{"id":"a6036282-6616-421b-b0c6-a48479d82289","arxiv_id":"2608.09768","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"ReliableNet trains classifiers under an explicit budget on the joint probability of high-confidence and incorrect predictions, and reports held-out certification on six benchmarks.","lead":"A new training method, ReliableNet, adds a constraint to deep classifiers that limits the probability of being simultaneously confident and wrong. Early tests on six datasets suggest it meets the target on every seed in distribution, while standard calibration, conformal, and selective-prediction baselines do not.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'only method certified' claim rests on a data-dependent confidence threshold and substantially lower coverage; the certificate may be an operating-point artifact rather than evidence of better confident-error control.","rationale":"The theoretical core of the paper is sound: the inner surrogate is conservative, the population-level implication psi_tau <= alpha => JCW <= alpha is correctly derived, and the Clopper-Pearson certificate is valid conditional on the selected model and threshold. The load-bearing weakness is in the experimental protocol that supports the headline claim. The reader already flagged threshold and checkpoint selection on the validation fold and the absence of fold-size reporting; this stress-test sharpens the concern by noting that the certificate operates at a data-dependent epsilon and at substantially reduced coverage, so the 'only certified' result has not been isolated from abstention effects or from the choice of epsilon. The proposed test would settle this by using pre-specified thresholds and matched-coverage operating points. Because the paper's theory and reported tables are internally consistent but the central practical claim requires this additional check, the reader's CONDITIONAL verdict remains appropriate; no verdict change is recommended.","tokens_in":26491,"tokens_out":18269,"duration_ms":179173,"concrete_test":"Re-run the in-distribution comparison under two fixed protocols: (i) with epsilon fixed in advance to values such as 0.7, 0.8, and 0.9 before any training or selection, and (ii) with operating points matched to equal coverage using the risk-coverage curves, computing the Clopper-Pearson certificate and empirical JCW at each matched point. If ReliableNet is no longer the only certified method at pre-specified thresholds, or if baselines become certified when coverage is matched, then the headline certification claim is an artifact of data-dependent threshold selection and lower coverage.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 4.7 gives a valid Clopper-Pearson certificate only conditional on a fixed model and a fixed threshold epsilon. In the experiments, epsilon* is not fixed a priori: it is chosen as the 80th percentile of misclassified selection-fold confidences after an ERM warm-up, and the final checkpoint is selected by validation-fold feasibility. Consequently, the reported 'certified within JCW budget' is a statement about a threshold selected to make the event favorable, not about a practitioner-specified confidence level. The central claim also depends on operating point: Table 3 shows ReliableNet achieves certification with substantially lower coverage than baselines (e.g., SyntheticBand 0.42 vs 0.75, CIFAR-10 0.52 vs 0.68, UNSW-NB15 0.85 vs 0.96). Since the JCW constraint can always be satisfied by abstaining more, the certification advantage may largely reflect a coverage-abstention trade-off rather than superior confidence control at a fixed operating point. The abstract's wording that ReliableNet remains 'very competitive in coverage' is not supported by these coverage gaps, and the 'only certified' claim has not been shown to survive matched-coverage or pre-specified-threshold comparisons.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"ReliableNet proposes a training-time approach to control the Joint Confident-Wrong (JCW) probability, the probability that a classifier predicts confidently and incorrectly. The problem is formulated as a chance-constrained ERM problem with constraint JCW(θ)≤α, encoded through a smooth conservative inner surrogate ψ_τ(θ) built from the Geletu-Hoffman smoothing family, so that ψ_τ≤α implies JCW≤α at the population level. A primal-dual algorithm (Algorithm 1) approximately solves the surrogate problem, and a one-sided Clopper-Pearson bound on an independent certification fold is used to certify the final hard JCW event. Experiments on four tabular and two image datasets compare ReliableNet with ERM, temperature scaling, confidence thresholding, conformal risk control, SelectiveNet, and Deep Gamblers, reporting that ReliableNet is the only method whose Clopper-Pearson certificate is below the budget on every dataset and seed, and that it attains the lowest empirical JCW under demographic, spurious-correlation, ambiguity, novel-class, and covariate shifts.","tokens_in":26772,"tokens_out":15287,"duration_ms":118810,"significance":"The paper has several strengths: the conservative smoothing implication (Eq. 16) is correctly derived from the existing Geletu-Hoffman family; the decomposition JCW = Cov × (1−Acc_hc) and the selective-risk bound are clean; and the Clopper-Pearson certificate in Theorem 4.7 is a valid conditional guarantee for a fixed model on an independent sample. The AURC and risk-coverage comparisons in Figure 2 are an appropriate way to address the operating-point confound. If the empirical claims withstand scrutiny, the method would integrate chance-constrained optimization with a practically relevant tail-risk objective. However, the central empirical claim is currently weakened by the data-dependent threshold choice, the absence of reported certification-fold sizes, and large coverage gaps relative to baselines on several datasets.","major_comments":[{"comment":"Theorem 4.6 gives a finite-sample feasibility guarantee only for outputs satisfying ψ̂_{τ,n}(θ) ≤ α − δ_n(τ,ρ), but Algorithm 1 does not enforce this margin; it optimizes a Lagrangian with a normalized violation v = (ψ̂ − α)/max(α,0.01) and no slack term. With the reported τ_min = 0.01, δ_n in Eq. (25) is typically large, making condition (26) impractically strict. Section 4.3 acknowledges the heuristic nature of the algorithm, but the abstract and Section 1 claim 'finite-sample results linking empirical and population surrogate feasibility' as a contribution. Please connect the theory to the algorithm, or restrict the finite-sample claim to the Clopper-Pearson certificate that is actually used.","section":"§4.2, Algorithm 1"},{"comment":"The certificate is valid only conditional on a fixed ε, but the experiments set ε* as the 80th percentile of misclassified selection-fold confidences after an ERM warm-up and select the final checkpoint by validation-fold feasibility. Thus the guarantee is not for a user-specified confidence threshold, and the abstract's 'only method certified' claim is an operating-point statement. The Limitations section acknowledges the joint-selection issue, but the abstract and conclusion present the claim without that caveat. Please quantify the sensitivity of certification to ε* or provide a certificate that controls for the selection procedure.","section":"§5.2, §4.3, Theorem 4.7"},{"comment":"The certification advantage is accompanied by substantially lower coverage on SyntheticBand (0.42 vs 0.74–0.76), CIFAR-10 (0.52 vs 0.63–0.68), and UNSW-NB15 (0.85 vs 0.94–0.96). Since the JCW constraint can always be satisfied by lowering coverage, as Remark 3.8 notes, the 'only certified' result may reflect a coverage-abstention trade-off rather than superior confident-error control at a fixed operating point. The risk-coverage curves in Figure 2 are a good partial response, but the in-distribution certification claim is not coverage-matched; the abstract's 'very competitive in coverage' is not supported by these numbers.","section":"Table 3"},{"comment":"The certification fold size m and the per-seed error counts K_m are not reported. The Clopper-Pearson upper bound UCP(K_m,m;ρ) is highly sensitive to m, so the statement '5/5 seeds certified' is uninterpretable without knowing m and the observed counts. Please report the certification fold size for each dataset and the per-seed K_m values (or a summary) for each method.","section":"§5.2, Table 3"},{"comment":"The comparison with Conformal Risk Control should be qualified: CRC's guarantee is E[R_{n+1}(ε̂)] ≤ α in expectation over the n+1-th exchangeable sample, not a high-probability bound on a fixed certification fold. Applying the same Clopper-Pearson test to CRC evaluates a different property than the one CRC promises. Please state this explicitly and consider reporting CRC's expected-risk guarantee separately.","section":"§4.4, Table 3"}],"minor_comments":[{"comment":"The abstract refers to a 'user-specified confidence threshold ε', but Section 3.3 states that ε is a data-driven threshold selected from the validation set. Please align the terminology.","section":"Abstract, §3.3"},{"comment":"The Deep Gamblers loss appears to have a typo: the standard loss is −log((p_{y_i} + p_{m+1})/o), but the displayed formula does not show the division by the reward parameter o. Please correct.","section":"Eq. (28)"},{"comment":"The dual update multiplies by the batch fraction B/n; this is unusual for projected dual ascent and its purpose is not explained. Please clarify or remove the factor.","section":"Algorithm 1"},{"comment":"The sizes of the training, selection, and certification folds are not stated for any dataset. They are needed to interpret the Clopper-Pearson certificate and should be reported.","section":"§5.1"},{"comment":"The risk budgets differ across datasets (α=0.05 for tabular, α=0.03 for CIFAR-10, α=0.01 for Colored-MNIST) without justification. Since the certificate's difficulty depends on α, please either use a common α or justify the per-dataset choices.","section":"§5.2"}],"recommendation":"major_revision","confidential_remarks":"The population-level theory is sound and the Clopper-Pearson certificate is valid in isolation. The main risk is that the headline 'only method certified' is presented without caveats on threshold selection and coverage, which may mislead readers. The authors acknowledge some of these limitations in the final section but do not carry them into the abstract. The missing certification-fold sizes and coverage-matched analysis are fixable in revision. The Geletu et al. (2017) framework is externally published and is legitimately cited, though one of the present authors is a co-author of that framework."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something real. Formalizing Joint Confident-Wrong probability as a training-time chance constraint, with a conservative smooth surrogate that provably implies JCW <= alpha, is a genuine step beyond post-hoc calibration, conformal risk control, and selective prediction. The decomposition JCW = Cov * (1 - Acc_hc) is elementary but useful, and the Clopper-Pearson certificate is valid for a fixed model on an independent sample. The authors also deserve credit for the breadth of their evaluation: six datasets, five shift types, and six baselines, including trained selective predictors. The stress-test results consistently show ReliableNet with the lowest JCW, and the risk-coverage curves at matched coverage suggest the improvement is not purely an abstention artifact on several datasets.\n\nThe soft spots are real and roughly in the order the stress-test note identifies. First, the threshold epsilon* is not fixed a priori: it is the 80th percentile of misclassified selection-fold confidences after an ERM warm-up, and the final checkpoint is selected by validation feasibility. The certificate in Theorem 4.7 is conditional on a fixed threshold and model; the selection process is not accounted for. The paper acknowledges this in its limitations section, which is honest, but the abstract's 'only method certified' claim is stronger than the procedure supports. Second, the coverage gaps are large. SyntheticBand 0.42 vs 0.75, CIFAR-10 0.52 vs 0.68. A constraint on JCW can always be met by abstaining more, so the certification advantage may partly be an operating-point artifact. The paper's phrase 'very competitive in coverage' is not supported; the AURC comparisons help, but matched-coverage or pre-specified-threshold tests would be needed to settle it. Third, the finite-sample feasibility theory (Theorem 4.6) requires solving with a margin, but Algorithm 1 uses bpsi <= alpha; the experiments instead rely on Clopper-Pearson. That disconnect should be addressed in revision, even if the practical certificate is the more relevant one.\n\nWho is this for? Researchers working on reliable ML, selective prediction, and risk-controlling training. They will find the formulation useful and the experimental evidence suggestive, though not definitive pending code and matched-coverage analysis. I would send it to peer review with major revisions: the core idea and theory are sound, the experiments are broad, but the central claim needs re-framing and the operating-point issue needs a direct comparison.\n\nI would cite this if I work on training-time reliability constraints, and it deserves a serious referee despite my skepticism about the headline claim.","headline":"A serious and mostly sound training-time method for controlling confident misclassification, but the headline certification claim rests on a data-dependent threshold and a substantial coverage trade-off.","tokens_in":27314,"tokens_out":1834,"would_cite":true,"duration_ms":17577,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T07","90C15"],"pacs":[],"model":"deepseek-v4-flash","headline":"Training can force a classifier to keep the probability of being simultaneously confident and wrong under a user-set budget, and the paper's ReliableNet is the only method that passes the held-out certificate on all six benchmarks.","keywords":["joint confident-wrong probability","chance-constrained optimization","reliable classification","selective prediction","calibration","Clopper-Pearson certification","distribution shift","deep learning"],"falsifier":"Train ReliableNet on any of the six benchmarks with the paper's protocol, freeze the model and the threshold $\\varepsilon^*$, draw a fresh certification fold from the same source distribution, and compute the one-sided Clopper-Pearson upper bound $U_{\\mathrm{CP}}(K_m,m;0.05)$ on the hard JCW event; the paper's central claim fails if any dataset-seed gives a bound above the per-dataset budget $\\alpha$.","tokens_in":26313,"feed_emoji":"🛡️","tokens_out":14771,"duration_ms":122068,"temperature":0.7,"pith_summary":"High-confidence mistakes are the dangerous kind: they sail past abstention and human review exactly when the model is wrong. The paper proposes training classifiers with an explicit constraint that the Joint Confident-Wrong (JCW) probability—the chance that a prediction is both confident and incorrect—stays below a user-chosen budget $\\alpha$. Technically, this is a chance-constrained empirical risk minimization problem, solved with a smooth conservative inner surrogate whose feasibility at the population level implies the original JCW constraint, and the final model is certified on an untouched fold by a Clopper-Pearson upper bound. The paper reports that across four tabular and two image datasets, this method is the only one certified within the JCW budget for every dataset and seed in distribution; under demographic, ambiguity, spurious-correlation, novel-class, and covariate shifts it attains the lowest empirical JCW while remaining competitive in accuracy, coverage, calibration, and selective ranking. If correct, the paper shows that reliability against confident errors can be engineered at training time rather than patched after training.","feed_headline":"One training scheme keeps confident-wrong errors within budget","feed_subtitle":"Why it matters: a confident wrong answer bypasses abstention and review; this method caps that risk at training time.","key_machinery":"The load-bearing objects are the scalar violation function $g_\\theta(Z)=\\min\\{c_\\theta(X)-\\varepsilon,\\ell_\\theta(X,Y)\\}$ and the paper's parametric smoothing family $\\zeta(\\tau,s)=\\frac{1+m_1\\tau}{1+m_2\\tau e^{-s/\\tau}}$, which is bounded, dominates the indicator $1\\{s\\ge0\\}$, and converges to it as $\\tau\\downarrow0$. Averaging $\\zeta(\\tau,g_\\theta(Z))$ and its reflection gives the bracket $1-\\psi_\\tau(\\theta)\\le \\Pr(g_\\theta(Z)\\le0)\\le \\phi_\\tau(\\theta)$, so the inner feasible set $\\{\\theta:\\psi_\\tau(\\theta)\\le\\alpha\\}$ sits inside the true JCW feasible set; the training solves only the inner problem and uses the outer value as a tightness diagnostic. The identity $\\mathrm{JCW}=\\mathrm{Cov}(1-\\mathrm{Acc}_{\\mathrm{hc}})$ links the constraint to selective risk and explains why accepted-region calibration improves as a byproduct. Optimization minimizes the ERM loss plus a multiplier-weighted violation, with descent on the parameters and projected ascent on the constraint multiplier.","core_discovery":"The central discovery is that the event of being confident and wrong can be encoded exactly as a scalar violation function $g_\\theta(Z)=\\min\\{c_\\theta(X)-\\varepsilon,\\ \\ell_\\theta(X,Y)\\}$, and that the probability of this event can be controlled as a probabilistic constraint during training. Under a generic no-tie assumption, the paper proves $\\Pr(g_\\theta(Z)>0)=\\mathrm{JCW}(\\theta)$ and derives the identity $\\mathrm{JCW}(\\theta)=\\mathrm{Cov}(\\theta)(1-\\mathrm{Acc}_{\\mathrm{hc}}(\\theta))$, so the budget $\\alpha$ is equivalent to a required accuracy on accepted inputs. To make the discontinuous event trainable, the paper uses a parametric smooth family $\\zeta(\\tau,s)$ that dominates the Heaviside step pointwise; since $\\psi_\\tau(\\theta)\\ge\\mathrm{JCW}(\\theta)$, any parameter with $\\psi_\\tau(\\theta)\\le\\alpha$ is feasible for the original constraint. It then gives uniform-concentration finite-sample guarantees and, in the experiments, certifies the final model with a one-sided Clopper-Pearson upper bound on the hard JCW event using an independent fold. On six benchmarks, the paper reports that this method is the only one whose certificate is below the budget on every seed in distribution, and that under five types of distribution shift it has the lowest empirical JCW among the compared methods while staying competitive in accuracy, coverage, calibration, and selective-risk ranking.","pith_inferences":["The certificate treats the confidence threshold and checkpoint as fixed before the certification fold is observed; a stronger design, not tested in the paper, would fold threshold and checkpoint selection into a single certificate so validation-set choices cannot inflate the reported guarantee.","The same violation-function construction could be applied to group-conditional JCW constraints; the paper's own per-family UNSW-NB15 analysis shows marginal feasibility does not guarantee subgroup feasibility, so group-level budgets are the natural next experiment.","The certificate is a one-time statement about an i.i.d. certification fold; deployment would need an ongoing monitor that re-estimates JCW on fresh data, because any distribution shift breaks the transfer of the guarantee."],"forward_implications":["A practitioner can set $\\alpha$ as an explicit reliability budget and obtain a classifier certified to keep the probability of a confident wrong prediction below $\\alpha$, while remaining competitive in accuracy.","Because $\\mathrm{JCW}=\\mathrm{Cov}(1-\\mathrm{Acc}_{\\mathrm{hc}})$, meeting the budget can mean abstaining more; the paper therefore reports coverage alongside JCW, and this trade-off is part of the method's intended behavior.","Under the tested shifts, post-hoc calibration and conformal thresholding track the unconstrained classifier almost exactly, whereas the constrained model keeps its slack and violates the budget later; if correct, this favors changing the model during training over wrapping it afterward.","On four of six datasets the constrained training improves selective risk at matched coverage, indicating the constraint reshapes the confidence ordering itself rather than only the operating threshold.","The theory implies a calibration byproduct: under overconfidence on accepted inputs, a JCW budget also bounds a weighted high-confidence calibration gap, explaining the improved calibration seen in experiments."],"supporting_citations":[{"why":"Supplies the inner-outer smoothing family whose inner feasible set implies the original chance constraint; this is the theoretical core of the training surrogate.","marker":"[Geletu et al., 2017]"},{"why":"Provides the chance-constrained approximation framework used to justify replacing the discontinuous JCW event with a smooth surrogate.","marker":"[Nemirovski and Shapiro, 2007]"},{"why":"Defines Conformal Risk Control, the post-hoc baseline with a finite-sample risk guarantee that ReliableNet must outperform.","marker":"[Angelopoulos et al., 2024]"},{"why":"Documents high-confidence overconfidence and defines temperature scaling, the calibration baseline used in comparisons.","marker":"[Guo et al., 2017]"},{"why":"Gives the classical rejection-rule view connecting a confidence threshold to an acceptance region, which the JCW formulation builds upon.","marker":"[Chow, 1957]"},{"why":"Motivates the two-timescale primal-dual optimizer for the nonconvex-concave Lagrangian of the surrogate problem.","marker":"[Lin et al., 2020]"},{"why":"Defines ERM, the unconstrained training objective that ReliableNet augments with the JCW constraint.","marker":"[Vapnik, 1998]"}],"fun_headline_variants":["Chance-constrained training caps confident-wrong errors","Training that bounds the risk of confident mistakes","ReliableNet: constraining confident-wrong probability during training","A training scheme that certifies low risk of confident errors","Deep learning with a budget on confident-wrong predictions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The guarantee depends on the certification fold being a fresh, representative sample from the deployment distribution, with the model, confidence threshold, and checkpoint fixed before that fold is seen; the paper itself notes that the threshold and checkpoint are chosen on the validation fold and are not part of the joint certificate.","fun_headline_variants_meta":{"raw":{"variants":["Chance-constrained training caps confident-wrong errors","Training that bounds the risk of confident mistakes","ReliableNet: constraining confident-wrong probability during training","A training scheme that certifies low risk of confident errors","Deep learning with a budget on confident-wrong predictions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000224,"raw_usage":{"total_tokens":1537,"prompt_tokens":1100,"completion_tokens":437,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":716,"completion_tokens_details":{"reasoning_tokens":360}},"tokens_in":716,"tokens_out":437,"duration_ms":4003,"temperature":1.0,"reasoning_tokens":360,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:09:29.456667+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train ReliableNet on any of the six benchmarks with the paper's protocol, freeze the model and the threshold $\\varepsilon^*$, draw a fresh certification fold from the same source distribution, and compute the one-sided Clopper-Pearson upper bound $U_{\\mathrm{CP}}(K_m,m;0.05)$ on the hard JCW event; the paper's central claim fails if any dataset-seed gives a bound above the per-dataset budget $\\alpha$.","supporting_citations":[{"cited_title":"Conformal risk control","cited_arxiv_id":null,"evidence_quote":"Defines Conformal Risk Control, the post-hoc baseline with a finite-sample risk guarantee that ReliableNet must outperform."}],"review_version":1}