{"id":"78ea85e5-c5b1-46ff-a9d5-f086b6d9ae4a","arxiv_id":"2501.14551","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Homogeneous deep ensembles shrink accuracy gaps between demographic groups without lowering overall accuracy, and the optimal training-data balance shifts toward the harder group when per-group task difficulty differs.","lead":"Ensembling several copies of the same deep network reduces accuracy gaps between demographic groups while improving accuracy for every group. The authors also find that when one group's task is harder, a balanced training dataset is not optimal: the harder group should be over-represented.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Real-data evidence for the suboptimality of balanced training rests on balance ratios selected on the test set without confidence intervals; the reported improvements may be in-sample optima rather than robust effects.","rationale":"The stress-test focuses on the real-data component of the central claim because that is where the paper moves from a controlled demonstration to a practical recommendation. The synthetic experiments are internally sound: they directly manipulate label noise or boundary rotation, and the monotonic shift of the optimal balance ratio with difficulty is visible in Figures 3 and 6. The difficulty-proxy concern raised by the reader is real and is acknowledged in Section 6, but it does not directly threaten the synthetic evidence; it threatens only the operationalization in real datasets. A more specific and less acknowledged threat is the selection-on-test protocol used to identify the 'ideal balance ratio' in Section 4.2. Choosing the best ratio from a grid by its test-set performance compares balanced training to the winner of a multiple-comparison sweep. Without confidence intervals or a validation split, the reported reductions (e.g., 3.4 points in CelebA) are exactly what one would expect from selecting the minimum of a noisy curve. The paper's 5 folds could have been used to quantify this, but no error bars or tests are reported. Therefore the real-data support for 'balanced datasets may be suboptimal' is currently unverified, although not necessarily false. Because the synthetic evidence and the positive-sum ensembling result remain plausible and partially supported by prior work, the appropriate verdict is still CONDITIONAL, but the conditions should include a proper validation-based re-analysis of the real datasets. This is why I report partial agreement with the reader: the proxy fragility is a related but distinct weakness; the missing statistical protocol is the load-bearing one.","tokens_in":9174,"tokens_out":11746,"duration_ms":113960,"concrete_test":"Re-run the real-data experiments with a validation-based selection protocol. For each of the 5 folds: split the balanced dataset into train and test. On the train portion, train models at each balance ratio (e.g., 10% steps) and select the ratio that minimizes a fairness/accuracy objective estimated on a validation split (or by cross-validation). Then evaluate the balanced ratio and the selected ratio on the held-out test fold. Report paired differences (gap and overall accuracy) across the 5 folds with bootstrap 95% confidence intervals. If the selected ratio does not outperform balanced training by a margin exceeding the bootstrap CI (or a paired non-parametric test), the claim that balanced training is suboptimal cannot be supported by the real data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central empirical claim that a balanced dataset can be suboptimal is supported in real settings by two demonstrations (CheXpert and CelebA, Section 4.2). The protocol for choosing the 'ideal balance ratio' is not specified; the text states that the authors 'could also find a non-balanced scenario' and later 'we find that a value exists (80-20 ratio)'. This indicates a search over balance ratios. If the ratio is selected by minimizing the gap / maximizing accuracy on the same test set used to report the result, then the balanced configuration is being compared to the best of many alternatives on that same test set. Random noise in the test accuracy curve guarantees that the best alternative will look better than the balanced point, even if no true advantage exists. The paper reports 5 folds but no confidence intervals, standard errors, or significance tests for the 3.4-point gap reduction (CelebA) or the 0.45% overall gain. In CheXpert the reported advantage is described as 'close to the balanced scenario', making selection noise even more plausible. Thus the real-data pillar of the headline claim is not statistically grounded. The synthetic experiments (Section 4.1), where difficulty is directly manipulated and the relationship between noise level and optimal ratio is monotonic, are more convincing, but they do not by themselves establish that balanced datasets are suboptimal in realistic settings with unknown, proxied difficulty.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates whether homogeneous deep ensembles improve group fairness (defined by protected attributes) without sacrificing overall performance, and how the interplay between subgroup under-representation and per-group task difficulty affects the optimal data balance. Using synthetic Gaussian binary classification tasks with controlled label noise or rotated decision boundaries, and two real image datasets (CelebA, CheXpert), the authors report that ensembles consistently increase accuracy for all groups while reducing the accuracy gap between groups ('positive-sum fairness'). They further report that when one subgroup's task is harder, the balance ratio that minimizes the gap also maximizes overall accuracy, and can be far from 50-50; a perfectly balanced dataset can be suboptimal. The conclusions are derived from accuracy comparisons across ensemble sizes and balance ratios.","tokens_in":9438,"tokens_out":4398,"duration_ms":40008,"significance":"If the findings hold, they offer a practical, architecture-agnostic fairness intervention (ensembling) that avoids the usual leveling-down trade-off, and they challenge the default assumption that balanced training data is always optimal for fairness. The synthetic experimental design is careful: 5 folds, 500 random ensemble draws, no fitted constants, and the ensemble-versus-single-model comparison is an independent measurement. The paper also explicitly discusses limitations of the difficulty proxy. However, the real-data evidence for the suboptimality of balanced training currently lacks statistical grounding, and the selection of 'ideal' balance ratios is under-specified, so the strength of the practical claims exceeds the current evidence.","major_comments":[{"comment":"The procedure by which the 'ideal balance ratio' (40-60 for CheXpert, 80-20 for CelebA) was chosen is not stated; if the ratio was selected by minimizing gap or maximizing accuracy on the same test set used for evaluation, the reported 3.4-point gap reduction and 0.45% overall gain are likely optimistic due to selection over multiple candidate ratios. Please specify the selection protocol (e.g., a validation split), and report the full balance-ratio sweeps with confidence intervals or bootstrap error bars for the headline numbers.","section":"Section 4.2, Figure 4"},{"comment":"The conclusion that harder groups need over-representation relies on the assumption that accuracy differences under balanced training measure intrinsic task difficulty. The paper acknowledges this in Section 6, but the Discussion (Section 5) states the conclusion without this caveat. Since the real-data demonstrations cannot separate intrinsic difficulty from other causes of performance gaps (e.g., sampling variability, label quality, model choice), the real-data claims should be explicitly conditional on the proxy, or supplemented with a more direct difficulty measure.","section":"Sections 3.1 and 6"},{"comment":"The statement that ensembles reduce the gap 'to be insignificant' (end of Section 1 and repeated in Section 5) is a statistical claim unsupported by any test or confidence interval. Please add a significance test (e.g., a bootstrap confidence interval for the gap difference) or rephrase to 'small' or 'near zero' to avoid the statistical connotation.","section":"Section 4.1 and Section 5"}],"minor_comments":[{"comment":"'Equal contributtion' should be 'Equal contribution'.","section":"Title page"},{"comment":"'We begun' should be 'We began'; 'raging from' should be 'ranging from'.","section":"Section 3.1"},{"comment":"The sentence 'the intrinsic difficulty of the task for different subgroups is not trivial to determine and.' has a dangling 'and.' and should be completed or removed.","section":"Section 1"},{"comment":"'forlabel noise scenario' is missing a space; it should read 'for label noise scenario'.","section":"Figures 2 and 3 captions"},{"comment":"In the CheXpert paragraph, 'the performance difference between males and females was not very significant' uses 'significant' informally; consider 'large' to avoid confusion with statistical significance.","section":"Section 4.2"},{"comment":"The phrase 'close to the balanced scenario (40%)' is ambiguous; clarify that 40% refers to the male proportion in a 40-60 M-F split.","section":"Section 4.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is an empirical study with a clearly stated limitations section; the main reason for major revision is the lack of uncertainty quantification and an undefined selection protocol for the 'ideal' balance ratios in the real-data experiments. With a validation-based selection and reported confidence intervals, the practical claims could be substantially strengthened. The topic seems suitable for the journal's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real news here is the interaction, not ensembling per se. Ko et al. already showed homogeneous ensembles help the worst target class, and Schweighofer et al. studied protected groups through the lens of predictive diversity. This paper manipulates both per-group task difficulty and under-representation in controlled synthetic experiments and shows two things: ensembling improves both groups without leveling down, and when one group's task is harder, the optimal training balance shifts in favor of that group. That is a genuinely useful and non-obvious result, especially the caution that a perfectly balanced dataset can be suboptimal.\n\nThe synthetic work is the strong part. Gaussian clusters, label noise or rotated boundaries, 5 folds, 500 ensemble draws, symmetric controls—this is careful. The monotonic shift of the ideal balance ratio with noise level is convincing, and the rotating-boundary appendix backs it up.\n\nThe soft spots are in the real-data section. The protocol for choosing the 'ideal balance ratio' in CheXpert and CelebA is not specified. The text says they could 'find a non-balanced scenario' and later that a value exists (80-20), which sounds like a test-set search. With five folds and no confidence intervals or significance tests, the 3.4-point gap reduction and 0.45% overall gain could easily be selection noise. The difficulty proxy—using balanced-dataset accuracy as task difficulty—is circular in principle, though the authors explicitly flag it in the limitations. That is honest, but it means the headline claim about balanced datasets rests on a proxy that can be contaminated by sampling variability or model choice. Also, no code is released, which limits reproducibility.\n\nNet: the central mechanism is likely real, and the synthetic evidence supports it. The paper needs error bars, a clear description of the ratio-selection protocol, and code before the real-data claims can be taken at face value. But it is a legitimate empirical contribution, not a house of cards.","headline":"A clean synthetic demonstration that homogeneous ensembles can give positive-sum fairness and that optimal balance shifts with task difficulty; the real-data support is thinner and needs error bars and a clear selection protocol.","tokens_in":9932,"tokens_out":1686,"would_cite":true,"duration_ms":17525,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Averaging several independently trained deep networks narrows accuracy gaps between protected groups while raising accuracy for every group, and when one group's task is harder, a perfectly balanced dataset is no longer optimal.","keywords":["deep ensembles","algorithmic fairness","group fairness","protected attributes","task difficulty","under-representation","positive-sum fairness","dataset balancing"],"falsifier":"Find a real or synthetic classification task where a group underperforms on balanced training data, then show that the underperformance vanishes when label noise is removed while balancing is unchanged, or that over-representing that group lowers overall accuracy and widens the gap; such a case would show the balanced-performance proxy confounds difficulty with data quality and break the recommended over-representation rule.","tokens_in":9016,"feed_emoji":"⚖️","tokens_out":4939,"duration_ms":45154,"temperature":0.7,"pith_summary":"This paper tries to establish two things. First, a plain homogeneous ensemble of deep networks—same architecture, same training data, different random initializations—narrows the accuracy gap between protected subgroups while improving accuracy for every subgroup, an outcome the authors call positive-sum fairness. Second, when subgroups differ in intrinsic task difficulty, a perfectly balanced training set is not the fairness-optimal choice: over-representing the harder group simultaneously improves overall accuracy and reduces the gap. The authors test this in controlled synthetic settings and in two real image datasets. If right, it means a simple, model-agnostic technique can act as a fairness intervention with no accuracy trade-off, and that standard rebalancing advice should be revised to account for per-group difficulty.","feed_headline":"Ensembles shrink accuracy gaps and lift every group","feed_subtitle":"When one group faces a harder task, the best training mix over-represents it—not 50-50.","key_machinery":"The central object is a homogeneous deep ensemble: several models with identical architecture and hyperparameters, trained independently on the same samples, differing only in initialization and training stochasticity, then averaged. The paper's second load-bearing idea is a proxy: when a balanced dataset yields a performance gap, they read that gap as relative task difficulty. The experiments manipulate difficulty in controlled synthetic ways (flipping labels in one subgroup, rotating one subgroup's optimal decision boundary) and vary the male/female sample ratio, then measure gap and accuracy as ensemble size grows. The ensemble does the fairness work because averaging reduces variance and disproportionately lifts the group with higher per-sample error.","core_discovery":"On the paper's own terms, the discovery is that homogeneous ensembling is a positive-sum fairness intervention: it consistently reduces the accuracy gap between protected subgroups while raising the accuracy of every subgroup, with no leveling-down trade-off. A second discovery is that under-representation and per-group task difficulty interact so that balance is not the fairness optimum: when one group's task is intrinsically harder, the sample ratio that minimizes the gap and maximizes overall accuracy over-represents the harder group, and a perfectly balanced dataset can hurt both.","pith_inferences":["Our inference: if ensemble gains are largest for the harder group and grow with difficulty, then using an ensemble may reduce the need for aggressive rebalancing; in some regimes ensembles could substitute for oversampling rather than complement it.","Our inference: the label-noise and rotated-boundary manipulations produce the same qualitative conclusion, which hints the effect is about irreducible per-group error rather than the specific mechanism; a direct test would vary per-group error structure while holding balanced accuracy fixed.","Our inference: the recommended over-representation level should depend on an estimate of per-group difficulty, so a practical workflow is to run a balanced pilot, estimate the gap, and oversample the underperforming group until gap and overall accuracy are jointly optimized; this follows from the paper's ideal-balance-ratio plots but is not stated by the authors."],"forward_implications":["For every synthetic and real setting tested, adding models to a homogeneous ensemble increased accuracy for both protected groups and shrank the gap, so fairness gains do not come at the cost of overall performance.","The representation ratio that minimizes the male-female gap also maximizes overall accuracy; as the harder group's difficulty grows, the optimal ratio shifts away from 50-50 toward over-representing the harder group.","A perfectly balanced dataset can be strictly worse than an imbalanced one on both overall accuracy and group gap when per-group task difficulty differs.","In the real datasets, non-balanced ratios (roughly 40-60 for one and 80-20 for the other) achieved positive-sum fairness, with the underperforming group improving the most as ensemble size grew."],"supporting_citations":[{"why":"Supplies the earlier finding that homogeneous deep ensembles favor worst-performing target classes, which this paper extends to protected attributes.","marker":"[15]"},{"why":"The closest prior work showing deep ensembles benefit protected groups unevenly via predictive diversity; the paper contrasts its own difficulty-and-representation account with this mechanism.","marker":"[26]"},{"why":"Provides the pretrained convolutional backbone used for the real-image experiments.","marker":"[11]"},{"why":"Provides the chest X-ray dataset and labels used to construct sex subgroups and the lung-opacity classification task.","marker":"[13]"},{"why":"Provides the face attribute dataset used to construct gender and hair-color subgroups in the real-world experiments.","marker":"[20]"},{"why":"Used to justify balancing CelebA across both gender and blond attribute, avoiding known spurious correlations in the setup.","marker":"[25]"},{"why":"Defines the leveling-down trade-off that the paper claims homogeneous ensembles avoid by achieving positive-sum fairness.","marker":"[32]"}],"fun_headline_variants":["Ensembles reduce accuracy gaps and lift all groups","Balanced data not always best for algorithmic fairness","To be fair, give harder groups more data","Ensembles improve fairness without hurting overall accuracy","Why over-representing hard groups beats 50-50 split"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole argument rests on treating the performance gap seen when training on perfectly balanced data as a true measure of task difficulty per group, rather than an artifact of sampling, label noise, or model choice.","fun_headline_variants_meta":{"raw":{"variants":["Ensembles reduce accuracy gaps and lift all groups","Balanced data not always best for algorithmic fairness","To be fair, give harder groups more data","Ensembles improve fairness without hurting overall accuracy","Why over-representing hard groups beats 50-50 split"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00033,"raw_usage":{"total_tokens":1815,"prompt_tokens":895,"completion_tokens":920,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":511,"completion_tokens_details":{"reasoning_tokens":847}},"tokens_in":511,"tokens_out":920,"duration_ms":8748,"temperature":1.0,"reasoning_tokens":847,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:01:57.716384+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Find a real or synthetic classification task where a group underperforms on balanced training data, then show that the underperformance vanishes when label noise is removed while balancing is unchanged, or that over-representing that group lowers overall accuracy and widens the gap; such a case would show the balanced-performance proxy confounds difficulty with data quality and break the recommended over-representation rule.","supporting_citations":[{"cited_title":"The Disparate Benefits of Deep Ensembles","cited_arxiv_id":"2410.13831","evidence_quote":"The closest prior work showing deep ensembles benefit protected groups unevenly via predictive diversity; the paper contrasts its own difficulty-and-representation account with this mechanism."},{"cited_title":"An Investigation of Why Overparameterization Exacerbates Spurious Correlations","cited_arxiv_id":"2005.04345","evidence_quote":"Used to justify balancing CelebA across both gender and blond attribute, avoiding known spurious correlations in the setup."}],"review_version":1}