuning 52.3. That is a huge regression, not an improvement. Unless it's a typo, it breaks the \"consistent performance patterns\" claim. Needs an explanation or correction.\n4. Accuracy numbers are claimed (up to 45.8%) but not tabulated anywhere.\n5. The deeper issue: confidence labels come from the base model's correctness before answer-tuning, and the confidence prompt at training contains the ground-truth answer; at inference it contains the fine-tuned model's own generations. Neither shift is tested. The low ECE may reflect the training distribution rather than calibrated deployment. A control with generated answers in the confidence prompt, or labels re-derived from the step-1 model, would settle this.\n\nBottom line: the core recipe may work, and the human eval gives it some teeth. But the paper needs a revision that adds variance estimates, fixes the reporting inconsistencies, and addresses the train/serve mismatch. I'd send it to review—there's a real idea here—but I wouldn't cite the numbers until they're cleaned up.","headline":"A plausible two-stage fine-tuning recipe for multi-problem confidence, undermined by missing error bars, an inconsistent headline claim, and an untested train/serve mismatch.","tokens_in":17692,"tokens_out":3034,"would_cite":true,"duration_ms":29540,"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":"Separating answer learning from confidence learning during fine-tuning gives large language models more reliable per-answer certainty in multi-problem prompts.","keywords":["multi-problem setting","confidence calibration","knowledge boundary","two-stage fine-tuning","hallucination mitigation","average precision","instruction tuning","large language models"],"falsifier":"Take a MAC-Tuning checkpoint and evaluate confidence twice on the same multi-question test prompts: once with the ground-truth answers inserted into the confidence prompt template and once with the model's own sampled answers. If the expected calibration error is substantially higher, or the ranking of \"sure\" versus \"unsure\" answers is much closer to random, in the generated-answer condition, the method's confidence mapping does not carry over to the actual inference distribution.","tokens_in":16774,"feed_emoji":"🎯","tokens_out":15178,"duration_ms":132286,"temperature":0.7,"pith_summary":"The paper targets the multi-problem setting, in which a single prompt asks an LLM to answer several distinct sub-questions at once. Its central claim is that confidence calibration in this setting improves when answer learning and confidence learning are separated into two fine-tuning stages rather than taught together. The proposed MAC-Tuning first fine-tunes on multi-question answer pairs only, then fine-tunes again to output a per-answer \"I am sure\" or \"I am unsure\" judgment, with confidence labels derived from whether the base model could answer each question correctly before tuning. Across six datasets and several base models, the method reports better average precision (how well the model's confidence ranks correct answers above wrong ones) and lower expected calibration error than answer-only, joint, and single-problem baselines, with gains up to 25% in AP and a human-verified gap between sure and unsure answers. A reader should care because batched or multi-query prompting is increasingly common for efficiency and cost, and per-answer confidence is what would let users trust or discard individual responses.","feed_headline":"Two-step fine-tuning lifts LLM answer confidence by up to 25%","feed_subtitle":"Separating answer learning from confidence learning helps models admit uncertainty in multi-question prompts.","key_machinery":"The load-bearing object is the two-stage training schedule named Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning). In stage one the model is fine-tuned on multi-question input/output pairs ($D_{\\mathrm{MultiQA}}$), maximizing $\\log P(A \\mid Q; \\Theta_0)$; in stage two it is fine-tuned on confidence pairs ($D_{\\mathrm{MultiQA,C}}$) in which the input already contains the question set and the answers, maximizing $\\log P(C \\mid Q, A; \\Theta_1)$. The confidence labels are generated before training by running the base model on the composed multi-problem prompts and comparing each answer to the ground truth, which the paper treats as locating the model's knowledge boundary. This separation is what carries the claim: the answer stage teaches the model to produce content in the multi-problem format, and the confidence stage teaches it to map a question-answer pair to a calibrated certainty judgment.","core_discovery":"On the paper's own terms, MAC-Tuning establishes that a language model can learn to solve multiple problems in one prompt and, separately, learn to say whether each answer is trustworthy, and that the separation is what makes the confidence signal work. The method is a two-step supervised fine-tuning recipe: step one maximizes the probability of the multi-answer sequence given the multi-question input; step two, with the step-one model as a starting point, maximizes the probability of the per-answer confidence sequence given the same questions and the already-generated answers. Confidence labels are assigned automatically by comparing the base model's outputs with ground-truth answers before any fine-tuning, so \"I am sure\" marks questions the model could already answer and \"I am unsure\" marks questions it could not. The paper reports that this recipe beats answer-only fine-tuning, joint answer-and-confidence fine-tuning, and single-problem fine-tuning on all tested datasets, with the largest advantage over the jointly trained baseline, and that the effect persists across different backbone models and model sizes.","pith_inferences":["The confidence stage is trained on prompts that already contain the correct answer, while inference fills the same template with the model's own generated answers; a direct extension would retrain the confidence stage on generated answers, or a mix of gold and generated answers, and measure whether the calibration gain survives that shift.","Because the confidence labels come from the base model's own correctness before fine-tuning, MAC-Tuning can be read as teaching the model to reproduce an external judge's verdict about itself; the same two-stage recipe could be adapted to other self-assessment tasks, such as abstention decisions or retrieval confidence, by changing what the second stage predicts.","The out-of-domain transfer results hint that part of what is learned is format-level, namely knowing when to emit per-answer \"sure\" or \"unsure\" tokens in a multi-answer response, rather than dataset-specific content. A testable extension would train only on easy independent questions and check whether the calibration transfers to hard sequential questions with no additional data."],"forward_implications":["On all six datasets (CoQA, ParaRel, GSM, MMLU, MTI-Bench, SQA), MAC-Tuning reports the best average precision and the lowest ECE among the tested baselines, with up to a 25% AP gain over the joint-training baseline and an average 23.7% accuracy gain over the base model.","Separate stages beat joint training: the Merge-AC baseline that learns answers and confidence in one pass is consistently worse, so the central claim is not merely that confidence language helps but that the stepwise separation matters.","A model fine-tuned on three-question prompts retains or improves single-question performance on easier datasets and transfers to five-question prompts, suggesting the multi-problem behavior is not just memorization of a fixed input length.","The confidence signal survives out-of-domain transfer: a model fine-tuned on SQA still improves AP and ECE over the base model on CoQA, ParaRel, MMLU, and MTI-Bench.","Human judges who rated outputs without seeing confidence labels confirmed the signal is real: answers marked \"I am sure\" were factually accurate 89.2% of the time versus 41.2% for \"I am unsure\", a 48-point gap."],"supporting_citations":[{"why":"Supplies the confidence-expression and knowledge-boundary approach that MAC-Tuning extends, plus the modified ParaRel and MMLU datasets used in evaluation.","marker":"(Zhang et al., 2024)"},{"why":"Defines the expected calibration error metric used to measure how well predicted certainty matches true accuracy.","marker":"(Chen et al., 2023)"},{"why":"Supplies CoQA, the conversational QA dataset used for independent-setting multi-problem experiments.","marker":"(Reddy et al., 2019)"},{"why":"Supplies GSM grade-school math problems used to test multi-problem arithmetic reasoning.","marker":"(Cobbe et al., 2021)"},{"why":"Supplies MMLU multiple-choice questions used to test world knowledge and problem solving in the multi-problem setting.","marker":"(Hendrycks et al., 2021)"},{"why":"Supplies ParaRel factual prompts, used as a main independent-setting dataset and for the human evaluation.","marker":"(Elazar et al., 2021)"},{"why":"Supplies MTI-Bench, the sequential multi-task benchmark used in the sequential setting.","marker":"(Son et al., 2024)"},{"why":"Supplies SQA sequential table-QA data used for training and for out-of-domain transfer tests.","marker":"(Iyyer et al., 2017)"},{"why":"Supplies the LLaMA3-8B-Instruct backbone on which the main experiments and baselines are run.","marker":"(Dubey et al., 2024)"},{"why":"Supplies the low-rank adaptation method used to carry out the two-stage supervised fine-tuning.","marker":"(Hu et al., 2021)"}],"fun_headline_variants":["Two-step fine-tuning improves LLM confidence by up to 25%","Separating answer and confidence learning boosts LLM multi-question accuracy","MAC-Tuning teaches LLMs to flag unsure answers in multi-problem prompts","Split answer and confidence training lifts LLM precision by 25%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"MAC-Tuning assumes that confidence judgments learned on prompts that include the ground-truth answer, with labels based on whether the base model answered correctly before fine-tuning, transfer to prompts filled with the model's own generated answers at inference.","fun_headline_variants_meta":{"raw":{"variants":["Two-step fine-tuning improves LLM confidence by up to 25%","Separating answer and confidence learning boosts LLM multi-question accuracy","MAC-Tuning teaches LLMs to flag unsure answers in multi-problem prompts","Split answer and confidence training lifts LLM precision by 25%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000188,"raw_usage":{"total_tokens":1288,"prompt_tokens":855,"completion_tokens":433,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":471,"completion_tokens_details":{"reasoning_tokens":355}},"tokens_in":471,"tokens_out":433,"duration_ms":4554,"temperature":1.0,"reasoning_tokens":355,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:54:02.665870+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a MAC-Tuning checkpoint and evaluate confidence twice on the same multi-question test prompts: once with the ground-truth answers inserted into the confidence prompt template and once with the model's own sampled answers. If the expected calibration error is substantially higher, or the ranking of \"sure\" versus \"unsure\" answers is much closer to random, in the generated-answer condition, the method's confidence mapping does not carry over to the actual inference distribution.","supporting_citations":[{"cited_title":"Measuring and Improving Consistency in Pretrained Language Models","cited_arxiv_id":"2102.01017","evidence_quote":"Supplies ParaRel factual prompts, used as a main independent-setting dataset and for the human evaluation."}],"review_version":1}