{"id":"b752c926-283a-439d-b847-5a7982c3ee3c","arxiv_id":"2505.16098","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"DANA, with dimension- and time-dependent momentum, provably outscales SGD on power-law random features when 2α>1, improving loss exponents and compute-optimal curves.","lead":"This paper proves that a carefully scheduled momentum algorithm, DANA, can improve the loss-scaling exponents of stochastic gradient descent on a power-law random features model. It also tests the claim on LSTMs, finding a small but consistent exponent improvement over SGD.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3.1 is proven for a simplified ODE plus deterministic equivalent, not for the exact discrete algorithm; the gap is acknowledged (Remark C.3) but untested, so the outscaling claim rests on an unproved reduction.","rationale":"The reader's weakest assumption identifies exactly the gap I consider most load-bearing: the theorems govern a simplified ODE/deterministic-equivalent model rather than the exact discrete stochastic momentum algorithm. This is not a manufactured concern; the paper itself flags it in Remark C.3 and in the paragraph introducing the deterministic equivalent, so the authors are aware of the missing link. What makes it load-bearing is that the outscaling exponents are derived from the simplified object, and the exact ODE contains extra terms that could in principle alter the dominant time scale theta(t) or the Volterra kernel. If those terms are not negligible in the t=d^ell regimes, the headline claim about DANA outscaling SGD would fail for the actual algorithm even though it holds for the SDE approximation. The proposed test settles this by checking the exact ODE against both the simplified ODE and the discrete simulation; if the exact ODE reproduces the simplified exponents, the gap is benign, and if it does not, the theorem needs to be reproved or qualified. I do not downgrade the paper: the numerical evidence in Fig. 8 is substantial, the derivation within the simplified model appears coherent, and the limitations are stated rather than hidden. A second, smaller concern is that Theorem 3.1's DANA-decaying statement requires (1/(2alpha))<kappa3<1 while the headline schedule uses kappa3=1/(2alpha); this endpoint case may be covered in Appendix I, but if not, a limiting argument is needed. This does not change the verdict from CONDITIONAL.","tokens_in":76666,"tokens_out":7227,"duration_ms":62082,"concrete_test":"Numerically compare the exact Poissonized ODE (22) with the simplified ODE (43) and with direct Gen-Mom-SGD simulation on PLRF for DANA-decaying with kappa3=1/(2alpha), using the same random instance W for d in {500,1000,2000,4000}, v=10d, alpha=1.4, beta=1.0, B=1. For each d, solve both ODE systems and simulate the discrete algorithm to t=d^1.5, then fit loss exponents over t in [d^0.5, d^1.5]. If the exact-ODE and direct-simulation exponents agree with each other but differ from the simplified-ODE exponent by more than the fit error, Theorem 3.1 does not describe the actual algorithm; if all three agree, the dropped terms are benign and the conditional verdict can be upgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The scaling laws in Theorem 3.1 are stated for the solution of the simplified Volterra equation (58), whose forcing and kernel use the simplified ODE system (43) and the deterministic equivalent measures (36). The actual discrete Gen-Mom-SGD algorithm, after Poissonization, satisfies the exact ODE system (22), which contains additional terms of order Delta^2, gamma3^2, gamma1*gamma3, and lambda^2. Lemma C.1 justifies the simplified ODE only as a non-degenerate high-dimensional limit in which learning rates are scaled to vanish with d, while Remark C.3 explicitly says the link between dropping those terms and the finite learning-rate regime used here (e.g., gamma2 on the order of 1 for 2alpha>1) is left for future work. The deterministic equivalent (33) is also supported only numerically (Fig. 3c), with the proof described as falling outside textbook RMT. If either reduction changes the effective time change theta(t) or the Volterra kernel at the t=d^ell scales, the predicted exponents, and therefore the central outscaling claim, would not describe Gen-Mom-SGD. The paper is transparent about both gaps, and the PLRF experiments in Fig. 8 validate the simplified ODE against direct simulation; however, they do not compare the exact ODE (22) with the simplified ODE (43), so the key reduction remains untested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies scaling laws for stochastic momentum methods on the power law random features (PLRF) model. The authors derive a Poissonized ODE system (22) and an associated Volterra equation for the expected loss, then introduce a simplified ODE system (43) and replace the random spectral measures by deterministic equivalents (33). The main result, Theorem 3.1, states scaling laws of the form P(t) ≍ F(ϑ(t)) + γ Kpp(ϑ(t)) for SGD, classic momentum (SGD-M), and two DANA variants, with explicit time changes ϑ(t) and stability conditions. It is claimed that SGD-M matches SGD exponents while DANA-constant and DANA-decaying improve the loss exponents for 2α > 1, including in compute-optimal scaling. The theoretical predictions are tested on PLRF simulations and on LSTM language modeling (Fig. 2).","tokens_in":77006,"tokens_out":10835,"duration_ms":85259,"significance":"If the theorem applied to the exact discrete algorithms, this would be a significant contribution: it would show that dimension- and data-dependent momentum schedules can change the exponent of scaling laws, not merely the constant, and would provide principled compute-optimal training regimes that differ from the Chinchilla d⋆ ≍ f^{1/2} law. The derivation has a notable strength: the time change ϑ(t) in (9) contains no fitted constants, and the loss exponents are derived from the model rather than fitted to simulation, so the theory makes falsifiable predictions. The paper is also transparent about its two main reductions, the simplified ODE and the deterministic equivalent, and supports them with extensive numerical studies, including a large-scale LSTM experiment. The main weakness is that the proven scaling laws apply to the simplified ODE with the deterministic equivalent, not to the exact discrete algorithm as stated in the introduction, and some theorem hypotheses appear inconsistent with the broad claims made in the main text.","major_comments":[{"comment":"The scaling-law statements in Theorem 3.1 are proven for the solution of the simplified Volterra equation (58), which combines the simplified ODEs (43) with the deterministic equivalent measures (33)/(36), rather than for the exact discrete Gen-Mom-SGD algorithm introduced in (13). The exact ODE (22) contains additional terms of order Δ², γ3², γ1γ3, and λ², and Lemma C.1 justifies the simplified ODE only as a non-degenerate high-dimensional limit in which learning rates are scaled inversely with dimension; Remark C.3 explicitly states that the link between dropping those terms and the finite learning-rate regime used here (e.g., γ2 on the order of 1 for 2α > 1) is left for future work. The deterministic equivalent is also supported only numerically (Fig. 3c). Because the central outscaling claim is about the algorithm class Gen-Mom-SGD, the theorem as stated does not directly prove the headline claim; the PLRF experiments (e.g., Fig. 8) validate the simplified ODE against direct simulation, but do not compare the exact ODE (22) with the simplified ODE (43), so this key reduction is not tested. I recommend that the authors either prove the reduction, add a direct numerical comparison of (22) and (43) across the regimes used in the scaling laws, or explicitly restate the theorem's conclusions as being about the simplified model rather than the discrete algorithm.","section":"Theorem 3.1, Remark C.3, §3.1"},{"comment":"The recommended and headline choice for DANA-decaying is κ3 = 1/(2α) (Remark B.4, Section 4, Fig. 3), but the summarized Theorem 3.1 imposes the additional requirement (1/2α) < κ3 < 1 for DANA-decaying, which excludes κ3 = 1/(2α). The stability conditions listed just above the theorem do include a branch for κ3 ≥ 1/(2α), so the exclusion appears to be a mismatch rather than a deliberate boundary issue. If Theorem I.2 in the appendix covers the endpoint κ3 = 1/(2α), the main text needs to state that; otherwise the paper's optimal-schedule outscaling claim is not supported by the proved result. This is load-bearing because all of the DANA-decaying claims in the title and abstract rest on the endpoint schedule.","section":"Theorem 3.1, §4, Remark B.4"},{"comment":"Theorem 3.1 assumes β ≤ α + 1, yet the paper claims DANA-decaying outscales SGD for all (α, β) with 2α > 1 and presents compute-optimal experiments in Phase IIIa with α = 1.4, β = 3.0 (Fig. 6), which violates β ≤ α + 1 = 2.4. The authors note in Section C.4 that they believe α > 1/4 and α + 1 > β are proof artifacts, but as stated the theorem does not cover the regime shown in their own figure. Either the theorem should be extended to β > α + 1, or the claim of universal outscaling for 2α > 1 should be flagged as conjecture with a supporting argument.","section":"Theorem 3.1, §4, Fig. 6"},{"comment":"The stability conditions in Theorem 3.1 are derived from the simplified ODEs, but the authors themselves warn that these can miss stability conditions of the original algorithm. In Appendix B.2, for SGD-M they observe that the simplified Volterra equation neglects Δ² terms, which makes any Δ > 0 appear convergent, and that the coin-flip ODEs (49) give an explicit condition 2δ(2−δ)/(2(2B+1)+δ(3B+1)) > γ3 > 0 with δ ∈ (0, 2). Since stability is a hypothesis of the scaling-law theorem, this discrepancy means the theorem may describe a regime that the actual algorithm does not enter. The LSTM sweep in Fig. 2a shows a divergence boundary near κ3 = 0.6, indicating the practical importance of getting the stability boundary right. The authors should reconcile the simplified-ODE stability conditions with the exact or coin-flip conditions, or at least verify by simulation that the stable set of the discrete algorithm contains the stable set claimed in the theorem.","section":"Appendix B.2"}],"minor_comments":[{"comment":"The definition of ≍ says the constants c and C are independent of d, but the scaling-law statements require comparison of functions of both t and d with constants uniform over the stated t-regimes; the definition should specify the full uniformity, e.g., independent of d and uniform in t over each scaling regime.","section":"Footnote 1"},{"comment":"The notation P(t) is used ambiguously: in (5) it is the expected loss of the discrete iterates, while in (39) and (58) it is the solution of the deterministic Volterra equation; Theorem 3.1 should state explicitly which object the ≍ bound refers to (Remark C.4 partially clarifies this, but not at the theorem statement).","section":"(5), (39), Theorem 3.1"},{"comment":"The abstract and Section 3 mention 'four distinct loss curve shapes', but the paper's phase diagrams (Fig. 11) contain subphases Ia, Ib, Ic, IIa, IIb, IIIa, IIIb, IVa, and IVb; the terminology should be aligned so that the reader can map the four shapes to the full phase structure.","section":"Abstract, §3.1, Fig. 11"},{"comment":"The colorbar label 'logd(time to reach irreducible loss)' is not informative about the base of the logarithm and whether it is per-algorithm or per-problem; please clarify the quantity being plotted.","section":"Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest and thorough, and the core idea is interesting and well positioned for this journal. However, the gap between the proven object (simplified ODE plus deterministic equivalent) and the claimed object (the discrete Gen-Mom-SGD algorithm) is substantial, and the inconsistencies between Theorem 3.1's hypotheses and the headline claims (κ3 = 1/(2α) endpoint, β > α + 1 regimes) are easily fixed only if the appendix theorems actually cover those cases. I would encourage the authors to close or clearly scope these gaps; the numerical work is already strong and the paper is likely to become impactful after a major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is the first paper I've seen that shows momentum can change the exponent in a scaling law, not just the constant. On the PLRF model, SGD-M provably matches SGD exponents, while DANA-decaying provably improves them for 2α > 1. Second, the proof of Theorem 3.1 is for a simplified ODE plus a deterministic equivalent, not for the discrete stochastic algorithm; the authors say so in Remark C.3, and the missing link is not directly tested.\n\nWhat's genuinely new: the exponent computation for DANA-constant and DANA-decaying, the compute-optimal curves that leave the Chinchilla t~d regime, and the proof that SGD-M is exponent-identical to SGD. The derivation has no fitted exponents—the time-change ϑ(t) comes out of the model. The LSTM experiment is a real out-of-model check, and the improvement (-0.062 vs -0.058) is small but consistent with the direction of the theory.\n\nWhere it's soft. The main theorem lives in the simplified Volterra equation (58) fed by the deterministic equivalent measures (36). The exact ODE (22) contains Δ², γ3², γ1γ3, λ² terms that the simplified ODE drops. Lemma C.1 justifies the simplification only as a non-degenerate high-dimensional limit with vanishing learning rates, which is not the finite-learning-rate regime used here. Remark C.3 says the link is future work. The deterministic equivalent itself is validated numerically (Fig. 3c), not proved. That said, the PLRF experiments in Fig. 8 compare the simplified ODE directly to runs of the actual algorithm, and they match well across d—so empirically the reduction is doing real work. The gap is theoretical completeness rather than a demonstrated failure. Two minor things: no code or data shipped, and the LSTM exponents lack error bars.\n\nWho this is for: people working on scaling laws, compute-optimal training, and high-dimensional optimization theory. It deserves a serious referee. I'd send it out and ask the authors to either close the exact-to-simplified gap or add a direct numerical comparison between the exact ODE (22) and the simplified ODE (43), plus more LSTM seeds.","headline":"DANA provably changes scaling exponents in a solvable model, but the headline theorem is proven one level removed from the actual algorithm; worth refereeing with the gap addressed.","tokens_in":77526,"tokens_out":2534,"would_cite":true,"duration_ms":25608,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68Q32","60B20","68W40"],"pacs":[],"model":"deepseek-v4-flash","headline":"The authors show that on power-law random feature models, a dimension- and data-adapted momentum schedule (DANA) improves the loss exponents of SGD in all training regimes $t=d^{\\ell}$ with $0<\\ell<2\\alpha$ when $2\\alpha>1$, while…","keywords":["scaling laws","stochastic momentum","Nesterov acceleration","random features","power law data","compute-optimal","loss exponents","hyperparameter scaling"],"falsifier":"On PLRF with fixed $(\\alpha,\\beta)$ such that $2\\alpha>1$, for example $\\alpha=1.4$, $\\beta=1.0$, run DANA-decaying with $\\kappa_3=1/(2\\alpha)$, $\\gamma_2=1/(2\\mathrm{tr})$, and $\\delta$ large against SGD with batch size $1$ across $d=100\\cdot 2^i$, and fit the empirical loss exponent in the regime $t=d$. If the DANA exponent is not strictly larger than SGD's beyond the reported fitting error, the central claim fails; alternatively, large-$d$ divergence between discrete runs and the simplified ODE system (43) would invalidate the model.","tokens_in":76460,"feed_emoji":"📉","tokens_out":8716,"duration_ms":72099,"temperature":0.7,"pith_summary":"The paper's central claim is that the scaling-law exponents of stochastic gradient descent are not fixed by the problem alone: a momentum schedule tuned to the model dimension and data complexity can provably change them, whereas classical constant momentum cannot. Working on the power-law random features (PLRF) model, the authors prove that SGD with a Nesterov-type schedule $\\Delta(t)=\\delta(1+t)^{-1}$ and a momentum learning rate $\\gamma_3$ scaled as a power of $d$ and $t$, the DANA rule, outscales SGD whenever $2\\alpha>1$ and $\\beta\\le\\alpha+1$, with four distinct loss-curve shapes across the $(\\alpha,\\beta)$ phase plane. DANA-decaying, with $\\kappa_3=1/(2\\alpha)$, improves the loss exponent for every training regime $t=d^{\\ell}$ with $0<\\ell<2\\alpha$; DANA-constant improves it for $1<\\ell<2\\alpha$; and SGD-M yields exactly the SGD exponents. If true, this means optimizer choice can enter neural scaling laws as an exponent, not just a constant, and compute-optimal parameter counts need not follow the $d\\asymp f^{1/2}$ Chinchilla rule.","feed_headline":"Dimension-tuned momentum outscales SGD in scaling laws","feed_subtitle":"DANA's κ3=1/(2α) schedule provably beats SGD's loss exponents for 2α>1; constant momentum does not.","key_machinery":"The load-bearing object is the pair of deterministic-equivalent measures $\\mu_F$ and $\\mu_K$, pure-point measures built from the fixed-point equation (33) for the resolvent of the projected covariance, together with the simplified ODE system (43) for the per-eigenmode moments $(\\rho_j^2,\\xi_j^2,\\chi_j)$. Solving these ODEs turns the expected loss into a Volterra equation $P(t)=F(t)+\\int_0^t K_t(s)P(s)\\,ds$, whose forcing and kernel functions have known power-law asymptotics. The decisive mechanism is the DANA time change $\\vartheta(t)=1+2\\gamma_2 Bt+(\\int_0^t\\sqrt{\\gamma_3(s)B}\\,ds)^2$: it reparameterizes the SGD loss curve so that momentum changes the argument at which the bias and variance terms are evaluated. DANA-decaying's schedule $\\gamma_3(t)\\asymp(1+t)^{-1/(2\\alpha)}$ is the concrete expression of the effective dimension $(tB)^{-1/(2\\alpha)}$, the number of feature-space directions that have been substantially updated by time $t$.","core_discovery":"On the PLRF model, a random-features least-squares problem whose data-coordinate and target-coordinate decays are parameterized by $\\alpha$ and $\\beta$, the expected loss of any algorithm in the general momentum class (Gen-Mom-SGD) is shown to follow a Volterra equation whose forcing and kernel terms are controlled by two explicit measures, $\\mu_F$ and $\\mu_K$, arising from a deterministic equivalent of the random feature covariance. The main theorem states that under $2\\alpha+2\\beta>1$, $\\alpha>1/4$, $\\beta\\le\\alpha+1$, fixed batch size, and stability conditions, the loss obeys $P(t)\\asymp \\hat F(\\vartheta(t))+\\gamma \\hat K_{pp}(\\vartheta(t))$ with the time change $\\vartheta(t)=1+2(\\gamma_2+\\gamma_3/\\delta)Bt$ for SGD-M and $\\vartheta(t)=1+2\\gamma_2Bt+(\\int_0^t\\sqrt{\\gamma_3(s)B}\\,ds)^2$ for DANA. Consequently SGD-M has identical scaling-law exponents to SGD, since its effective learning rate is $\\gamma_2+\\gamma_3/\\delta$, while the DANA time change accelerates the argument of the forcing function. With $\\gamma_3(t)\\asymp(1+t)^{-1/(2\\alpha)}$, DANA-decaying outscales SGD for all regimes $t=d^{\\ell}$, $0<\\ell<2\\alpha$, in the $2\\alpha>1$ region, and the authors derive explicit compute-optimal parameter, loss, and data exponents showing that DANA's compute-optimal curve is not $d\\asymp f^{1/2}$.","pith_inferences":["The effective-dimension interpretation suggests a test outside quadratics: estimate $\\alpha$ from the spectral decay of a real dataset's covariance, set $\\kappa_3=1/(2\\alpha)$, and check whether the loss-exponent improvement persists; the paper treats this only as an open question.","If DANA's gain carries over to preconditioned or adaptive optimizers, then Adam plus a DANA-style decaying momentum term could change exponents on real networks; the paper lists this as future work, so it is an extension, not a claim.","The result implies empirical compute-optimal frontier fits should report the optimizer: two algorithms that differ only in momentum can have different $d_\\star(f)$ exponents, so a single Chinchilla exponent is not an algorithm-independent constant.","For $2\\alpha<1$, all analyzed momentum variants collapse to SGD scaling, so the practical window for outscaling is precisely the regime where data power-law decay is strong enough; whether another algorithm can cross the high-dimensional line remains open."],"forward_implications":["DANA-decaying with $\\kappa_3=1/(2\\alpha)$ gives strictly better loss exponents than SGD in every training regime $t=d^{\\ell}$, $0<\\ell<2\\alpha$, for $2\\alpha>1$, and is more sample-efficient and compute-efficient than both SGD and DANA-constant.","SGD-M with any fixed momentum $\\delta$ reproduces the SGD exponents exactly; its only effect is to replace $\\gamma_2$ by the larger effective learning rate $\\gamma_2+\\gamma_3/\\delta$.","DANA-constant, with $\\kappa_3=0$ and $\\gamma_3\\asymp\\gamma_2/d$, behaves like SGD for $t\\le d$ and outscales SGD for $1<\\ell<2\\alpha$, a regime that exists only when $2\\alpha>1$.","At compute-optimality for $2\\alpha>1$, DANA-decaying never uses $d_\\star(f)\\asymp f^{1/2}$; depending on the phase it undertrains or overtrains relative to the Chinchilla ratio, and it lowers the compute-optimal loss exponent.","On LSTMs trained on text, DANA-decaying's empirical loss exponents vary smoothly with $\\kappa_3$, recover the predicted divergent, outscaling, and SGD-like regimes, and improve on SGD near $\\kappa_3\\approx0.7$."],"supporting_citations":[{"why":"supplies the deterministic-equivalent measures $\\mu_F$ and $\\mu_K$ and the SGD scaling laws on PLRF that Theorem 3.1 extends","marker":"[79]"},{"why":"introduced DANA and the simplified ODE/SDE system for momentum dynamics on quadratics used as the analytic starting point","marker":"[77]"},{"why":"introduced the power-law random features model with the $\\alpha,\\beta$ complexity parameters that the whole analysis runs on","marker":"[68]"},{"why":"independently proposed a 1-memory SGD schedule similar to DANA-decaying whose scaling rates this paper proves","marker":"[106]"},{"why":"provides AcSGD, the accelerated method whose hyperparameters and conjectured scaling behavior are compared to DANA-constant","marker":"[93]"},{"why":"provides Schedule-Free SGD, rewritten in the Gen-Mom-SGD class and shown empirically to scale like SGD","marker":"[32]"},{"why":"is the empirical Chinchilla compute-optimal law that this paper's compute-optimal exponents are compared against","marker":"[49]"},{"why":"supplies the continuized-acceleration framework and the stochastic Nesterov divergence result used in the stability and comparison discussion","marker":"[37]"}],"fun_headline_variants":["DANA's dimension-tuned momentum beats SGD's scaling laws","Adaptive momentum (DANA) outperforms SGD in loss scaling","Dimension-aware momentum achieves better scaling than SGD","DANA outscales SGD by adapting momentum to data complexity","Momentum scaling matters: DANA beats SGD in scaling laws"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The scaling-law exponents are proved for a simplified differential-equation model with a deterministic stand-in for the random covariance, not for the exact discrete stochastic momentum algorithm; if that reduction is unfaithful in some training regime, the predicted exponents may not describe the actual algorithm.","fun_headline_variants_meta":{"raw":{"variants":["DANA's dimension-tuned momentum beats SGD's scaling laws","Adaptive momentum (DANA) outperforms SGD in loss scaling","Dimension-aware momentum achieves better scaling than SGD","DANA outscales SGD by adapting momentum to data complexity","Momentum scaling matters: DANA beats SGD in scaling laws"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000926,"raw_usage":{"total_tokens":4018,"prompt_tokens":1047,"completion_tokens":2971,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":663,"completion_tokens_details":{"reasoning_tokens":2887}},"tokens_in":663,"tokens_out":2971,"duration_ms":19741,"temperature":1.0,"reasoning_tokens":2887,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:06:17.623526+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On PLRF with fixed $(\\alpha,\\beta)$ such that $2\\alpha>1$, for example $\\alpha=1.4$, $\\beta=1.0$, run DANA-decaying with $\\kappa_3=1/(2\\alpha)$, $\\gamma_2=1/(2\\mathrm{tr})$, and $\\delta$ large against SGD with batch size $1$ across $d=100\\cdot 2^i$, and fit the empirical loss exponent in the regime $t=d$. If the DANA exponent is not strictly larger than SGD's beyond the reported fitting error, the central claim fails; alternatively, large-$d$ divergence between discrete runs and the simplified ODE system (43) would invalidate the model.","supporting_citations":[{"cited_title":"On the importance of initialization and momentum in deep learning","cited_arxiv_id":null,"evidence_quote":"provides AcSGD, the accelerated method whose hyperparameters and conjectured scaling behavior are compared to DANA-constant"}],"review_version":1}