{"id":"f5d28dcb-db20-4f97-8b47-107f1aca8cff","arxiv_id":"2505.20954","paper_version":5,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"A nested local-entropy-bias ensemble reveals a delocalized cluster of connected solutions in the symmetric binary perceptron, with a predicted stability threshold where solution paths shatter.","lead":"This paper builds a statistical-physics tool that looks for solutions to constraint problems that are linked by short steps into a connected cluster, rather than isolated solutions, and applies it to the symmetric binary perceptron model. It predicts a threshold below which these connected solution paths destabilize, and its Monte-Carlo simulations start to slow down at roughly that threshold.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The cluster's existence and threshold rest on a local-stability criterion applied to an Ansatz that Eq. (57) shows is never a stationary point; the perturbation in Eq.","rationale":"The reader's weakest-assumption analysis identifies exactly the load-bearing issue: the no-memory Ansatz is globally unstable (Eq. 57), and the subsequent local-stability criterion (Eqs. 58-60) is an ad hoc diagnostic rather than a proper stationary-point analysis. My stress-test agrees, and I would not move the verdict away from CONDITIONAL. The paper deserves credit for being transparent about the instability and for producing concrete, in-principle falsifiable predictions (the compressed margin distribution, the exponential decorrelation profile, and the algorithmic transition). It also makes a real methodological contribution by extending the chain formalism of [38] to a local-entropy biased ensemble. However, the central claim 'we demonstrate its stability' is stronger than what the argument supports. The numerical Monte-Carlo study uses a loss derived from the very Ansatz whose stability is in question, with an additional approximation for G_λtop; observed agreement therefore cannot settle whether the no-memory cluster is physical or merely an artifact of the bias. The proposed test — varying the perturbation exponent and using an independent algorithm — directly targets this weakness. Since the reader already conditioned the verdict on resolving this issue, my read leaves the verdict unchanged.","tokens_in":37064,"tokens_out":7234,"duration_ms":88332,"concrete_test":"Recompute the local-stability boundary of Fig. 5 with the perturbation Q_{Pk,P'k'} = m^{|k-k'|-a} for a ∈ {1,2,3} (not only a=2), for α ∈ {0.3, 0.5, 0.75}, taking m→1 at fixed k_f(1-m). If the resulting κ^{no-mem}_{loc.stab.}(α) shifts by more than a few percent, the transition is an artifact of the arbitrarily chosen exponent in Eq. (60) rather than a property of the solution space. As a complementary check, rerun the Sec. 4 annealing with the unapproximated G_λtop (Eq. 41) and with a bias not derived from the no-memory L_eff, for example chain-constrained Metropolis on the original SBP loss; if the decorrelation-time divergence does not occur at the same κ, the numerical support is not independent of the Ansatz.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (57) is the crux: for every non-ancestor pair and for all α and κ, δφ/δQ_{Pk,P'k'} > 0, so the no-memory overlap matrix is not a saddle point of the connected free energy (Eq. 26). The paper explicitly leaves open whether this means the no-memory manifold is merely subdominant or is non-physical, and no later step closes that dichotomy. The local-stability computation does not repair the gap: Eqs. (58-60) evaluate the response of s_loc to a single prescribed perturbation Q_{Pk,P'k'} = m^{|k-k'|-2}, with the exponent −2 chosen for convenience in App. D.2, and then declare the sign of δs_loc to be the stability indicator. Because the unperturbed geometry is non-stationary, first-order variations of the free energy dominate the measure; a sign change of δs_loc along one arbitrary direction is not a Hessian criterion and does not establish that no-memory paths are the relevant connected configurations, nor that they shatter at κ^{no-mem}_{loc.stab.}. The numerical section cannot independently resolve this: the Monte-Carlo loss is L_eff built from the same no-memory Ansatz, with G approximated by Eq. (62), so agreement with P_edge and the divergence near the predicted line is partly in-sample. The phase boundary in Fig. 6 is also obtained by fitting only four points. Thus the central claim that the cluster is stable until κ^{no-mem}_{loc.stab.} is not warranted by the current evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces a statistical-mechanics ensemble for connected solutions in constraint satisfaction problems, built from iterated local-entropy biases, and applies it to the symmetric binary perceptron (SBP). Under a no-memory overlap ansatz, with all Lagrange multipliers set to one, m→1, and an infinite chain length, the paper derives an effective edge loss, edge and core margin distributions, and edge and local entropies, and identifies a delocalized, star-shaped cluster of SBP solutions. It then proposes a local-stability criterion for the local entropy, defines a threshold κ_loc.stab., and presents Monte-Carlo simulations using an effective loss with a simplified kernel, reporting that the algorithm decorrelates down to κ≈κ_loc.stab..","tokens_in":37471,"tokens_out":8110,"duration_ms":89852,"significance":"If the central claim were established, the paper would provide a genuinely new statistical-mechanics tool for characterizing dynamically accessible connected solution clusters in rugged landscapes, going beyond standard Franz-Parisi computations. The manuscript is creative, technically ambitious, and unusually transparent about the main technical caveat, Eq. (57). It also makes falsifiable predictions about margin distributions and algorithmic decorrelation times and compares them with simulations at several system sizes. However, the load-bearing stability argument is not currently valid as a saddle-point or Hessian analysis, its sign convention is internally inconsistent in the text, and the numerical validation is largely in-sample because the algorithm is built from the same no-memory ansatz whose physical relevance is at issue. These concerns must be resolved before the paper's main conclusions can be accepted.","major_comments":[{"comment":"The global instability result, Eq. (57), states that the no-memory ansatz is never a stationary point of the connected free energy: δϕ/δQ > 0 for all non-ancestor overlap pairs, for all α and κ. The paper correctly acknowledges the two logical possibilities, that the no-memory manifold is subdominant or non-physical, but the proposed local-stability calculation does not resolve this dichotomy. Equations (58)-(60) evaluate the response of the local entropy s_loc along one prescribed perturbation, Q_{Pk,P'k'} = m^{|k-k'|-2}, with the exponent −2 chosen for convenience in App. D.2, and then declare the sign of δs_loc to be the stability indicator. Because the unperturbed geometry is not stationary, first-order variations of the free energy dominate the measure; a sign change of δs_loc along a single arbitrary direction is not a Hessian criterion and does not establish that no-memory paths are the relevant connected configurations, nor that they shatter at κ_loc.stab. To support the central claim, the manuscript needs either to identify a true stationary point of the connected free energy whose Hessian is computed, or to explicitly reframe the claim as a property of the no-memory ansatz rather than of the physical solution manifold.","section":"Sec. 3.3, Eqs. (57)-(60)"},{"comment":"The sign convention for the local-stability criterion is internally inconsistent. The text states that negative δs_loc means the path geometry is stable and positive δs_loc means it is destabilized. A few paragraphs later, however, it says that in a range of parameters the core is 'locally unstable -δsloc(k,k')<0-', which contradicts the earlier convention. Figure 5's caption also equates stability with δs_loc negative for all distances. Since the threshold κ_loc.stab. is defined entirely by a change of sign of this quantity, the paper must correct this contradiction and state unambiguously which sign corresponds to destabilization.","section":"Sec. 3.3, after Eq. (59) and the paragraph containing δs_loc(k,k')<0"},{"comment":"The numerical validation is partly in-sample. The Monte Carlo loss is L_eff from Eq. (45), which is derived from the same no-memory ansatz whose stability is the central claim, and the simplified kernel G̃ in Eq. (62) is chosen by comparison with the theoretical G_λtop. Agreement between the predicted and measured margin distributions and decorrelation profiles therefore confirms that the algorithm samples the designed biased measure; it does not independently establish that this measure corresponds to a physical, dominant cluster of SBP solutions. An independent test of the cluster geometry, for example measuring overlap distributions among solutions found by an unbiased or differently biased solver, is needed to break this circularity.","section":"Sec. 4, Eqs. (45), (61)-(62), Figs. 8, 10, 11"},{"comment":"The claim that t_dec 'diverges' near κ_loc.stab. is not supported by the data as presented, because the protocol stops each annealing round when no full decorrelation is observed for t/N < 1500. The plotted t_dec is therefore capped at 1500N, and the apparent divergence may just reflect the finite observation window. The paper should distinguish a true divergence from a sharp increase beyond the cutoff, for instance by showing survival probabilities or longer runs near the predicted threshold.","section":"Sec. 4, Fig. 8 and the paragraph defining the stopping criterion"},{"comment":"The critical line κ_loc.stab. is obtained by fitting only four points (the black dots in Fig. 5, reproduced in Fig. 6), and the text does not report error bars, sensitivity to the value of m, or the dependence on the chosen perturbation amplitude. Since the entire phase diagram and the comparison with simulations hinge on this line, a more systematic determination is needed before the threshold can be considered quantitative.","section":"Sec. 3.3, Fig. 5 and Fig. 6"}],"minor_comments":[{"comment":"The text says 'given the constraint equations (31, 31)' but should refer to Eqs. (31)-(32); this is likely a typo.","section":"Eq. (31)"},{"comment":"The captions list N = {1250, 2500, 500, 10^4}, but the text and Fig. 10 use N = 5000; the captions should be corrected to 5000.","section":"Captions of Figs. 8 and 9"},{"comment":"The simplified kernel G̃_λtop is introduced with 'lim_{m→1} G ≈ G̃', but G̃ is independent of m and no convergence rate or quantitative accuracy measure is given; Fig. 11 shows the approximation deteriorates with increasing α, so a quantitative statement of its validity range would be useful.","section":"Sec. 4, Eq. (62)"},{"comment":"The sentence stating that the edge entropy s_x0 'effectively counts the total number of minima in the entire cluster' is not derived in the text and is somewhat counterintuitive given the edge distribution is used; a brief justification would improve clarity.","section":"Sec. 3.2.2, Eq. (54)"}],"recommendation":"major_revision","confidential_remarks":"The paper has an interesting core idea and is unusually honest about its main technical obstacle, but the current version does not establish the central claim. The local-stability criterion is not a valid Hessian analysis, the sign convention is contradictory, and the numerical section is substantially in-sample. These are fixable in principle if the authors can either place the no-memory ansatz on a proper variational footing or reframe the paper's contribution as a characterization of the ansatz rather than of the physical solution manifold. I recommend major revision rather than rejection, because the framework may be salvageable and the numerical observations remain suggestive."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper builds a genuinely new statistical-mechanics ensemble for connected solutions and applies it to the SBP, producing a concrete phase diagram and a threshold kappa^{no-mem}_{loc.stab.}. It is clearly written, unusually candid, and the nested local-entropy bias (Eqs. 13-15) is a real extension of the author's prior no-memory chain formalism. The margin-compression prediction and the divergence of decorrelation time near the threshold are concrete, falsifiable predictions. I also give the author credit for flagging Eq. 57 explicitly and stating the two possible readings, subdominant or non-physical, rather than burying the problem.\n\nThe soft spot is load-bearing. Eq. 57 shows the no-memory overlap matrix is never a stationary point of the connected free energy, for all alpha and kappa. That means first-order variations dominate the measure, and the local-stability criterion in Eqs. 58-60 does not repair the gap: it evaluates the response of s_loc along one prescribed perturbation with exponent -2 chosen for convenience in App. D.2, then declares the sign of delta s_loc to be the stability indicator. That is not a Hessian criterion, and it does not establish that no-memory paths are the relevant connected configurations nor that they shatter at kappa^{no-mem}_{loc.stab.}. The paper never closes the subdominant vs. non-physical dichotomy it raises.\n\nThe numerics are partly in-sample: the Monte-Carlo algorithm uses the same effective loss L_eff that defines the cluster, and the simplified kernel G-tilde was chosen by comparing with the theory's G_{lambda_top}. Agreement with the predicted margin distribution and the threshold is therefore expected. The phase boundary in Fig. 6 is a fit through four points. These are real limitations, and the abstract's \"we demonstrate its stability\" overstates what the current evidence supports. That said, the paper is not careless; it derives the instability, proposes a diagnostic, and gives reproducible-looking simulations. A theory-independent algorithm or a resolved stability analysis could confirm the threshold; until then, CONDITIONAL is the right verdict.\n\nWho is this for? Statistically-minded researchers working on perceptron landscapes, algorithmic accessibility, or flat minima. It deserves a serious referee, but the referee should be asked to address whether the local-stability criterion can be justified despite the non-stationarity, or whether the conclusions should be weakened. My recommendation: send to peer review, treat as promising but not established.","headline":"Genuinely new connected-solutions ensemble with concrete predictions, but the central cluster-stability claim rests on an Ansatz the paper itself shows is never a saddle point.","tokens_in":38010,"tokens_out":2016,"would_cite":true,"duration_ms":23113,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The symmetric binary perceptron hosts a delocalized cluster of connected solutions that is stable only above a threshold $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}(\\alpha)$; below it the connecting paths shatter.","keywords":["symmetric binary perceptron","connected solutions","no-memory Ansatz","local entropy","replica method","constraint satisfaction problem","statistical mechanics of disordered systems","Monte-Carlo annealing"],"falsifier":"Measure the typical overlap between a solution and its grandparent along connected chains just below the predicted threshold: if non-ancestor overlaps grow beyond the no-memory value $m^2$, the Ansatz and the predicted $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}$ are wrong. A second falsifier is to rerun the annealed Monte-Carlo at $\\alpha=0.75$ with the exact $G^{\\rm energ}_{\\lambda_{\\rm top}}$ kernel instead of the quadratic approximation and check whether decorrelation still stops at the predicted threshold.","tokens_in":36705,"feed_emoji":"🧠","tokens_out":10335,"duration_ms":103558,"temperature":0.7,"pith_summary":"The paper sets out to show that local-entropy biases—which favor configurations surrounded by other low-energy configurations—are the first step toward a statistical-mechanics description of connected solution clusters, and that such clusters can be computed well enough to predict where algorithms stall. The testbed is the symmetric binary perceptron, where typical solutions are isolated yet local algorithms still find solutions in part of the $(\\alpha,\\kappa)$ plane. The author defines an ensemble over chains of solutions whose consecutive members overlap by $m$, takes the no-memory Ansatz in which each solution only correlates with its direct ancestor, and sends $m \\to 1$ while the chain length diverges. The result is a star-shaped cluster of delocalized connected solutions that is locally stable only above a threshold $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}(\\alpha)$; below it the paths composing the cluster shatter, a transition that conventional Franz-Parisi computations miss. A Monte-Carlo dynamics built on the derived effective loss decorrelates until roughly the same threshold, confirming the prediction.","feed_headline":"Connected perceptron solutions shatter at a predicted threshold","feed_subtitle":"A biased Monte-Carlo finds solutions right up to that threshold, linking cluster geometry to algorithmic hardness.","key_machinery":"The central object is the no-memory Ansatz: an assumption on the replica overlap matrix of a chain of configurations in which $Q^{-1}_{P_k,P'_{k'}}$ and $\\hat{Q}_{P_k,P'_{k'}}$ are nonzero only between each configuration and its direct ancestor, forcing overlaps $m^{|k-k'|}$ along a path and an ultrametric (Bethe-tree) geometry. Under this Ansatz the replica free energy reduces to an iterative energy kernel $G^{\\rm energ}_{k}(w_k,m,\\{y_l\\})$, and for $y_k=1$ the iteration converges to its leading eigenvector, which generates the delocalized cluster. The load-bearing quantity is the local entropy $s_{\\rm loc}(k)$, the number of configurations gained when the connected chain is extended from layer $k-1$ to layer $k$; its perturbation $\\delta s_{\\rm loc}(k,k')$, defined by changing an ancestor overlap from $m^{|k-k'|}$ to $m^{|k-k'|-2}$, is the stability criterion, and the line where its sign changes is the predicted transition $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}(\\alpha)$.","core_discovery":"The central claim is that the symmetric binary perceptron contains a subdominant but algorithmically relevant manifold: a star-shaped cluster of delocalized connected solutions, each linked along a chain to its direct ancestor. In the construction, all Lagrange multipliers are set to one, the overlap between consecutive solutions goes to $m \\to 1$, and the chain length is sent to infinity so that the endpoints become fully uncorrelated; the cluster then has an edge of less-robust minima and a core of more-robust minima whose margin distributions are both computed explicitly. The paper proves that this no-memory geometry is globally unstable as a saddle point of the connected free energy, so the cluster does not dominate the measure; what governs it instead is the local stability of the entropy $s_{\\rm loc}(k)$, the number of solutions gained by extending a path, perturbed by re-correlating a solution with a distant ancestor. When the perturbation $\\delta s_{\\rm loc}(k,k')$ changes sign, the connecting paths destabilize at $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}(\\alpha)$, and the paper argues and then verifies numerically that the same threshold marks where a Monte-Carlo algorithm sampling the edge with the effective loss stops decorrelating. The Franz-Parisi potential overestimates the clustering transition, and the discrepancy is traced to the divergence of the margin cost function as $|w|$ approaches $\\kappa$.","pith_inferences":["Inference: the nested local-entropy construction should transfer to other constraint satisfaction problems with isolated typical solutions; if their margin kernels also diverge at $|w|=\\kappa$, the local-stability criterion may generically precede the Franz-Parisi transition.","Inference: the quadratic approximation $(\\kappa-w)(\\kappa+w)/\\kappa^2$ to $G^{\\rm energ}_{\\lambda_{\\rm top}}$ degrades as $\\alpha$ grows, so using the exact eigenvector kernel could shift the predicted threshold; a direct numerical evaluation would settle whether $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}$ is approximation-independent.","Inference: the divergence $\\partial_w^2 \\log G \\approx (\\kappa-|w|)^{-2}$ implies the landscape around connected minima becomes steeper with $N$, predicting an $N$-dependent algorithmic slowdown even above the threshold; the damped loss in Appendix E partially removes this effect and could be used to measure it quantitatively.","Inference: the paper leaves open whether clusters with memory (nonzero couplings beyond the direct ancestor) survive below $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}$; perturbing around a two-step-memory Ansatz would test for a secondary transition and might explain what happens to solutions below the threshold."],"forward_implications":["The annealed Monte-Carlo with the effective loss should decorrelate for $\\kappa$ above $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}(\\alpha)$ and fail below it; simulations for $\\alpha = 0.3, 0.5, 0.75$ show the decorrelation time $t_{\\rm dec}/N$ diverging near the predicted threshold.","The no-memory cluster is a subdominant manifold, so standard replica computations that select the dominant isolated minima cannot see the shattering transition; local-entropy stability is the quantity that detects it.","The Franz-Parisi potential overestimates the clustering transition for the symmetric binary perceptron, so the local-stability criterion is the sharper diagnostic whenever the margin cost diverges at the constraint edge.","The effective-loss construction gives a principled design rule for dynamics: target the edge of the connected cluster by compressing margins toward zero, rather than sampling typical isolated solutions.","Below $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}$ the edge solutions develop an overlap gap and behave like a frozen one-step replica-symmetry-broken phase, explaining why local algorithms get trapped even though solutions remain exponentially numerous."],"supporting_citations":[{"why":"Defines the symmetric binary perceptron, proves the SAT threshold, and establishes the isolated-solution structure that motivates the search for connected clusters.","marker":"[30]"},{"why":"Supplies the no-memory chain Ansatz and the chain-of-equilibria formalism that the connected ensemble generalizes; also shows unbiased Monte-Carlo cannot escape atypical regions.","marker":"[38]"},{"why":"Introduces the local-entropy bias that the paper's nested construction builds on, together with the sampling idea behind targeting dense regions.","marker":"[43]"},{"why":"Characterizes atypical robust solutions of the SBP and shows why a simple local-entropy bias alone is insufficient, motivating the nested chain construction.","marker":"[33]"},{"why":"Establishes that typical SBP solutions are isolated (frozen one-step replica symmetry breaking), the baseline picture the connected cluster is contrasted with.","marker":"[28]"},{"why":"Defines the Franz-Parisi potential used as the comparison observable for clustering transitions, which the local-stability criterion is shown to generalize.","marker":"[35]"},{"why":"Describes the star-shaped solution-space geometry in the spherical negative perceptron that the SBP cluster is found to resemble.","marker":"[27]"},{"why":"Formulates the overlap-gap property used to interpret why isolated or clustered solutions block local algorithms.","marker":"[22]"}],"fun_headline_variants":["Perceptron solution chains shatter at a computable threshold","Local stability predicts shattering of connected perceptron solutions","Where perceptron solution paths break: a sharp threshold","Algorithm finds delocalized solutions until their paths shatter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction rests on the assumption that the connected solutions of interest arrange into chains in which each configuration is correlated only with its direct ancestor, and that the particular perturbation size chosen is the right probe for when those chains destabilize.","fun_headline_variants_meta":{"raw":{"variants":["Perceptron solution chains shatter at a computable threshold","Local stability predicts shattering of connected perceptron solutions","Where perceptron solution paths break: a sharp threshold","Algorithm finds delocalized solutions until their paths shatter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000406,"raw_usage":{"total_tokens":2167,"prompt_tokens":1055,"completion_tokens":1112,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":671,"completion_tokens_details":{"reasoning_tokens":1046}},"tokens_in":671,"tokens_out":1112,"duration_ms":9446,"temperature":1.0,"reasoning_tokens":1046,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:44:04.674757+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the typical overlap between a solution and its grandparent along connected chains just below the predicted threshold: if non-ancestor overlaps grow beyond the no-memory value $m^2$, the Ansatz and the predicted $\\kappa^{\\rm no\\text{-}mem}_{\\rm loc\\, stab.}$ are wrong. A second falsifier is to rerun the annealed Monte-Carlo at $\\alpha=0.75$ with the exact $G^{\\rm energ}_{\\lambda_{\\rm top}}$ kernel instead of the quadratic approximation and check whether decorrelation still stops at the predicted threshold.","supporting_citations":[{"cited_title":"Local entropy as a measure for sampling solutions in constraint satisfaction problems.Journal of Statistical Mechanics: Theory and Experiment, 2016(2):023301, 2016","cited_arxiv_id":null,"evidence_quote":"Introduces the local-entropy bias that the paper's nested construction builds on, together with the sampling idea behind targeting dense regions."},{"cited_title":"On the atypical solutions of the symmetric binary perceptron.Journal of Physics A: Mathematical and Theoretical, 57(19):195202, 2024","cited_arxiv_id":null,"evidence_quote":"Characterizes atypical robust solutions of the SBP and shows why a simple local-entropy bias alone is insufficient, motivating the nested chain construction."},{"cited_title":"Recipes for metastable states in spin glasses.Journal de Physique I, 5(11):1401–1415, 1995","cited_arxiv_id":null,"evidence_quote":"Defines the Franz-Parisi potential used as the comparison observable for clustering transitions, which the local-stability criterion is shown to generalize."},{"cited_title":"The overlap gap property: A topological barrier to optimizing over random structures.Proceedings of the National Academy of Sciences, 118(41), 2021","cited_arxiv_id":null,"evidence_quote":"Formulates the overlap-gap property used to interpret why isolated or clustered solutions block local algorithms."}],"review_version":2}