{"id":"59635e83-cf68-4fed-916e-2752d862baa7","arxiv_id":"2607.26422","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Ensemble ML plus brute-force regression formulas predict cRPA-derived Ueff, V, and J for transition-metal oxides from electronic, structural, and elemental descriptors, with reported RMSEs of 0.148, 0.062, and 0.007 eV.","lead":"The authors trained random-forest, gradient-boosting, and XGBoost models on constrained-RPA data for 54 transition-metal oxides to predict Hubbard U, inter-site V, and Hund's J, reporting RMSEs of 0.148, 0.062, and 0.007 eV. A generalist might read this because fast, interpretable estimates of Hubbard parameters could accelerate screening of correlated materials without expensive cRPA calculations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Selection bias in reported LOOCV after best-subset/BFS screening is the key unresolved threat: with 54 targets, selecting the best of 4,095 feature combinations and top BFS models on the same data likely inflates RMSE/R² and breaks the transferability claim.","rationale":"I read the paper as a genuinely useful attempt to build ML surrogates for cRPA Hubbard parameters, with physically motivated descriptors and qualitative trends consistent with earlier cRPA studies. The cRPA calculations appear carefully done, and the correlations with W and Dd-p are plausible. However, the numerical claims rest on LOOCV after model selection on the same 54 data points. This is not a minor technicality: LOOCV is unbiased for a fixed model, but not for the best model chosen after evaluating thousands of candidates on the same data. With 54 samples, the gap between selected-model LOOCV and true generalization error can be large. The BFS equations are especially vulnerable because their functional forms are selected by fitting the full dataset; reporting LOOCV on the top-three candidates after that selection does not undo the selection. The J result, despite its small RMSE, is also affected because the three-feature set was chosen from 4,095 subsets. The paper does include a code repository, which is good, but the data are not released and no external cRPA values are used for validation. Therefore the reader's conditional verdict is appropriate: the physics is credible, but the numerical accuracy and the transferability of Eqs. 2-6 remain unproven until a nested or external validation is performed. I do not see a different load-bearing concern that would change the verdict; the selection-bias issue is the central one.","tokens_in":20817,"tokens_out":4117,"duration_ms":50525,"concrete_test":"Run a nested leave-one-out cross-validation: for each of the 54 compounds, repeat the full feature-subset search (all 4,095 combinations) and the BFS model search (all compound-feature combinations) using only the other 53 targets, then evaluate the model chosen in that fold on the held-out compound. Aggregate the nested RMSE/R² and compare with the reported values in Secs. 3.2-3.4. If the nested Ueff RMSE exceeds roughly 0.20 eV (or the nested V/J RMSEs degrade by >30%), the reported accuracy is selection-biased and the analytical formulas are not validated. A complementary check: hold out one entire structure family (e.g., spinels) during all selection and fitting, then test on that family.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claims are the LOOCV RMSEs of 0.148 eV (Ueff), 0.062 eV (V), and 0.007 eV (J), plus the analytical BFS formulas (Eqs. 2-6). For the claim to hold, these errors must estimate how the selected models will perform on new TMOs. That condition is not secured: in Sec. 2.2 the authors screen all 4,095 feature subsets and report the best LOOCV model, and the BFS procedure fits all candidate compound features on the full dataset before selecting top-three models for LOOCV. This makes the reported LOOCV a selected-model estimate, not an unbiased generalization error: each held-out point has already influenced feature and model choice. With n=54, best-subset selection can exploit noise substantially, especially for J, where the best of thousands of models gives R²=0.989. The BFS formulas are equally affected because their functional forms are chosen on the same 54 targets; the equations are fits, not independent derivations. No nested CV, holdout set, grouped split, or external cRPA benchmark is provided, and the data are not released. Thus the headline accuracy and the claimed transferability of Eqs. 2-6 could be materially optimistic.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents an ML workflow for predicting cRPA-derived Hubbard parameters (Ueff, V, J) for transition-metal oxides. Using 54 compounds and 12 features, including electronic descriptors W and Dd-p, the authors train RF, GBR, and XGB models; for each model, all 4,095 feature subsets are screened and LOOCV is used. They report best XGB RMSE/R2 values of 0.148/0.899 for Ueff, 0.062/0.784 for V, and 0.007/0.989 for J. A regression-based brute-force search (BFS) yields analytical expressions (Eqs. 2-6). The authors claim these enable efficient cRPA-quality parameter prediction and provide physical insight into localization, hybridization, and structural effects.","tokens_in":1397,"tokens_out":2476,"duration_ms":71281,"significance":"If the reported predictive errors were honest estimates of generalization, this would be a useful contribution: cRPA is computationally expensive, and an interpretable surrogate for three Hubbard parameters is valuable for oxide screening. The paper provides a multi-family cRPA dataset, uses physically motivated descriptors, and releases code. However, the central quantitative claim is not secured because feature selection and BFS model selection are performed on the same 54 targets before LOOCV. The reported RMSEs are selected-model scores rather than unbiased generalization estimates. This issue is load-bearing and requires additional validation before the headline accuracy can be accepted.","major_comments":[{"comment":"The reported LOOCV errors are optimistically biased. All 4,095 feature combinations are screened on the full dataset, and only the best subset per model is then evaluated by LOOCV. Each held-out sample has already influenced feature selection, so the LOOCV score is not an unbiased estimate of generalization. This is particularly sharp for J, where the three-feature model achieves R2=0.989 (Sec. 3.4). Please add nested CV in which feature selection is performed inside each training fold, or provide a holdout set or external cRPA benchmark, and report the distribution of RMSE across selection repeats.","section":"Sec. 2.2; Sec. 3.2; Fig. 3"},{"comment":"The BFS equations are also selected on the full data before LOOCV. For each mCnF configuration, all candidate compound features are screened by fitting the full dataset and the top-three models are then evaluated by LOOCV. Consequently Eqs. 2-6 are fits selected on all 54 points, and their reported errors do not account for model selection. The physical interpretations in Secs. 3.2-3.4 are post-hoc readings of fitted coefficients rather than tests of an independent derivation. A nested or split evaluation is required before these formulas can be claimed as transferable.","section":"Sec. 2.2; Eqs. 2-6"},{"comment":"The dataset is not i.i.d.: compounds are grouped by structure family (perovskite, olivine, spinel, layered, layered perovskite) and by 3d/4d TM series. Standard LOOCV can overstate accuracy for new materials of different families. To support the transferability claim, use grouped CV such as leave-one-family-out and report the resulting errors alongside the LOOCV numbers.","section":"Table S1"}],"minor_comments":[{"comment":"The typeset formulas are corrupted in the provided text, making them unverifiable. Please fix the rendering and list the equations in a machine-readable form in the SI.","section":"Eqs. 2-6"},{"comment":"The data are only available from the authors upon request. To enable reproduction of the selection protocol and independent validation, deposit the full target and feature table alongside the code.","section":"Data Availability"},{"comment":"Hyperparameters for RF, GBR, and XGB are not stated. Clarify whether they are fixed and, if tuned, describe whether tuning was performed inside or outside the CV folds.","section":"Sec. 2.2"},{"comment":"The x-axis indicates number of selected features, but the curves show the best subset of each cardinality rather than sequential addition. Please clarify this in the caption.","section":"Fig. 3 caption"}],"recommendation":"major_revision","confidential_remarks":"The selection-bias issue is the main obstacle but is fixable with nested CV, a holdout set, or family-grouped splits. If the authors add such validation and provide the dataset, the paper could become useful. I would also ask the editor to verify that the released code implements the exact protocol described; if it runs the same screening on all data, the reported numbers should be restated as selected-model scores."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this paper gives you a cheap ML surrogate for cRPA-derived Ueff, V, and J in transition-metal oxides, with explicit analytical formulas. The physics story is sensible — localization and d-p hybridization matter for Ueff, hybridization and structural compactness for V, and J is mostly atomic. But the headline numbers (RMSE 0.148/0.062/0.007 eV) are not trustworthy as generalization errors, because the same 54 compounds were used to select the feature subsets and BFS models before running LOOCV. That is optimistic by construction, especially with 4,095 feature combinations searched. I agree with the stress-test concern: nested CV or a real holdout set is needed before quoting those errors.\n\nWhat's actually new: previous ML papers targeted DFT+U or DFPT linear-response U/V; this is the first to target cRPA values, and using W and Dd-p as descriptors is physically motivated. The BFS analytical expressions (Eqs. 2-6) are new and useful as quick estimates. The trends they find match previous cRPA work — e.g., Ueff decreases with bandwidth and increases with d-p separation — so the qualitative conclusions are credible. Code is on GitHub, which is good. Data not released is not.\n\nSoft spots, in order of severity. First and biggest: the feature selection and BFS screening use the full dataset, so LOOCV is not an unbiased estimate of how the selected models will perform on new TMOs. The n=54 sample makes this worse, and the J result (R²=0.989 with three features) is exactly what you'd expect from picking the best fit out of thousands. Second: the analytical formulas are fits, not derivations. The \"physical insight\" is a reading of fitted coefficients; it's reasonable, but it shouldn't be oversold. Third: the dataset is small and dominated by 3d perovskites and layered oxides; transferability to other chemistries is unproven. Minor: the band-center energy windows and disentanglement windows are per-compound choices, which are fine but do add user freedom that could affect reproducibility.\n\nWho this is for: people who want quick U/V/J estimates for oxide screening, or who want to benchmark ML against cRPA. The paper deserves a serious referee — it's a real contribution with testable claims — but it needs a major revision: nested CV or grouped split, external validation, and releasing the input data. I'd send it to review, not desk reject.","headline":"Useful ML surrogate for cRPA U/V/J, but the headline errors are likely optimistic because feature and model selection happened on the same 54 compounds before LOOCV.","tokens_in":21652,"tokens_out":2555,"would_cite":true,"duration_ms":27613,"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 paper claims machine learning on a few physical descriptors reproduces cRPA-quality Hubbard parameters for transition-metal oxides to within about 0.15 eV, with explicit formulas linking U_eff to electron localization and d-p hybridizat","keywords":["Hubbard parameters","cRPA","transition-metal oxides","machine learning","ensemble regression","Hund's coupling","inter-site Coulomb interaction","descriptor-based regression"],"falsifier":"Compute cRPA-derived U_eff, V, and J for a handful of transition-metal oxides outside the 54, for example NiO, LaCrO3, or a 5d oxide such as SrIrO3, and plug their descriptors into Equations 2-6; if the U_eff errors systematically exceed roughly 0.15 eV, the selected formulas are specific to the training set rather than general physical relations.","tokens_in":20697,"feed_emoji":"⚛️","tokens_out":7331,"duration_ms":76782,"temperature":0.7,"pith_summary":"The paper tries to show that cRPA-quality Hubbard parameters do not require a cRPA calculation for every new oxide: a small set of descriptors, including the transition-metal d-band width and the d-band/O-p band-center separation, suffices to predict U_eff, V, and J with root-mean-square errors near 0.15, 0.06, and 0.007 eV on 54 transition-metal oxides. The payoff is practical, because fast parameter estimates can accelerate DFT+U, DFT+U+V, and DMFT-style workflows, and physical, because explicit formulas assign distinct drivers to each interaction: localization and hybridization for U_eff, hybridization plus structural compactness for V, and atomic identity for J. A sympathetic reader would take the central claim to be that correlation parameters can be estimated cheaply and interpretably at cRPA-level accuracy within the oxide families studied.","feed_headline":"Machine learning predicts oxide Hubbard parameters within 0.15 eV","feed_subtitle":"Cheap formulas stand in for expensive cRPA runs, making fast screening of correlated oxides feasible.","key_machinery":"The central object is the pair of electronic-structure descriptors: W, the bandwidth of the transition-metal d-band, and Dd-p, the energy separation between the TM-d and O-p band centers, which quantify d-electron localization and d-p hybridization. These are supplemented by atomic, compositional, and structural features such as d-electron count, oxidation state, and volume per formula unit. The mechanism that carries the argument is the regression-based brute-force search (BFS): each primary feature is transformed through a predefined set of nonlinear functions, the transformed variables are combined multiplicatively into compound features, and linear regressions of the form g = w0 + sum wi","core_discovery":"The paper's central claim is that the three cRPA-derived interaction parameters of transition-metal oxides can be predicted accurately from a compact set of twelve electronic, structural, and atomic descriptors. Leave-one-out cross-validation on the 54-compound dataset gives root-mean-square errors of 0.148 eV for the effective on-site U_eff, 0.062 eV for the inter-site V, and 0.007 eV for Hund's J with the best ensemble model. A regression-based brute-force search then produces explicit closed-form expressions (Eqs. 2-6) in which U_eff is written in terms of the TM-d bandwidth W and the TM-d/O-p band-center separation Dd-p, V in terms of structural compactness and Dd-p, and J essentially in","pith_inferences":["A natural test the paper leaves implicit is to hold out entire structure families, say all spinels or all layered oxides, and fit on the rest; if errors remain near the reported LOOCV values, the feature selection generalizes to new geometries, and if not, the reported RMSEs are likely optimistic.","Because U_eff is written explicitly in terms of W and Dd-p, and both respond to strain and pressure, the formulas could be used to predict how Hubbard parameters change under epitaxial strain or compression without new cRPA runs.","Since J tracks the atomic number and group of the transition metal so closely, a periodic-table lookup or a one-line formula could replace the empirical Hund's coupling in many TMO calculations, removing one adjustable parameter from DFT+U workflows.","The same descriptor-plus-brute-force-search workflow could be exported to other correlated chemistries such as sulfides or fluorides, provided W and Dd-p are recomputed for those systems; the paper does not test this transfer."],"forward_implications":["If the models are correct, cRPA calculations can be bypassed for screening: U_eff, V, and J for a new transition-metal oxide can be estimated from a few standard DFT or even purely compositional/structural quantities.","The analytical formulas separate the physical drivers: U_eff responds to d-band localization and TM-d/O-p hybridization, V to hybridization and structural compactness, and J mostly to the transition-metal's atomic identity.","The four-feature set nd, nox, Nu.c, and Vf.u already nearly saturates the best ensemble model for U_eff, suggesting that accurate predictions may be possible without electronic-structure descriptors in some regimes.","For Hund's coupling, a single descriptor such as the TM atomic number reaches R^2 near 0.95, and a simple linear formula using only the group number of the TM reproduces J within 0.015 eV.","The resulting equations are simple enough to be embedded directly in DFT+U or DFT+U+V codes, replacing empirical parameter choices with descriptor-based estimates."],"fun_headline_variants":["ML predicts Hubbard U, V, J for oxides within 0.15 eV","Closed-form equations replace costly cRPA for Hubbard parameters","Hubbard parameters from descriptors: ML matches cRPA accuracy","Fast ML for oxide Hubbard U, V, J: errors under 0.15 eV"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The reported accuracies come from testing each compound one at a time with models whose best feature combination was chosen after looking at all 54 cRPA targets, so a new oxide outside this set could be predicted less accurately than the stated errors suggest.","fun_headline_variants_meta":{"raw":{"variants":["ML predicts Hubbard U, V, J for oxides within 0.15 eV","Closed-form equations replace costly cRPA for Hubbard parameters","Hubbard parameters from descriptors: ML matches cRPA accuracy","Fast ML for oxide Hubbard U, V, J: errors under 0.15 eV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"total_tokens":1311,"prompt_tokens":868,"completion_tokens":443,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":362}},"tokens_in":612,"tokens_out":443,"duration_ms":5662,"temperature":1.0,"reasoning_tokens":362,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T16:12:40.345651+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute cRPA-derived U_eff, V, and J for a handful of transition-metal oxides outside the 54, for example NiO, LaCrO3, or a 5d oxide such as SrIrO3, and plug their descriptors into Equations 2-6; if the U_eff errors systematically exceed roughly 0.15 eV, the selected formulas are specific to the training set rather than general physical relations.","supporting_citations":[],"review_version":1}