{"id":"673b0aa1-d2c1-4074-9455-c55ed088d0c9","arxiv_id":"2507.23167","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A linear probe over layer-wise logit-lens probabilities ranks LLM confidence well enough to slightly beat voting or probability-based baselines in QA ensembles.","lead":"This paper proposes LENS, a method that learns a confidence score for each large language model from its internal hidden states, then picks the answer from the model that seems most confident. The approach aims to improve multi-model question answering by going beyond simple voting or probability averaging.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline 'substantial margin' is not supported by Table 1: with 250 test examples and no significance testing, most reported gains are within sampling error; the paper's own conclusion asks for 'rigorous empirical evaluations' (Sec. 5).","rationale":"Good faith reading: LENS is a plausible, cheap method; it freezes base models, uses logit-lens probabilities, and trains per-model linear probes. The central claim, however, is empirical and quantitative: 'outperforms traditional ensemble methods by a substantial margin.' The evidence is one table with 250 test examples per dataset, no error bars, no repeated splits, and no significance tests. The margins over Majority Vote are 0.8, 5.9, 0.9, -0.1, 1.5, and 0.5 percentage points; over Probability Max, 0.8, 3.2, 2.3, 6.5, 1.5, and 2.5 points. For n=250, a single accuracy estimate has standard error around 3 points, so most differences are within one standard error. Even the 5.9-point BoolQ gain is not guaranteed to be significant without a paired test. The paper's own Section 5 limitation statement concedes the need for 'rigorous empirical evaluations.' I therefore do not attack the mechanism: the logit-lens features might be informative and the learned confidence scores might be comparable. The immediate load-bearing weakness is that the quantitative claim is not established by the reported experiment. This is not an accusation of error; it is a request for the statistical evidence that the claim requires. The reader's verdict of CONDITIONAL is appropriate; my concern does not move it, but it sharpens the condition: either add significance testing with the existing split or rerun with larger or repeated samples. If those tests show no significant margin, the verdict would need to become REJECT. The reader's weakest_assumption focused on cross-model comparability of logit-lens features; I share that as a mechanism risk, but I see the missing statistical support as the more immediate threat to the central claim, so my agreement is partial.","tokens_in":5899,"tokens_out":8899,"duration_ms":108042,"concrete_test":"Use the saved predictions from the five models on the 250 test instances per dataset (or re-run the pipeline) to compute a paired McNemar test between Max Confidence and the stronger of Majority Vote and Probability Max for each dataset, and bootstrap 95% confidence intervals for the accuracy difference. Additionally, repeat the full 500-instance sampling and 250/250 split procedure 20 times and report the mean and standard deviation of the per-dataset margins. If the lower bound of the confidence interval is below 0 on at least 3 of 6 datasets, or the mean margin over repetitions drops below 1 percentage point, the 'substantial margin' claim in the abstract should be withdrawn.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To establish the central claim, Table 1 must show LENS (Max Confidence) beating Majority Vote and Probability Max by a substantial margin. It does not. On 250 test instances, a 5-percentage-point difference corresponds to only ~12 correct answers, and the standard error of an accuracy estimate near 0.5 is ~3.1 points, so pairwise differences of 0.5-3.2 points (CoinFlip, PrOntoQA, SWAG, MathQA) are easily noise. The only >5-point gains are BoolQ over Majority Vote and ProofWriter over Probability Max, and no confidence interval, McNemar test, or repeated-split variance is reported. The paper itself concedes in Section 5 that 'future work could benefit from rigorous empirical evaluations.' Without error bars or a paired significance test, 'consistently outperforms' and 'substantial margin' are unsupported, even though the method may well work. The reader's concern about cross-model comparability of logit-lens features is secondary: even if the features are informative, the reported evidence cannot carry the quantitative claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes LENS, a method for ensembling decoder-only LLMs by training a lightweight per-model linear confidence predictor on layer-wise logit-lens probability vectors. At inference, the system selects the prediction of the model with the highest predicted confidence. The method is evaluated on six multiple-choice and boolean QA datasets with five open-weight LLMs, comparing against majority voting and probability-max selection. The abstract claims that LENS outperforms traditional ensemble methods by a substantial margin, and Table 1 reports the best accuracy on 5 of 6 datasets, with the paper concluding that internal representations are useful for confidence estimation and ensemble learning.","tokens_in":6093,"tokens_out":3802,"duration_ms":44251,"significance":"If the claimed gains are statistically real, LENS would be a simple and inexpensive contribution: it requires no fine-tuning of base models, adds only O(L) parameters per model, and makes use of otherwise discarded internal representations. The authors are transparent about their training protocol, use a held-out split for the confidence predictors, and describe the model selection procedure. However, the significance of the empirical contribution is currently limited by the small test sets (250 instances per dataset), the absence of any uncertainty quantification or paired significance testing, and the narrow baseline set. These issues are not merely cosmetic: they directly affect whether the abstract's 'substantial margin' claim is supported. The manuscript also contains an explicit self-acknowledged limitation in Section 5, which asks for 'rigorous empirical evaluations' in future work.","major_comments":[{"comment":"The central claim of a 'substantial margin' over baselines is not supported by the reported numbers. With 250 test instances per dataset, the standard error of an accuracy estimate near 50% is roughly 3.1 percentage points, so the reported gains of 0.8–3.2 points on CoinFlip, PrOntoQA, SWAG, and MathQA are well within sampling noise. Only the BoolQ gain over Majority Vote and the ProofWriter gain over Probability Max exceed 5 points, and no confidence intervals, McNemar tests, bootstrap estimates, or repeated-split variance are provided. The manuscript itself concedes in Section 5 that 'future work could benefit from rigorous empirical evaluations.' To support the abstract's quantitative claim, the authors should add paired significance tests or bootstrap confidence intervals, and ideally report results over multiple random splits.","section":"§4.4, Table 1"},{"comment":"The method assumes that applying the language-modeling head to every layer's last-token hidden state and softmaxing over answer choices yields probability vectors that are informative about correctness and comparable across five architectures with different tokenizers, hidden-state normalizations, and layer counts. This assumption is load-bearing for LENS because the confidence predictors are trained on these features, but the paper provides no diagnostic evidence for it. A minimal sanity check would be to report the correlation or AUROC of the per-layer probabilities (or the learned confidence scores) against correctness on the development set, or a calibration analysis for each model; without such evidence, the mechanism by which LENS could improve over probability-max is not established.","section":"§3.2, Eqs. (1),(2)"},{"comment":"The baseline set is too narrow to support the claim that LENS 'outperforms traditional ensemble methods by a substantial margin.' Majority voting and raw probability max are two simple aggregation rules, but they do not control for the effect of learning a selection rule on held-out data. The authors should add at least one learned baseline that operates on final-layer probabilities or logits (e.g., logistic regression or a small MLP on the probability vector), plus an oracle upper bound that always selects the correct model. This would clarify whether the gains come from internal features specifically or from any learned model-selection procedure.","section":"§4.3"}],"minor_comments":[{"comment":"PrOntoQA is described as a dataset for 'pronoun resolution and contextual understanding,' but PrOntoQA is a proof-based ontology question-answering dataset; the description should be corrected.","section":"§4.2"},{"comment":"The sentence 'Train-validation split: 80%-20% of the training data' is ambiguous given the preceding description of 250 training and 250 test instances; please clarify whether the validation set is drawn from the 250 training instances and how the best checkpoint is selected.","section":"§4.4"},{"comment":"The text says the Max Confidence method 'consistently outperforms or matches the baseline approaches,' but the ProofWriter row shows Max Confidence at 75.2, below Majority Vote at 75.3; this statement should be rephrased to acknowledge the one exception.","section":"§4.5, Table 1"},{"comment":"The title and author block contain formatting and typographical artifacts, including 'L EARNING', 'A NSWER INTE-GRATION', and an email address that appears as 'sjtu18640985163'; these should be proofread.","section":"Title and author block"},{"comment":"The citation 'de Caritat Mis et al. (1785)' is an unusual way to reference Condorcet's jury theorem; a standard modern citation would be more appropriate and helpful to readers.","section":"§2, related work"},{"comment":"Equation (5) defines the binary cross-entropy loss for a scalar confidence score, but the paper does not discuss how the argmax selection in Eq. (6) behaves if two models receive exactly equal confidence scores; a tie-breaking rule should be stated.","section":"§3.3, Eq. (5)"}],"recommendation":"major_revision","confidential_remarks":"The paper's idea is reasonable and the writing is generally clear, but the empirical evidence is the main weakness. The authors' own Section 5 acknowledges the need for more rigorous evaluation, which supports treating the statistical issues as fixable rather than fatal. I would also suggest the editors consider whether the manuscript's novelty relative to existing confidence-based ensemble methods is sufficiently articulated, since the related work section is brief and does not discuss learned model-selection approaches in detail."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the take: LENS is a sensible, small-scale idea for using logit-lens features to pick the most confident model in an LLM ensemble, but the paper's \"substantial margin\" is not backed by the numbers. On 250 test examples, gains of 0.5-3.2 points are sampling noise, and the only two >5-point gains (BoolQ over majority vote, ProofWriter over probability max) have no confidence intervals or paired tests. The stress-test note has it right.\n\nWhat's actually new: the specific combination—training one linear probe per model on layer-wise softmax probabilities, then selecting the highest-confidence prediction—isn't in the cited literature. Each ingredient is known, but the application to ensemble selection is a reasonable extension. The experimental setup is honest in one key respect: the probes are trained on a held-out split, so there's no circularity. The model set (LLaMA-2, Mistral, BLOOM, GPT-J, Pythia) is diverse and the writing is clear.\n\nSoft spots, in order: (1) The main claim is statistically weak; the paper itself concedes in Section 5 that it needs \"rigorous empirical evaluations.\" (2) Baselines are limited—no LLM-Blender, mixture-of-agents, or even self-consistency. (3) The parameter count claim is wrong as stated: concatenating K-class probabilities over L layers gives O(L*K) parameters, not O(L). (4) Implementation details about token mapping and prompt formatting are missing. (5) Cross-model comparability of logit-lens probabilities is a real concern but secondary to the statistical issue.\n\nWho is this for? People working on ensemble methods or using internal representations for confidence. It's not a major contribution, but it's a plausible stepping stone. As is, I wouldn't cite it as evidence for an ensemble gain, but I'd cite it as a method description if I were comparing approaches.\n\nRecommendation: If an editor asks, I'd send it to peer review rather than desk-reject—the idea is not broken, and a serious referee could demand the larger test sets, significance tests, and stronger baselines. But the paper needs major revision before the claims can be taken at face value.","headline":"A plausible but thinly-evidenced confidence-selection method for LLM ensembles; the headline 'substantial margin' claim is not supported by the reported numbers.","tokens_in":6619,"tokens_out":2832,"would_cite":false,"duration_ms":32347,"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":"A per-model confidence probe trained on layer-by-layer answer probabilities beats voting across six QA datasets.","keywords":["LLM ensemble","confidence estimation","logit lens","internal representations","linear probe","multiple-choice question answering","boolean question answering","max-confidence selection"],"falsifier":"On fresh random splits of the same datasets, train the per-model linear probes on 250 sampled instances and evaluate on the held-out 250; if the model with the highest learned confidence is not correct more often than the model with the highest raw answer probability across repeated splits, the central claim that internal-state confidence improves ensemble decisions would be falsified.","tokens_in":5674,"feed_emoji":"🧠","tokens_out":3702,"duration_ms":41576,"temperature":0.7,"pith_summary":"The paper claims that a lightweight linear probe can learn, for each LLM, how confident that model should be in its own prediction, and that selecting the prediction of the most confident model improves ensemble accuracy. This matters because common ensemble methods such as majority voting or picking the highest raw probability ignore whether a model is reliable in a particular context. The authors extract layer-wise probabilities from each model's internal states, train a separate confidence predictor per model, and then choose the answer from the model with the highest predicted confidence. On six multiple-choice and boolean question-answering datasets, this max-confidence strategy achieves the best accuracy on five of six datasets compared with the two baselines. The central idea is that internal representations, normally discarded after inference, carry useful signals about which model is most likely to be correct on a given question.","feed_headline":"A confidence probe over LLM internals beats majority voting","feed_subtitle":"On five of six QA datasets, LENS picks the model whose internal layers look most certain, beating vote-based and probability-based…","key_machinery":"The logit lens: for each transformer layer $l$, the last-token hidden state $H_l$ is passed through LayerNorm and the model's language-modeling head, then softmaxed over the answer choices to give a probability distribution $p_l$. Concatenating these per-layer distributions forms a feature vector $f_i$ for each model $M_i$. A per-model linear probe $P_i(f_i) = \\sigma(W_i f_i)$ is trained with binary cross-entropy on whether that model's prediction was correct, yielding a confidence score $c_i$; the final ensemble prediction is $\\hat{y} = y_{\\arg\\max_i c_i}$. This mechanism transfers the burden from model-specific logits to learned, context-dependent confidence estimates that are comparable across architectures.","core_discovery":"The paper's central claim is that a linear confidence predictor trained on layer-wise logit-lens probabilities can estimate a model's confidence in its own prediction well enough to drive ensemble decisions. For each model, the method applies the language-modeling head to every layer's last-token hidden state, softmaxes over the answer choices, concatenates those probability vectors, and trains a sigmoid-linear probe to predict whether the model's answer is correct. At test time, the ensemble simply takes the answer from the model with the highest predicted confidence. The paper reports that this max-confidence rule outperforms majority voting and probability-max baselines on most datasets, with Table 1 showing best accuracy on five of six tasks.","pith_inferences":["Beyond the paper: if confidence is learnable from internal states, a natural extension is to test whether a probe trained on one dataset transfers to another, which the authors list as future work and which would distinguish per-instance reliability from dataset-specific artifacts.","Beyond the paper: since the features are probabilities over answer-choice tokens, the same pipeline could be adapted to open-ended generation by defining a small candidate set of tokens, creating a testable link between this method and calibration research.","Beyond the paper: the paper only reports max-confidence selection, so a testable alternative is to use the learned confidences as weights in a soft ensemble; if confidence estimates are well-calibrated, weighted averaging should match or exceed the max rule."],"forward_implications":["If the central claim holds, internal representations of LLMs can serve as a practical signal for ensemble selection without modifying the base models.","The method adds only $O(L)$ trainable parameters per model, where $L$ is the number of layers, so it remains feasible even when the constituent models are large.","The reported results suggest that learned confidence can outperform both majority voting and raw-probability selection on multiple-choice and boolean question-answering tasks.","Because the confidence predictors are trained per model and per dataset, the approach can be applied to any set of decoder-only pretrained LLMs without task-specific fine-tuning."],"supporting_citations":[{"why":"Supplies the logit lens technique used to extract layer-wise probability features in equations (1) and (2).","marker":"nostalgebraist (2020)"},{"why":"Provides LLaMA-2-7B, one of the five member models in the ensemble.","marker":"Touvron et al. (2023)"},{"why":"Provides Mistral-7B, a second member model.","marker":"Jiang et al. (2023)"},{"why":"Provides BLOOM-7B1, a multilingual member model.","marker":"Le Scao et al. (2023)"},{"why":"Provides GPT-J-6B, a member model.","marker":"Wang & Komatsuzaki (2021)"},{"why":"Provides Pythia-6.9B, a member model used for its interpretability-oriented design.","marker":"Biderman et al. (2023)"},{"why":"Supplies the CoinFlip dataset and the few-shot direct-answer prompting setup used in experiments.","marker":"Wei et al. (2022)"},{"why":"Supplies the BoolQ dataset used to evaluate boolean question answering.","marker":"Clark et al. (2019)"}],"fun_headline_variants":["Probing internal states to find the confident LLM for ensembles","Confidence probe on neural states picks the LLM for ensemble","Internal confidence beats majority voting for LLM ensembles","LENS: Learn confidence from internal states to weight LLM predictions","Linear probe on hidden states selects confident model for ensemble"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that applying the same kind of logit-lens transformation to each layer of five different large language models produces probability vectors that are comparable across architectures and informative about which model is actually correct; if those features are not comparable or not informative, the trained confidence probes cannot pick a better model than the probability-max baseline.","fun_headline_variants_meta":{"raw":{"variants":["Probing internal states to find the confident LLM for ensembles","Confidence probe on neural states picks the LLM for ensemble","Internal confidence beats majority voting for LLM ensembles","LENS: Learn confidence from internal states to weight LLM predictions","Linear probe on hidden states selects confident model for ensemble"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000506,"raw_usage":{"total_tokens":2431,"prompt_tokens":872,"completion_tokens":1559,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":488,"completion_tokens_details":{"reasoning_tokens":1477}},"tokens_in":488,"tokens_out":1559,"duration_ms":12327,"temperature":1.0,"reasoning_tokens":1477,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T10:58:53.528263+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On fresh random splits of the same datasets, train the per-model linear probes on 250 sampled instances and evaluate on the held-out 250; if the model with the highest learned confidence is not correct more often than the model with the highest raw answer probability across repeated splits, the central claim that internal-state confidence improves ensemble decisions would be falsified.","supporting_citations":[],"review_version":1}