Title: An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds
Venue: NeurIPS 2025
Accepted: yes
Keywords: statistical query

Franz-Parisi criterion

computational hardness in statistical inference
Abstract: Bandeira et al. (2022) introduced the Franz-Parisi (FP) criterion for characterizing the computational hard phases in statistical detection problems. The FP criterion, based on an annealed version of the celebrated Franz-Parisi potential from statistical physics, was shown to be equivalent to low-degree polynomial (LDP) lower bounds for Gaussian additive models, thereby connecting two distinct approaches to understanding the computational hardness in statistical inference. 
In this paper, we propose a refined FP criterion that aims to better capture the geometric ``overlap" structure of statistical models. Our main result establishes that this optimized FP criterion is equivalent to Statistical Query (SQ) lower bounds---another foundational framework in computational complexity of statistical inference.  Crucially, this equivalence holds under a mild, verifiable assumption satisfied by a broad class of statistical models, including Gaussian additive models, planted sparse models, as well as non-Gaussian component analysis (NGCA), single-index (SI) models, and convex truncation detection settings. For instance, in the case of convex truncation tasks, the assumption is equivalent with the Gaussian correlation inequality (Royen, 2014) from convex geometry. In addition to the above, our equivalence not only unifies and simplifies the derivation of several known SQ lower bounds—such as for the NGCA model (Diakonikolas et al., 2017) and the SI model (Damian et al., 2024)—but also yields new SQ lower bounds of independent interest, including for the computational gaps in mixed sparse linear regression (Arpino et al., 2023) and convex truncation (De et al., 2023).


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work takes a significant step toward unifying methods for predicting computational hardness in high-dimensional hypothesis testing. The basic setting is as follows. the goal is to distinguish between a family of planted distributions $\\mathcal{P} = \\\\{P_u^{\\otimes m} \\mid u \\in \\Theta_n\\\\}$ and $\\mathcal{Q} = Q^\\{\\otimes m\\}$, where m denotes the number of samples and we implicitly consider a sequence of hypothesis testing problems indexed by the data dimension (or instance size) parameter $n$. Note that by assuming a prior $\\pi$ over the parameter space $\\Theta_n$, the testing effectively becomes a (high-dimensional) simple vs simple testing problem for which likelihood ratio traditionally plays a central role.\n\nThere has been a growing recognition that many techniques for predicting computational hardness are closely related, as they rely on common intermediate quantities derived from the likelihood ratios $L_u = P_u/Q$. However, formal connections between these approaches have only recently begun to be established, with the first such unification appearing in the work of Brennan et al. (2021).\n\nThis work represents the latest coordinated effort toward unification, this time building connections between the Franz-Parisi potential heuristic from statistical physics and statistical query (SQ) lower bounds from learning theory. In particular, the authors introduce the generalized Franz-Parisi (GFP) criterion and establish its equivalence to a notion of statistical dimension for SQ algorithms, which provides a sufficient (though not necessary) condition for SQ hardness. The criterion is \"generalized\" because the authors demonstrate that the original FP criterion, introduced in previous work, is overly conservative in its predictions of computational hardness.\n\nThe established equivalence also enables a straightforward proof of a new SQ lower bound for the convex truncation problem.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n1. **Building bridges between fields that speak different technical languages.** This work situates the GFP criterion within its historical context in statistical physics. By establishing the GFP-SQ equivalence, it connects statistical physics and learning theory, fostering the cross-pollination of intuitions and ideas between these fields.\n2. **Simplicity and elegance of the GFP criterion.** The GFP criterion introduced by the authors is a simple, elegant quantity that formalizes a hunch shared by many experts: that existing notions of computational lower bounds, while technically defined differently, largely feel similar in spirit and appear to be different shades of the same \"hardness core.\" By formally establishing the equivalence between GFP and SQ, the work provides a satisfying justification for these intuitions.\n3. **Clear and well-organized exposition.** The clear and well-structured exposition makes the main results accessible and allows readers from diverse backgrounds to follow the technical developments.\n\n### Weaknesses\n\n1. **Statistical dimension does not characterize SQ hardness.** The statistical dimension-based criterion is conservative and often predicts problems as \"not hard\" even when they are, in fact, hard for SQ algorithms. In other words, statistical dimension (Definition 3) provides is a sufficient but not necessary condition for SQ hardness, as noted in [Brennan et al., 2021, Appendix B]:\n    \n    > *However, since SDA is **not** a characterization for VSTAT …*\n    > \n    \n    Hence, referring to Definition 3 as \"SQ hardness\" can be misleading, especially for readers who may not be aware of this subtlety.\n    \n    I suspect that exponentially thin Gaussian pancakes may provide yet another example of the aforementioned gap between statistical dimension and SQ hardness. Notably, Diakonikolas et al. (2024) demonstrated that even pancakes with zero thickness remain SQ-hard.\n    \n2. **The role of GFP in the equivalence.** The $\\rho_G$-FP criterion appears to be the main workhorse in establishing the equivalence to SQ. Is there reason to believe that GFP is a more fundamental quantity? I agree that the $\\rho_G$ criterion seems somewhat ad hoc, as multiple symmetry groups $G$ can correspond to the same high-dimensional testing problem $(\\mathcal{P}, \\mathcal{Q})$, each giving rise to a different notion of the \"overlap potential\" $\\rho_G$.\n\n**References**\n\n- Ilias Diakonikolas, Daniel Kane, Lisheng Ren, Yuxin Sun. SQ Lower Bounds for Non-Gaussian Component Analysis with Weaker Assumptions. *NeurIPS* 2024.\n\nQUESTIONS:\n1. What should one conclude if Assumption 1 does not hold and the GFP and SQ criteria give different predictions of hardness? Which one is a more reliable indicator of computational hardness when equivalence breaks down?\n2. The example illustrating the necessity of Assumption 1 in Section A.3.2 appears to be missing some important details. In particular, is there a constraint on the parameters for the planted distributions $P_u$ that ensures the example works as intended?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript refines the Franz–Parisi (FP) geometric criterion for average-case computational hardness in high-dimensional inference. The authors introduce a Generalized FP (GFP) criterion that optimizes the choice of “overlap” event and prove an equivalence between GFP-hardness and Statistical-Query (SQ) lower bounds under a mild symmetry assumption . The equivalence is shown to hold for a broad family of detection problems.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Conceptual advance. Optimizing the overlap event yields a unified hardness criterion that aligns with SQ lower bounds across many canonical detection tasks; this is theoretically neat and practically useful for researchers who favour the SQ framework and unite it with the low degree approach\n- Broad theoretical applicability. The mild group-symmetry assumption is verified for several popular models (GAMs, sparse PCA, NGCA, single-index, convex truncation), demonstrating real scope.\n- Illustrative counter-example. Section 4 convincingly shows that GFP can succeed where the classical FP criterion misfires, underlining that the refinement is substantive.\n\nWeaknesses\n\nEssentially, the paper is not easy not read, and a lot can be done to enhance clarity:\n\n- Detection vs Estimation not foregrounded. The work targets detection tasks, whereas the original Franz–Parisi potential in physics predicts hardness of estimation. Although this is stated in the abstract, the title and early sections still refer generically to “Franz–Parisi” and \"Hardness\" which risks confusion. I suggest amending the title (e.g. “An Optimized Franz–Parisi Criterion for Detection”) and maybeadding a short subsection that contrasts annealed FP (used here) with the quenched/estimation version (used in physics and in AMP)?\n\n- Relation to Bandeira et al. (2022) under-explained. Section 4 asserts that GFP and FP diverge, but the presentation is terse and the reader is left unsure why Bandeira’s overlap-based criterion fails in the constructed model. A crisper comparison—perhaps tabulating the two notions side-by-side and walking through a minimal counter-example—would better highlight the novelty. It weould be really a plus in the paper to have more concrete, worked-out examples. The paper claims GFP handles cases where “overlap” is meaningless, yet only one synthetic example is detailed. Additional, simpler examples (even toy 1-D priors) illustrating how the optimized event departs from |〈u,v〉| ≤ ε would help readers grasp the intuition and appreciate originality beyond a minor improvement of Bandeira.\n\nSide note: Additional related-work gap (single-index models).\nIn discussing the single-index model, the authors cite only Ref. [11] for the characterization of the easy (GE = 1) and hard (GE = 2) phases. Yet these phase diagrams were established several years earlier in two independent lines of work:\n• J. Barbier, F. Krzakala, N. Macris, L. Miolane & L. Zdeborová, Optimal errors and phase transitions in high-dimensional generalized linear models, PNAS 116 (2019): 5451 – 5460.\n• M. Mondelli & A. Montanari, Fundamental limits of weak recovery with applications to phase retrieval, 2018.\n\nQUESTIONS:\n* Title and scope. Will the authors consider adding “Detection” to the title and a short paragraph contrasting annealed FP (detection) with quenched FP (estimation)?\n\n* Clarifying the leap beyond Bandeira et al. Can the authors provide an explicit toy model (in addition to the Section 4 construction) where overlap-based FP passes but GFP detects hardness, and explain the geometric intuition? ALso, in all the exampel provided, can they explain if Bandeira et al applied or fail?. Beyond the Section 4 Rademacher-product example, are there natural models (e.g. permutation-invariant priors) where |〈u,v〉| is irrelevant yet Assumption 1 holds? Including one would strengthen claims of generality.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper explores the computational hardness of statistical inference problems. The paper extends the Franz--Parisi criterion to rigorously characterize hardness beyond the class of Gaussian additive models which was the focus of the existing work. The paper defines a generalized notion of the Franz--Parisi criterion that classifies SQ hardness in a broad class of models beyond the Gaussian additive models.\n\nSTRENGTHS AND WEAKNESSES:\nThe main body of this paper provides a nice preview and overview of the original Franz--Parisi criterion and its generalization. However, the nature of the paper is quite technical and much of the proofs are deferred to the appendices. The paper does a adequate job motivating the results and the intuition behind the assumptions, but the constraint on page limit means that the explanations are brief. The appendices are referenced several times in the main body, and perhaps a precise pointer to the relevant section of the appendices to help readers jump to the relevant section. \n\nThe connection to detection problems is quite remarkable, as typically from the statistical physics point of view this involves an understanding of the fluctuations. The link with the Franz--Parisi potentials and detection is not obvious at all. The original paper by Bandeira et al is of great importance and this follow-up paper is a strong continuation of this line of work. So although this connection is not new and was established in the earlier work, the extension to statistical query is new and quite interesting as well. The generalization beyond Gaussian additive models is also very powerful.\n\nQUESTIONS:\n1. Is there some intuition why the annealed Franz--Parisi potential is the right object to look instead of the quenched one? It seems possible that in the regimes of parameters than you can show or disprove hardness might coincide with the regimes that quenched and annealed quantities are the same. \n\n2. In what sense is the generalized notion of the GFP hardness optimal? Is it true that if GFP hardness fails, then we also get the absence of SQ hardness? A nice example of the failure of FP criterion to detect SQ hardness is explained in section 4. Is a similar example known if GFP hardness fails to detect hardness in a problem. \n\n3. Is there a simple explanation on how the two notions of hardness in Theorem 2 and Theorem 3 equivalent. Namely the second point makes it a bit hard to parse how the second notion of hardness implies the first due to the extra conditions that appear in the second point. \n\n4. How important is the criterion that $u$ is supported on the sphere on line 55? Is it because if we weakened this condition, then the overlap is not the only quantity we care about, but also the norm of both $u$ and $v$? If that is the case, can we get similar results if we consider the normalized overlap $\\frac{\\langle u, v \\rangle}{\\|u\\| \\|v\\|}$ in FP/GFP hardness?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies information-computation tradeoffs in the context of SQ lower bounds and the Franz-Parisi (FP) criterion. According to the FP criterion (inspired by work from statistical physics) a hypothesis testing problem of distinguishing between a null hypothesis and another distribution family ${P_v}$ parameterized by a (random according to some prior) vector is called FP-hard (with parameters $m,q,\\epsilon$) if the average inner product of m-sample likelihood ratios between two members $P_u,P_v$ of the alternative distribution family, where the average is over the a \"typical\" region for the inner product of $u$ and $v$ is upper bounded by $1+\\epsilon$. Prior work (e.g., Bandeira et al. 2022) showed that FP-hardness captures SQ-hardness (in both directions) for Gaussian additive models, and partially for sparse planted models, but also gave counterexamples where the equivalence fails. The present paper proposes a Generalized Franz-Parisi (GFP) criterion. The modification, provided in Definition 2 consists of relaxing the notion of \"typical\" event to use a more general condition instead of the standard inner product. The paper shows that this is now is equivalent to bound on the Statistical Query dimension. The result relies on an assumption (Assumption 1) which is a correlation condition  required to hold over a group that preserves the prior distribution.\n\nThe main equivalence theorem comes in two steps where the authors first show that the \"typical\" event in the GFP criterion takes a specific form, and then show that the resulting simplified form of the GFP criterion is equivalent to bound on the SQ dimension bound. The combination yields the main result in Theorem 3. The final result also requires the hypothesis problem to be have information-theoretic optimal sample complexity that is lower bounded. A convenient simplified version of the theorem is that if the problem requires $m = \\omega(\\log n)$ samples information-theoretically, then super-polynomial SQ lower bounds are equivalent to GFP hardness with $q$ (the proxy for runtime) being super-polynomial.\n\nFinally, the paper demonstrates that several well-studied statistical models satisfy the correlation assumption, hence the equivalence applies. These include:\n\n- Gaussian additive models\n- Planted sparse models (which includes Gaussian sparse regression, sparse phase retrieval  and sparse PCA) for which the authors show new SQ and GFP-hardness results.\n- Non-Gaussian component analysis to which many statistical problems like GMMs estimation and robust mean/regression are reducible to\n- Single index models\n- Gaussian convex truncation models, for which the paper shows a connection to the correlation inequality for convex bodies in probability theory\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- There’s significant ongoing interest in characterizing computational-statistical tradeoffs, and this paper builds meaningfully on that direction.\n- The generality of the main result is a positive aspect of the paper. Also the paper includes several applications and examples/counter examples to demonstrate why assumptions are needed.\n\nWeaknesses:\n\n- All of the technical work is deferred to the appendix, which makes the main body feel light and the appendix a bit dense.\n\nOverall, I do not have any major concerns about the paper and I would recommend acceptance.\n\nQUESTIONS:\nIs there any intuition for understanding the role of $k$ in Assumption 1?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose a refinement of the Franz Parisi criterion for the detection of planted signals and the understanding of statistical to computational thresholds introduced by Bandeira et al. in 2022. They show that this optimized criterion is equivalent to Statistical Query lower bounds (which according to the authors can be considered as a representative approach which closely aligns with best known algorithms, together with the low degree polynomial lower bounds)\n\nSTRENGTHS AND WEAKNESSES:\n- The paper engages with a subject that is particularly relevant in the current context but at this point, it lacks sufficient clarity and organization. I believe it would be more reasonable to take some time to carefully organize it and consider submitting to a journal which favors longer expositions. The main focus of the paper is the Franz Parisi criterion but this criterion is not properly introduced. The idea is great and the paper demonstrates a wide scientific culture but in order for the full depth and implications of this idea to be thoroughly understood, the foundations have to be more clear. In short, the idea is very interesting but it must be reworked (with the objective for the paper to be self contained which is currently not the case). New results are often messy and such messiness should not be a criterion for how novel and influential an idea is. That being said, communication also matters and at this point my feeling is that the structure of the paper does not facilitate a clear understanding of the idea.\nMost of the text at this point barely consists of descriptions of the formulas. Central to the generalized Franz Parisi criterion is the notion of group. But the intuition behind this novelty is never fully discussed. Another important notion which is not clearly introduced is the product <L_u, L_v>. Most of the definitions involve tuples of parameters (e.g. the Generalized Franz Paris criterion is defined with respect to a triple (q, m, epsilon)) I think it would be good to recall the meaning of those parameters from time to time in the text. E.g. In lines 107 - 109, the authors give an intuition for q.\n\n- I find it surprising that the Generalized Franz Parisi criterion is group dependent. I feel that this should be further addressed. For example in section 3 you indicate that GAM are FP hard with respect to the group Z_2. Then you say that planted sparse models satisfy assumption 1 w.r.t. the trivial group.. Perhaps I’m missing something but shouldn’t there be a relation. I.e. if a problem is hard with respect to a group, shouldn’t it be hard with respect to the other groups as well ? and if it is not the case, why?\n\n\n- I think the paper should be reorganized around a practical example such as the Gaussian additive model. At each step, one could then illustrate the different concepts based on this model. It is a bit disappointing given how important the result is and given that the main assumption of the Theorem is satisfied for those models, to not have a clear illustration with more intuition.  \n\n- The theoretical definitions 2 and 3 are interesting but better intuition should be provided\n\nQUESTIONS:\nSection 1\n\n- lines 51 - 62, you should give an example of a detection problem (even the simple rank one detection problem) illustrating the meaning of P, Q u and v. \n- lines 52-56 are not very clear. Why not give an example. Isn’t the planted distrbution the same as the null distribution except that the parameters are updated. E.g. In the additive model with Gaussian noise, if I’m not wrong, the addition of a planted signal corresponds to changing the mean and variance of the original distribution doesn’t it?\n- line 58: what are vanishing type I or type II errors ?\n- line 63 - 65, in definition 1, from what I understand, the expectation is taken with respect to u and v? I would explicitly indicate this.  \n- Definition 1 again. From what I understand, you only look at levels of overlap that can be demonstrated for a sufficiently large number of solutions. But then you average over solutions that are more different than the level of overlap delta  \n- Lines 65-67, The likelihood ratio (dP_u/dQ) should be properly introduced. I strongly encourage a complete introduction such as in e.g. Kunisky et al. “Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood Ratio” (Definition 1.7). I also encourage mentioning the annealed upper bound (and its connection to the FP potential) in the main paper. \n- Again on the likelihood ratio, I really recommend moving (11) from appendix A.2 to section 1 and properly introduce the notation L_u^{\\times m} in relation to the independence of the Y_i\n- The definition of the Franz Paris potential that you give in appendix A2, line 945, is also quite vague.  What does the Potential represent? There is no intuition given. Moreover several explanations are missing. E.g. why do you need the Franz Parisi criterion to be less than 1+epsilon. You should explain somewhere that an O(1) FP criterion corresponds to a regime in which string detection is impossible and that a 1+o(1) FP criterion corresponds to a regime in which weak detection is impossible. Perhaps also indicate that FP is always larger than 1. Perhaps just indicate that the smaller the FP criterion, the harder the problem. I.e. Honestly I think you should at least add part of Bandeira et al 2022, section 1.1. (the reminders on the likelihood ratio and the importance of the squared norm of this ratio)\n- it seems that in Equation (1) the inner product should be <L_u, L_v >_Q\n- line 68: I really think that appendix A.2. should be moved to section 1 or that you should at least give a better introduction to the notations in Definitions 1 and 2. The notations L_u, L_v really come out of the blue which makes the understanding quite difficult.  \n- lines 70-73, if you want to provide an additional explanation for (1)-(2) it is good. But your explanation should bring more information. What you do here is you merely describe the formulation. In fact you could do more simple: The left-hand side … corresponding to the constraint. —> this is just a description of what’s already given in (1)-(2). Now if you really want to add a sentence make it simpler: “”we integrate over the region <u,v><=\\delta. \n- To me, lines 68 to 77 do not bring a lot more information. Except for the sentence on the landscape. \n- line 89: “and an one-sided” —> “and a one-sided”?\n\nSection 1.1.\n\n- line 95: “Our main contribution of this work” —> “The main contribution of this work” or “Our main contribution” ?\n- lines 98 - 100, you use arguably twice, perhaps replace of the occurrences by another word?\n- In (3) it is not clear what \\pi represents. \\pi seems to be a distribution over u and v? so that \\pi^{\\otimes 2} is the distribution over independent (u,v). This should be clarified\n- In Definition 3, again, no intuition is given. \n- Informal statement of Theorem 1: “which we assume (1) it satisfies … and (2) it is…” —> “which we assume (1) satisfies.. and (2) is” ?\n- line 135 : “On top that ” —> “On top of that”\n- lines 142 - 161, you list examples of tasks that satisfy your assumption before introducing those models. You mention the models in section 1.1 but the reader has to wait for section 3 for those models to be clearly defined. I strongly recommend moving lines 142 to 166 to section 3. \n\nSection 2\n\n- Equation (5), what is the meaning of Unif(G) ?\n- line 187: “over the a group” —> “over a group orbit that…”?\n- line 189: Isn’t the expecation already applied through the 1/4 and the average over the group? I.e shouldn’t the equation read as 1/4(<L_u, L_v> +<L_{-u}, L_v> + ….) ?\n- line 191 : “This averaging approach allows for much greater generality” —> why ? this is not clear to me. Expand or remove.\n- line 193 - 194 : “in our examples Section 3” —> “In our examples in section 3”?\n- Generally speaking, I would recommend moving Remark 2.1. to section 3 as it does not improves readability of section 2.\n- lines 203 - 204 : “Given a group G … it turns out that ..” —> why ? again this it not rigorous.\n- lines 217 - 219: “First both the requirement of the parity…” this should go. Either you do it or don’t. But if you don’t, mentioning it reduces readability and should be considered as noise. \n- The dependence on the cardinality of the group G is quite interesting and to my opinion would deserve some additional comments. \n\nSection 3\n\n- lines 257 - 258, I would recall 189 - 190 to improve readability ?\n- line 272 : “and obtain internet new hardness results” —> Here I’m not sure what you mean\n- lines 280 - 283: your definition of the non Gaussian Analysis model is not clear/self contained. In particular what is meant by “replace the component <x, u> \\cdot u” by z\\cdot u. Is z\\cdo u an inner product ? then why not write <z, u> and if it is not, then why not write zu ? also where should one replace the component <x, u> u by zu? The model is not clearly defined. In fact, here again I would advocate less details to gain clarity on the reduced information you provide. By wanting to show more, you lose the readers on everything you want to explain. Is it really necessary to detail all the models in section 3? I would focus on one or two (and perhaps briefly indicate that it works in the other settings as well, without entering into the details)\n\nBibliography and Appendices\n\n- It is a detail but it would be convenient to add hyperlinks to the bibliographic references. \n- The references of the supplementary material do not match the references in the abbreviated paper.  \n\nAppendix A.2.\n\n- line 941. Why do you add variable v in the definition of the posterior, why not keeing u as the only variable for the planted signal?\n- line 947 : “of the loca dynamics” —> “of the local dynamics”?\n- line 971 : “one get” —> “one getS”\n- line 977: “as we elaborated in the Introduction ” —> “as we elaborated in the introduction”\n- line 980 “it is mathematical connection” —> “it is A mathematical connection”?\n- In appendix A.2. lines 937 to 973, if feel there is some confusion with the distributions. In 945 - 946 u has distribution p and v has distribution \\nu. In 957 -958, u has distribution p and v has distribution \\pi. Finally in 971-972 both u and v have distribution p.\n\nLIMITATIONS:\nsee above", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-17"}