{"id":"dffa4bc8-cd0a-407b-8ef8-622aec2a67e1","arxiv_id":"2510.08906","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Weighting furthest-point sampling distances by force norms yields training sets that reduce kernel-ridge energy errors and error variance on MD17 molecules.","lead":"GGFPS is a new way to pick which molecular structures to include in an AI training set: it adds atomic force magnitudes to the classic furthest-point sampling rule. Across six small molecules and a toy function, models trained on GGFPS-selected points show lower and more stable energy-prediction errors than standard furthest-point or random sampling.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"ST data-efficiency claim rests on learning curves with unmatched test sets: GGFPS/FPS test on the L−N leftover points while URS uses a fixed test set, so the twofold reduction may be an artifact.","rationale":"The reader's weakest_assumption focuses on whether molecular force norms are a valid proxy for local label variance. That is a legitimate mechanistic concern, but it is secondary to the empirical claim: even if force norms are imperfect proxies, GGFPS might still select useful training sets, and the paper's MD17 results could stand. The reader's rationale does mention 'clarify test-set protocol' as one of the needed corrections, but the specific problem is sharper: the ST learning curves use different test sets at different N, and the paper explicitly acknowledges an MAE artifact. This directly undermines the most quantitative headline claim (twofold training-cost reduction on ST), which is the strongest_claim item (i). The algorithm inconsistency and missing PCov baselines are reproducibility/completeness issues, not as directly tied to the numerical result. Setting the verdict to UNCHANGED is appropriate: the paper still merits conditional acceptance, but the test-set protocol must be fixed and the ST data-efficiency claim re-evaluated on a fixed held-out set.","tokens_in":18828,"tokens_out":9265,"duration_ms":80356,"concrete_test":"Fix a single independent test set for the ST experiment (e.g., 5,000 points drawn uniformly from [−4,4]^2) and hold it constant for every sampler and every training size N. Re-run the full pipeline: draw labeled sets of each size L, run URS/FPS/GGFPS for N ∈ {50,100,250,500,950}, tune KRR hyperparameters and β by CV on each training set, and report MAE and RMSE on the fixed test set. If GGFPS still matches or beats FPS at half the training size on this fixed test set, claim (i) stands; if the advantage shrinks or reverses, the reported twofold reduction is an artifact of variable test sets.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim (i) — up to twofold training-cost reduction versus FPS on the Styblinski-Tang function — depends directly on the learning curves in Figure 3. The protocol in Section IIIA states: 'Labeled sets of sizes {50,100,250,500,1,000} are selected via URS. GGFPS and FPS training sets are sub-sampled from these labeled sets, with the remainder used for testing.' Thus for a labeled set of size L, the test set for GGFPS/FPS at training size N is exactly the L−N leftover points. The test set therefore varies with N: at N=950 the model is evaluated on only 50 points, while at N=50 it is evaluated on 950 points. Meanwhile the URS learning curves are described as 'invariant to the initial labeled set size', implying URS errors are computed on a different, fixed test set. Comparing GGFPS at N=950 (50 leftover test points) with URS at N=1,000 (fixed test set) is not an apples-to-apples comparison. The paper itself notes this in Figure 3: 'At N=950 the GGFPS learning curve is lower than the URS learning curve at N=1,000. This is an artifact of using the MAE metric, and disappears when RMSE is used instead.' That admission confirms the reported advantage is at least partly a metric/test-set artifact. Because the 'twofold reduction' headline is derived from these unmatched learning curves, the central ST efficiency claim is not yet supported by a controlled comparison.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Gradient-Guided Furthest Point Sampling (GGFPS), an extension of furthest point sampling that weights the FPS distance score by molecular force norms raised to an exponent β, with an alternating exponent schedule intended to balance high- and low-gradient regions. The method is evaluated with kernel ridge regression on the two-dimensional Styblinski–Tang function and on six MD17 molecular trajectories, comparing against uniform random sampling (URS), FPS, and constant-exponent variants. The authors report that GGFPS improves data efficiency and robustness, particularly for equilibrium and strained molecular configurations, and reduces prediction-error variance. The paper is empirical, with no formal derivations; the main evidence consists of learning curves, error-surface plots, and distribution analyses over bootstrap repetitions.","tokens_in":19285,"tokens_out":7243,"duration_ms":62633,"significance":"If the empirical claims hold, GGFPS would be a simple, practical contribution to training-set selection for molecular machine learning, where force labels are often already available from reference calculations. The benchmark is broad (six molecules, training sizes 50–1000, bootstrap repetitions), and the comparison includes both standard baselines and supervised FPS-style selectors. A notable strength is that the MD17 experiments consistently show lower mean errors and lower error variances for GGFPS across many training-set sizes, not just at a single favorable operating point. The paper also identifies a potentially important failure mode of plain FPS on Boltzmann-distributed molecular data. However, the central quantitative efficiency claim for the toy system rests on a comparison protocol with unmatched test sets, and the stated algorithmic mechanism for achieving low-gradient coverage is contradicted by the pseudocode as written. These issues need to be resolved before the contributions can be accepted at face value.","major_comments":[{"comment":"The alternating β sequence is described as interpolating between −β and β and as 'flipping index signs during interpolation' to ensure that the sparse early training set contains both low- and high-gradient points. As written, however, the sequence does not alternate signs. With β_list ordered from −β to β, the reindexed sequence is β_N (positive), −β_2 (positive, since β_2 is negative), β_{N−1} (positive), −β_3 (positive), and so on. Since β_j is negative only for j < (N+1)/2, the even-indexed terms stay positive through roughly the first half of the iterations; for even N only the final term is negative, and for odd N no term is negative. Thus the algorithm as pseudocoded strongly favors high-gradient points and does not implement the stated low-gradient inclusion mechanism. This is load-bearing because the MD17 interpretation (Sec. IIIB, Figs. 6–8) attributes the method's success at l","section":"Sec. IIB and Algorithm 1 (Appendix, lines 5–9)"},{"comment":"The Styblinski–Tang learning curves for FPS and GGFPS are not computed on a fixed test set. The text states that labeled sets of size L are split into training sets of size N and test sets of the remaining L−N points, while URS learning curves are 'invariant to the initial labeled set size,' implying URS is evaluated on a separate fixed test set. Cross-N comparisons—such as the claim that GGFPS reaches the same accuracy as FPS with half the training points—therefore confound sampling quality with changes in test-set size and composition. The authors' own note in the Fig. 3 caption, that the apparent advantage of GGFPS at N=950 over URS at N=1,000 is an artifact of MAE, confirms that the protocol is not fully controlled. The ST efficiency claims should be recomputed with a common held-out test set for all methods and training-set sizes, and the factor-of-2 claim should be verified under t","section":"Sec. IIIA and Fig. 3"}],"minor_comments":[{"comment":"Algorithm 1 is referred to as being in the SI, but it appears in the Appendix; the reference should be fixed.","section":"General"},{"comment":"The statement that molecular force norms 'indirectly describe the variance of molecular energy labels' is a heuristic motivation. A quantitative analysis relating force norms to local label variance (e.g., residuals of a descriptor-space model) on the MD17 sets would substantially strengthen the conceptual basis of the method.","section":"Sec. IIB"},{"comment":"The y-axis label 'MAE ST Function [arb. u.]' and the caption use inconsistent notation for β and β′; please unify notation across the figure and text.","section":"Fig. 3 and SI Fig. 9"},{"comment":"The abstract contains a typo ('Styblinksi-Tang'); the correct spelling is Styblinski–Tang.","section":"Abstract and Sec. I"},{"comment":"No data or code availability statement is provided. For an empirical benchmark paper, making the implementation and bootstrap scripts available would be important for reproducibility and for resolving the algorithmic ambiguity above.","section":"Reproducibility"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely of interest to the ML-for-materials/chemistry community if the controlled ST comparison and algorithm consistency are resolved. The MD17 evidence is broad and internally consistent, which gives me confidence that a corrected version could be publishable. The main risk is that the actual implementation may differ from the pseudocode; without code, this cannot be checked, which is why I treat the Algorithm 1 inconsistency as a major issue rather than a minor presentation flaw."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper identifies a real problem: FPS on Boltzmann-distributed molecular data systematically undersamples equilibrium structures. Weighting FPS by force norms with a tunable exponent is a natural fix, and the MD17 results across six molecules consistently show lower error variance and better coverage of low- and high-force regions. That part is genuinely useful. Second, the headline efficiency claim on the Styblinski-Tang function is not controlled. The learning curves put FPS/GGFPS on the leftover points of the labeled set while URS is on a fixed test set, so the comparison mixes protocols. The paper admits at N=950 the GGFPS curve dropping below URS at N=1000 is an artifact of the MAE metric and disappears with RMSE. Since the twofold-reduction claim is derived from those curves, it is currently unsupported.\n\nThere is also an internal inconsistency in Algorithm 1. The reindexing rule produces a sequence of exponents that are all nonnegative for typical N, defeating the stated purpose of alternating between -beta and beta to keep the sparse training set mixed. That could be a typo in the SI, but as written the mechanism contradicts the text.\n\nWhat the paper does well: the distributional analysis is thoughtful, the bootstrapping is reasonable, and the variance reduction is systematic across all molecules tested. The GGFPS score is a simple and new combination of existing ingredients. The missing PCov-FPS and PCov-CUR baselines promised in the abstract are not in the body, and no code is provided, which makes the algorithm inconsistency harder to resolve. The MD17 protocol also deserves a clearer statement of the test set.\n\nWho is this for? People building ML potentials with kernel methods who care about training set construction. With corrected evaluation, an accurate algorithm description, code, and the promised baselines, the MD17 claims would be worth taking seriously. As submitted, it is a solid idea with shaky evidence on one of its two main claims.\n\nRecommendation: send it to peer review, not desk reject. The referee should demand a controlled ST learning-curve comparison and a corrected algorithm. The core idea is legitimate.","headline":"GGFPS is a sensible idea with a solid MD17 story, but the main ST data-efficiency claim is undermined by an uncontrolled test-set protocol, and the SI algorithm contradicts its own sign-alternation mechanism.","tokens_in":19684,"tokens_out":4013,"would_cite":false,"duration_ms":31531,"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":"This paper claims that weighting furthest-point sampling distances by molecular force norms, with an alternating exponent that favors both high- and low-gradient structures, builds training sets up to twice as data-efficient as plain FPS wh","keywords":["training set selection","furthest point sampling","gradient-guided sampling","kernel ridge regression","potential energy surfaces","molecular dynamics","data efficiency","model robustness"],"falsifier":"On a potential-energy surface engineered so that force norms and label variance are anticorrelated (for example, a steep-walled valley with constant energy and a flat region with a sudden energy cliff), run GGFPS and FPS at N=50; GGFPS's advantage should reverse. More directly, on an MD17 molecule, bin test configurations by force norm and check whether GGFPS's gains vanish when the kernel is changed to one that already includes gradient information.","tokens_in":18779,"feed_emoji":"⚛️","tokens_out":6226,"duration_ms":87111,"temperature":0.7,"pith_summary":"The paper introduces GGFPS, a training-set selection rule that multiplies furthest-point-sampling distances by a power of the molecular force norm, with the power alternating between positive and negative values across the selection run. The authors argue that because force norms track the local variance of energy labels, this weighting covers both descriptor space and label space, avoiding FPS's blind spot: FPS systematically under-samples equilibrium geometries in MD17 trajectories. On a two-dimensional multimodal test function and six MD17 molecules, GGFPS matches or beats FPS and uniform random sampling, achieving the same accuracy with up to half the training data and cutting prediction-error variance. If true, the result means simple gradient information, already a byproduct of reference calculations, can substantially lower the data cost and improve robustness of learned potential-energy surfaces.","feed_headline":"Gradient-aware sampling halves training data for molecular ML","feed_subtitle":"Weighting furthest-point sampling by force norms cuts errors and variances on molecular potential-energy surfaces.","key_machinery":"The load-bearing mechanism is the GGFPS score function s_j = g_j^{beta_k} d_j, combining the Euclidean distance from already-selected points with the L2 norm of the atomic forces. The hyperparameter beta defines an interval [-beta, beta] whose linearly spaced values are re-ordered alternately, so early selections alternate between high- and low-gradient points rather than committing to one regime; beta = 0 recovers plain FPS. The first point is also drawn with probability proportional to gradient norm. This device converts a purely geometric greedy selector into a supervised selector that trades coverage against label variance.","core_discovery":"The central discovery is that pure descriptor-space coverage is not enough: FPS selects configurations that are mutually far apart in representation space, and on the non-uniform molecular datasets those far-apart points are systematically strained, high-energy structures. GGFPS instead scores every candidate by d_j times g_j raised to an exponent that alternates between negative and positive values across the selection. This makes the sparse early training set contain both low- and high-gradient points, then fills in medium-gradient configurations as sampling proceeds. The result is a training set that spans the entire dataset while intentionally over-weighting regions where force norms ind","pith_inferences":["My inference: the alternating-exponent trick could improve other greedy selectors, such as active-learning queries or stratified sampling, since the pathology it fixes (early commitment to one regime) is not specific to FPS.","My inference: GGFPS's variance reduction suggests it should also improve uncertainty quantification; a testable extension is whether error bars from an ensemble of GGFPS-trained models are better calibrated than those from FPS or uniform-sampling ensembles.","My inference: the paper only tests interpolative settings where train and test come from the same potential-energy surface; the method's value for extrapolation across chemical space is an open, testable question that the authors themselves flag.","My inference: using force norms as a label-variance proxy could backfire on surfaces where gradients are large but energies are smooth; a cheap diagnostic on new datasets would be to compare GGFPS against FPS on a held-out validation set before committing to the beta schedule."],"forward_implications":["On the Styblinski-Tang function, GGFPS training sets reach the full-labeled-set mean absolute error with 50% fewer points and match FPS accuracy with up to half the training points.","On MD17, GGFPS training sets lower prediction errors for equilibrium and strained structures relative to both FPS and uniform random sampling, with the largest gains in the low-data regime.","GGFPS reduces prediction-error variance across all six MD17 molecules, by up to an order of magnitude relative to FPS and up to about 7x relative to uniform random sampling for aspirin, so models are less prone to sporadic large errors.","The distributional analysis implies that FPS's poor MD17 performance is systematic, not a tuning accident: it under-samples low-force-norm equilibrium geometries, and GGFPS explicitly corrects this.","Because forces are a standard byproduct of reference electronic-structure calculations, the method adds no new data-acquisition cost and can be applied to existing labeled datasets."],"fun_headline_variants":["Force-aware sampling halves molecular ML training cost","GGFPS beats coverage-only selection on MD17","Gradient-guided sampling trims data needs for chemistry","Why FPS fails: force norms fix molecular sampling","Smarter training sets via gradient-guided FPS"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that force norms act as a reliable proxy for local energy-label variance: if a surface has large forces in regions of nearly constant energy, or flat forces where energies vary sharply, the weighted scores will push sampling in the wrong direction.","fun_headline_variants_meta":{"raw":{"variants":["Force-aware sampling halves molecular ML training cost","GGFPS beats coverage-only selection on MD17","Gradient-guided sampling trims data needs for chemistry","Why FPS fails: force norms fix molecular sampling","Smarter training sets via gradient-guided FPS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00019,"raw_usage":{"total_tokens":1181,"prompt_tokens":753,"completion_tokens":428,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":497,"completion_tokens_details":{"reasoning_tokens":355}},"tokens_in":497,"tokens_out":428,"duration_ms":24822,"temperature":1.0,"reasoning_tokens":355,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T10:41:57.192321+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a potential-energy surface engineered so that force norms and label variance are anticorrelated (for example, a steep-walled valley with constant energy and a flat region with a sudden energy cliff), run GGFPS and FPS at N=50; GGFPS's advantage should reverse. More directly, on an MD17 molecule, bin test configurations by force norm and check whether GGFPS's gains vanish when the kernel is changed to one that already includes gradient information.","supporting_citations":[],"review_version":1}