{"id":"8ed188f5-e611-4279-8737-1154c7d271c5","arxiv_id":"1908.10831","paper_version":5,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Under the Polyak-Lojasiewicz condition, a proximal primal-dual algorithm and an AdaGrad-style variant maximize AUC with deep networks at O~(1/epsilon) sample complexity, with adaptive iteration complexity under slow cumulative gradient growth.","lead":"This paper designs two optimization algorithms for training deep neural networks to maximize the Area Under the Curve (AUC) metric, which is useful when classes are imbalanced. The algorithms come with formal convergence rate guarantees if a common Polyak-Lojasiewicz condition holds for the network objective.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing risk is Assumption 1(1): the O~(1/epsilon) and adaptive rates in Theorems 2-3 all require a PL condition on phi that is neither proved for the deep AUC objective nor empirically checked.","rationale":"The reader identifies Assumption 1(1), the PL condition on phi, as the weakest assumption. I agree. The conditional theorems are detailed and appear internally consistent: the recursions in Theorems 2 and 3 follow from Lemma 2 and Lemma 3 under Assumption 1, and I found no fatal algebraic error in the main proof chain. The load-bearing gap is external validity: the paper asserts the PL condition for the deep AUC objective without proving it for the actual network and without measuring it, and the Appendix A.7 example is far more restrictive than the experimental setting. Because all fast rates collapse if the PL constant is not positive, this is a genuine contingency. However, this is an addressable gap rather than a disproof: the conditional rates are meaningful, and a careful empirical check of the PL ratio could settle whether the condition holds in practice. The reader's CONDITIONAL verdict is therefore appropriate; my review does not move it. I also note that Lemma 1's transfer from P(w) to phi appears to omit a p(1-p) scaling factor in places, but since the main theorems assume phi-PL directly rather than deriving it, this does not change the conditional validity and is secondary to the unverified nature of Assumption 1(1).","tokens_in":46949,"tokens_out":15333,"duration_ms":155510,"concrete_test":"On the exact finite-sample AUC surrogate used in the paper, train a ResNet-20 on an imbalanced CIFAR10 split with PPD-SG. At the end of each outer epoch k, compute the empirical PL ratio rho_k = ||grad phi_n(bar v_k)||^2 / (2(phi_n(bar v_k) - phi_n^*)), where phi_n^* is the best value found by a long run (or a lower bound from running all methods). If min_k rho_k is close to zero or decreases as training progresses rather than staying above a positive constant, Assumption 1(1) is not satisfied in the claimed setting and the O~(1/epsilon) rates do not apply. As a control, also compute rho_k for the Appendix A.7 one-hidden-layer Leaky ReLU example under the stated distributional assumptions to confirm the PL ratio is positive there.","verdict_should_be":"UNCHANGED","load_bearing_attack":"All theoretical claims in Theorems 2 and 3 depend on the Polyak-Lojasiewicz condition on phi(v) in Assumption 1(1); every contraction step in the proofs (Eqs. 14-16 and 30-32) uses the inequality phi(bar v_k)-phi(v*) <= (1/(2 mu)) ||grad phi(bar v_k)||^2. If mu = 0 or is not bounded away from zero, the geometric decay of the function gap disappears and the best supported complexity falls back to the O~(1/epsilon^3) baseline discussed after Theorem 1. The paper does not establish this condition for the actual deep AUC objective. Lemma 1 only transfers PL from P(w) to phi, and the remark after Lemma 1 explicitly defers proving PL for P(w); the only concrete example, Appendix A.7, treats a one-hidden-layer Leaky ReLU network with zero-mean class-conditional features and does not cover ResNet-20 or the benchmark data. The cited PL results for deep networks are largely for square-loss regression, not for the pairwise AUC surrogate (1). The experiments report test AUC but never measure the PL ratio during training, so the central rate claim rests on an unverified assumption about the objective landscape.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies stochastic AUC maximization when the scoring function is a deep neural network. It uses a squared surrogate loss and the saddle-point reformulation of Ying et al. to cast the problem as a nonconvex-concave min-max problem in the primal variables (w,a,b) and dual variable α. The authors propose two stochastic primal-dual algorithms built on the proximal-point framework of Rafique et al.: PPD-SG, which uses a geometrically decaying step-size sequence and a closed-form dual correction, and PPD-AdaGrad, which uses AdaGrad-style adaptive preconditioning. Under Assumption 1, which includes a Polyak-Łojasiewicz condition on φ(v)=max_α f(v,α), they prove an O~(LG^2/(μ^2 ε)) iteration complexity and O~(L^3 σ^2/(μ^2 ε)) sample complexity for PPD-SG (Theorem 2), and for PPD-AdaGrad an iteration bound of O~((L δ^2 d/(μ^2 ε))^{1/(2(1-α))}) under a cumulative-gradient-growth condition (Theorem 3). Experiments on Cat&Dog, CIFAR10, CIFAR100, and STL10 compare test AUC against PGA, OAUC, and SGD baselines.","tokens_in":47258,"tokens_out":6230,"duration_ms":68412,"significance":"The conditional rates are substantial improvements over the O(1/ε^3) baseline from Rafique et al., and the proof structure is careful: the one-epoch analyses in Lemmas 2 and 3, the use of strong convexity of the proximal subproblem, and the function-gap contraction via the PL condition are transparent and internally consistent. The paper is honest about the main gap: the remark after Lemma 1 states that proving PL for P(w) is not the focus, and Appendix A.7 gives only a one-hidden-layer example. The idea of exploiting PL in primal-dual nonconvex-concave optimization, and the adaptive AdaGrad-style extension, are likely to be useful beyond AUC maximization. The main weakness is that the advertised improvements for deep networks are conditional on an unverified landscape condition and on unknown constants, so the contribution is best understood as a conditional complexity analysis rather than an end-to-end guarantee for deep AUC maximization as implemented.","major_comments":[{"comment":"The advertised O~(1/ε) iteration and sample rates in Theorems 2 and 3 all require the PL condition μ(φ(v)−φ(v*)) ≤ (1/2)‖∇φ(v)‖^2. The paper does not establish this condition for the deep AUC surrogate objective (1) with networks such as ResNet-20. Lemma 1 only transfers PL from P(w) to φ, and the remark after Lemma 1 explicitly defers the proof of PL for P(w); Theorem 4 in Appendix A.7 covers only a one-hidden-layer Leaky ReLU network under zero-mean conditional features and E[xx'^T | y=1, y'=−1] = 0, which does not cover the experimental architectures or data. The experiments report only test AUC, not the ratio (φ(v)−φ(v*))/‖∇φ(v)‖^2, so the central rate claims rest on an unverified condition. I request that the authors either prove PL for a broader class of deep AUC objectives relevant to the experiments, or add an empirical measurement of the PL ratio during training on the benchmark datasets, and if this is not possible, state explicitly in the abstract and introduction that all rates are conditional on a PL assumption that is not verified for the studied models.","section":"Assumption 1(1), Lemma 1, Appendix A.7"},{"comment":"The theoretical schedules in Theorems 2 and 3 are specified in terms of unknown constants μ, L, G, and σ; Section 4.3 only provides heuristics such as decreasing η by a constant factor when validation performance saturates. The experiments in Section 5 use η_s = η0/3^s and T_s = T0·3^s, which is not the exact schedule exp(−(k−1) μ/L / (5+μ/L)) required by the theorems, and no estimates of μ, L, G, or σ are reported. Consequently, the experimental results do not directly instantiate the theoretical guarantees. Please either provide a parameter-free or easily estimable schedule with a matching guarantee, or clearly separate the heuristic implementation from the theoretical algorithm and explain why the reported experiments are a meaningful test of the conditional rates.","section":"Sections 4.1, 4.3, and 5"},{"comment":"The claimed adaptive advantage of PPD-AdaGrad rests on the assumption ‖ĝ_{1:T_k,i}‖_2 ≤ δ T_k^α for 0 ≤ α ≤ 1/2. This is an assumption on the realized stochastic gradient path that is neither derived from the model class nor verified empirically; the paper does not report cumulative gradient norms on the benchmark tasks. As with the PL condition, the adaptive improvement is therefore conditional on an unmeasured quantity. I ask the authors to state this caveat more prominently and, if possible, to provide empirical evidence about the growth exponent α on the datasets considered.","section":"Theorem 3"}],"minor_comments":[{"comment":"The dual correction in Step 12 divides by the numbers of negative and positive examples in the minibatch; if a minibatch happens to contain no positive or no negative example, the denominators are zero. The paper should state how this event is handled in the implementation or in the analysis.","section":"Algorithm 2, Step 12"},{"comment":"In the version I received, the legends of Figures 1 and 3 contain garbled text (e.g., 'uni00000006/...'), which makes it impossible to identify which curve corresponds to which method; please replace these with readable labels.","section":"Figures 1 and 3"},{"comment":"The extension for unknown p claims that the estimators for p and p(1−p) are unbiased, but the update rule in Algorithm 4 is described without a proof of unbiasedness; a short derivation or a reference would help.","section":"Section 4.3"},{"comment":"There is a typo in the dataset description: 'positve' should be 'positive'.","section":"Appendix A.8"}],"recommendation":"major_revision","confidential_remarks":"The conditional theory is internally consistent and the paper is transparent about the unproved PL transfer, so I would not reject solely for that reason. However, the main advertised claims are the fast rates, and they are not verified on the actual deep networks and datasets used in the experiments. Adding an empirical PL-diagnostic or proving PL for a more realistic deep AUC objective would substantially strengthen the paper. The scheduling gap between theory and experiments is also worth addressing. This is a borderline case between major revision and minor revision; I lean major because the load-bearing assumption is central to the paper's novelty."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe real news here is that Liu et al. give the first O~(1/epsilon) stochastic primal-dual rates for AUC maximization with deep networks, and they also get the first AdaGrad-style adaptive analysis for nonconvex-concave min-max. That combination is new, and the proofs are worked through carefully. I checked the one-epoch lemmas and the recursion in Theorem 2; the algebra holds up.\n\nThe paper is also honest about its main assumption. Assumption 1(1) says phi satisfies PL, and Lemma 1 just transfers PL from P(w) to phi; the remark explicitly says proving PL for deep P(w) is not the focus, and Appendix A.7 gives only a one-hidden-layer Leaky ReLU example with zero-mean features. That is a real gap, and it is load-bearing: if mu is not bounded away from zero, the geometric contraction in Eqs. (14)-(16) disappears and you fall back to the O~(1/epsilon^3) baseline. The experiments do not measure the PL ratio, so we get no empirical evidence that the condition holds on ResNet-20 or any benchmark.\n\nThat said, I would not call it a fatal flaw. A conditional rate under PL is a legitimate theoretical contribution, and the paper frames the assumption as reasonable rather than claiming to prove it for all deep nets. The more annoying soft spots are the schedule gap and the experimental reporting. The theorems set eta_k, T_k, m_k using mu, L, G, sigma; the experiments use a stagewise decay by a factor of 3, tuned on validation. So the experiments are not a test of the theory, just a heuristic evaluation. And there are no error bars, no code release, and the figures are hard to read.\n\nBottom line: this paper deserves a serious referee. The right request would be to either prove PL for a wider class (or at least the surrogate (1)) or to measure mu/PL ratio empirically on the actual training objectives. The core ideas are sound, the novelty is genuine, and the assumption gap is addressable.\n\nI'd bring it to reading group.\n\nCheers.","headline":"First O~(1/epsilon) rates for deep AUC via PL in a primal-dual setting, with an honest but load-bearing unverified PL assumption.","tokens_in":47764,"tokens_out":3425,"would_cite":true,"duration_ms":38698,"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":"This paper extends provable AUC maximization from linear scoring models to deep neural networks, achieving an O~(1/ε) stochastic convergence rate through a proximal primal-dual method that exploits the Polyak-Łojasiewicz condition.","keywords":["AUC maximization","deep neural networks","non-convex concave min-max optimization","Polyak-Łojasiewicz condition","primal-dual stochastic gradient","AdaGrad","imbalanced classification"],"falsifier":"Run PPD-SG on a deep network (e.g., ResNet-20 on an imbalanced CIFAR10 split) and along the trajectory estimate the surrogate gap $\\varphi(v)-\\varphi(v^*)$ and the squared gradient norm $\\|\\nabla\\varphi(v)\\|^2$; if the effective PL coefficient $\\|\\nabla\\varphi(v)\\|^2/(2(\\varphi(v)-\\varphi(v^*)))$ is near zero or shrinks toward zero as training proceeds, the premise fails and the claimed $\\widetilde{O}(1/\\epsilon)$ rate cannot hold. A sharper, easier disproof: exhibit a dataset and architecture for which the squared-loss AUC surrogate has a spurious local minimum, since PL forbids that by definition.","tokens_in":46749,"feed_emoji":"📈","tokens_out":18118,"duration_ms":162398,"temperature":0.7,"pith_summary":"AUC maximization, the standard objective for learning from imbalanced data, had provable stochastic algorithms only for linear scoring models, leaving deep networks without convergence guarantees for this objective. This paper claims to close that gap: it rewrites the squared-loss surrogate of AUC as a saddle-point problem (non-convex min over network weights plus two offsets, concave max over one dual scalar) and proves that two stochastic primal-dual algorithms reach an ε-accurate objective under the Polyak-Łojasiewicz condition. PPD-SG uses geometrically decaying step sizes and a closed-form dual refresh to achieve $\\widetilde{O}(L G^2/(\\mu^2 \\epsilon))$ iterations and $\\widetilde{O}(L^3 \\sigma^2/(\\mu^2 \\epsilon))$ samples; PPD-AdaGrad achieves an adaptive $\\widetilde{O}((L\\delta^2 d/(\\mu^2 \\epsilon))^{1/(2(1-\\alpha))})$ rate when cumulative gradients grow slowly. Both rates improve the generic $\\widetilde{O}(1/\\epsilon^3)$ bound for one-sided non-convex concave min-max problems, and experiments on four image benchmarks with a ResNet-20 support the effectiveness claim.","feed_headline":"O(1/ε) convergence proven for deep-network AUC training","feed_subtitle":"Area-under-curve training for imbalanced data now matches plain SGD's convergence rate.","key_machinery":"Four objects carry the argument. The saddle-point reformulation (Proposition 1) expresses the pairwise AUC probability through a min over weights $(w,a,b)$ and a max over a single dual scalar $\\alpha$, making the stochastic gradient computable from one example. On top of it, the Polyak-Łojasiewicz condition $\\mu(\\varphi(v)-\\varphi(v^*)) \\le \\frac12\\|\\nabla\\varphi(v)\\|^2$ is the engine: it asserts that small gradients force near-optimality of $\\varphi$, which turns the per-epoch suboptimality bound of each proximal solve into a geometric contraction of the gap across epochs, and Lemma 1 shows this property is inherited from a PL condition on the plain minimization objective $P(w)$. The algorithmic skeleton is the inexact proximal point method — each outer loop approximately solves the strongly convex-concave subproblem $\\min_v\\max_\\alpha \\{f(v,\\alpha)+\\frac{1}{2\\gamma}\\|v-\\bar v_{k-1}\\|^2\\}$; PPD-SG differs from the generic template in its geometrically decaying step size $\\eta_k=\\eta_0\\exp(-(k-1)(\\mu/L)/(5+\\mu/L))$ and its minibatch estimate of the optimal dual variable. PPD-AdaGrad swaps the inner primal-dual update for an AdaGrad-preconditioned step with $H_t=\\delta I+\\mathrm{diag}(s_t)$, whose per-coordinate scaling converts a bound on cumulative gradient growth into an adaptive iteration count.","core_discovery":"The paper's central claim is that the Polyak-Łojasiewicz (PL) gradient-dominance property, known to hold for several classes of overparameterized networks trained with square loss, transfers to the AUC min-max surrogate and unlocks provably faster convergence for deep AUC maximization. The route is: replace the AUC indicator by the squared loss, which by Proposition 1 turns the pairwise objective $\\min_w P(w)$ into $\\min_{w,a,b}\\max_{\\alpha} \\mathbb{E}_z[F(w,a,b,\\alpha;z)]$, a non-convex-concave stochastic min-max problem in which each gradient step consumes one sample. Assuming $\\mu(\\varphi(v)-\\varphi(v^*)) \\le \\frac12 \\|\\nabla\\varphi(v)\\|^2$ for $\\varphi(v)=\\max_\\alpha f(v,\\alpha)$ (Assumption 1(1)), Theorem 2 shows that PPD-SG returns a point with $\\mathbb{E}[\\varphi(\\bar v_K)-\\varphi(v^*)]\\le\\epsilon$ in $\\widetilde{O}(L G^2/(\\mu^2\\epsilon))$ iterations using $\\widetilde{O}(L^3\\sigma^2/(\\mu^2\\epsilon))$ samples, where the two algorithmic keys are a geometrically decaying step size across outer loops and a minibatch refresh of the dual variable to its closed-form optimum $\\alpha^*=\\mathbb{E}[h(w;x)|y=-1]-\\mathbb{E}[h(w;x)|y=1]$. Theorem 3 gives the AdaGrad-style variant a matching sample bound and an adaptive iteration count $\\widetilde{O}((L\\delta^2 d/(\\mu^2\\epsilon))^{1/(2(1-\\alpha))})$ under a growth condition on cumulative gradients. The paper presents these as the first non-asymptotic guarantees for stochastic AUC maximization with deep networks and as strictly better than the $\\widetilde{O}(1/\\epsilon^3)$ cost of the generic proximal framework.","pith_inferences":["The empirical value of the construction rests on how often the PL condition actually holds along real training trajectories; since the paper's PL evidence is by analogy (square-loss networks, a one-hidden-layer example), a direct measurement of the effective PL coefficient during PPD-SG runs on deep networks would settle the question.","A natural extension the paper does not explore: combining the geometric-restart schedule with variance-reduced inner loops (an SVRG-style estimator) could plausibly remove the $\\sigma^2$ sample-factor, since the contraction argument only needs unbiased gradients.","The same saddle-point-plus-PL blueprint should transfer to other pairwise objectives, such as ranking surrogates and metric learning, whenever the inner maximization is convex and admits a closed form; the dual-refresh trick is the piece that generalizes most directly."],"forward_implications":["If the PL condition holds, deep AUC maximization is asymptotically no harder than plain SGD training: the $\\widetilde{O}(1/\\epsilon)$ iteration rate matches the standard stochastic-gradient rate under PL, and the sample count $\\widetilde{O}(L^3\\sigma^2/(\\mu^2\\epsilon))$ is independent of the model dimension.","The generic inexact proximal framework for non-convex concave min-max problems costs $\\widetilde{O}(1/\\epsilon^3)$; this paper's rates improve on that in both $\\epsilon$ and the dependence on the conditioning parameters, so any one-sided min-max problem whose outer objective satisfies PL inherits the speedup.","PPD-AdaGrad supplies the first adaptive convergence guarantee for non-convex concave min-max problems: when cumulative gradient norms grow like $\\delta T^\\alpha$ with $\\alpha < 1/2$, its iteration bound $\\widetilde{O}((L\\delta^2 d/(\\mu^2\\epsilon))^{1/(2(1-\\alpha))})$ beats the non-adaptive rate.","The closed-form dual refresh, estimating $\\alpha^*=\\mathbb{E}[h(w;x)|y=-1]-\\mathbb{E}[h(w;x)|y=1]$ from a small minibatch, removes dual-error accumulation and extends to any min-max problem with a conditional-expectation maximizer.","The same framework covers multi-class AUC and online settings with unknown class prior (Section 4.3), so the rates carry over with only the overhead of maintaining estimators for $p$ and $p(1-p)$."],"supporting_citations":[{"why":"Supplies the saddle-point reformulation of the squared-loss AUC surrogate that the paper reproduces as Proposition 1.","marker":"Ying et al., 2016"},{"why":"Provides the inexact proximal point algorithmic framework both algorithms build on, and the generic O~(1/ε^3) baseline that Theorems 2 and 3 improve.","marker":"Rafique et al., 2018"},{"why":"The stochastic-gradient-under-PL analysis whose O(1/ε)-type rate Theorem 2 parallels.","marker":"Karimi et al., 2016"},{"why":"Establishes the PL condition for deep linear residual networks with square loss, the main cited evidence for Assumption 1.","marker":"Hardt & Ma, 2016"},{"why":"Proves gradient dominance for one-hidden-layer Leaky ReLU networks, the closest prior support for PL on non-linear network objectives.","marker":"Charles & Papailiopoulos, 2017"},{"why":"Characterizes regularity and gradient-dominance conditions for neural networks, backing the PL assumption's plausibility.","marker":"Zhou & Liang, 2017"},{"why":"Defines the AdaGrad update and supplies the gradient-norm-sum bound (its Lemma 4) that drives the PPD-AdaGrad adaptive rate.","marker":"Duchi et al., 2011"},{"why":"The adaptive convergence analysis for non-convex minimization whose techniques the PPD-AdaGrad proof adapts to the min-max setting.","marker":"Chen et al., 2019"}],"fun_headline_variants":["PL condition cracks deep AUC training speed","Deep AUC now trains as fast as plain SGD","Saddle-point trick speeds up deep AUC learning","Polyak-Lojasiewicz boosts deep AUC convergence"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the Polyak-Łojasiewicz condition on the AUC surrogate objective, $\\mu(\\varphi(v)-\\varphi(v^*)) \\le \\frac12\\|\\nabla\\varphi(v)\\|^2$: the assumption that every low-gradient point is within a proportional gap of the global minimum, which the paper supports only with PL results for square-loss networks and a one-hidden-layer example rather than a proof or empirical check for deep networks, and without which all claimed $\\widetilde{O}(1/\\epsilon)$ and adaptive rates fall back to the generic $\\widetilde{O}(1/\\epsilon^3)$.","fun_headline_variants_meta":{"raw":{"variants":["PL condition cracks deep AUC training speed","Deep AUC now trains as fast as plain SGD","Saddle-point trick speeds up deep AUC learning","Polyak-Lojasiewicz boosts deep AUC convergence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00026,"raw_usage":{"total_tokens":1676,"prompt_tokens":1122,"completion_tokens":554,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":738,"completion_tokens_details":{"reasoning_tokens":497}},"tokens_in":738,"tokens_out":554,"duration_ms":6041,"temperature":1.0,"reasoning_tokens":497,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:33:27.954072+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run PPD-SG on a deep network (e.g., ResNet-20 on an imbalanced CIFAR10 split) and along the trajectory estimate the surrogate gap $\\varphi(v)-\\varphi(v^*)$ and the squared gradient norm $\\|\\nabla\\varphi(v)\\|^2$; if the effective PL coefficient $\\|\\nabla\\varphi(v)\\|^2/(2(\\varphi(v)-\\varphi(v^*)))$ is near zero or shrinks toward zero as training proceeds, the premise fails and the claimed $\\widetilde{O}(1/\\epsilon)$ rate cannot hold. A sharper, easier disproof: exhibit a dataset and architecture for which the squared-loss AUC surrogate has a spurious local minimum, since PL forbids that by definition.","supporting_citations":[{"cited_title":"Stochastic online auc maximization","cited_arxiv_id":null,"evidence_quote":"Supplies the saddle-point reformulation of the squared-loss AUC surrogate that the paper reproduces as Proposition 1."},{"cited_title":"Stability and Generalization of Learning Algorithms that Converge to Global Optima","cited_arxiv_id":"1710.08402","evidence_quote":"Proves gradient dominance for one-hidden-layer Leaky ReLU networks, the closest prior support for PL on non-linear network objectives."},{"cited_title":"Universal stagewise learning for non-convex problems with convergence on averaged solutions","cited_arxiv_id":null,"evidence_quote":"The adaptive convergence analysis for non-convex minimization whose techniques the PPD-AdaGrad proof adapts to the min-max setting."}],"review_version":1}