{"id":"390d932a-c825-4aca-89c8-c380f5ccc77d","arxiv_id":"2505.18141","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"INN-FF is claimed to match or beat state-of-the-art machine learning force fields on water and rMD17 using far fewer parameters and training samples.","lead":"The paper presents INN-FF, a machine learning force field built from interpolating neural networks and tensor decomposition, and reports state-of-the-art energy errors on water and rMD17 benchmarks with very few training samples. A generalist might read it because data-efficient force fields could lower the cost of molecular dynamics simulations in drug discovery and materials design.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never defines how atomic configurations are encoded into the INN inputs, and Section 7 concedes that no physical symmetries are enforced; benchmark errors on fixed-orientation datasets cannot establish an MD-capable force field.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing gap: the input representation is never defined, and the admitted lack of symmetry enforcement makes the model unsuitable as a transferable force field. My independent reading confirms this. The paper's central claim is that INN-FF is an accurate, data-efficient ML potential for molecular dynamics. For that claim to be true, the model must map atomic configurations to energies in a physically consistent way: invariant under rotations, translations, and atom permutations. No such descriptor or symmetry layer is described anywhere; Section 7 explicitly concedes the architecture does not enforce physical symmetries. The benchmarks, even if taken at face value, were generated on datasets with fixed orientation and atom ordering, so they cannot establish the physical transferability required for MD. The missing input definition is an even more fundamental problem: without knowing what the I-dimensional input is, the results cannot be reproduced or even fully interpreted. This is not a disagreement with community consensus; it is an internal incompleteness that undermines the central claim. I therefore support the reader's REJECT verdict with high confidence. The proposed concrete test would settle the concern definitively: if the model fails invariance under rotation/translation/permutation, the central claim fails; if the authors can specify a descriptor that provides invariance, the claim would need reassessment. No code is provided, and Appendix A.4 withholds it due to patent considerations, so an independent computational test cannot currently be run; the analytical test of requiring a complete input definition is the appropriate first step.","tokens_in":10079,"tokens_out":3859,"duration_ms":34915,"concrete_test":"Ask the authors to specify the exact mapping from atomic coordinates and elements to the I inputs of Eq. (2). Then, using that mapping (or, if none is supplied, the model as described), take a held-out water or rMD17 configuration and apply: (a) a random SO(3) rotation, (b) a rigid translation, and (c) a permutation of two identical atoms; recompute the predicted energy and forces. If any transformation changes the predicted energy by more than numerical tolerance (~1e-6 eV), the potential is not invariant and cannot be used in molecular dynamics, so the benchmark claims would not support the headline.","verdict_should_be":"UNCHANGED","load_bearing_attack":"For the central claim to hold, INN-FF must be a function of atomic coordinates, species, and simulation cell that is invariant to rigid rotations, translations, and permutations of identical atoms, with forces obtained by differentiation. The paper supplies no such representation. Section 3.2 defines the model only for a generic I-dimensional input x_i; Eq. (2) is a CP tensor product of univariate interpolants with no reference to atomic coordinates, elements, or neighbor lists. Appendix A.3 gives only segments and modes, not the input features. Section 7 explicitly states: 'the architecture does not explicitly enforce physical symmetries, which may affect generalization in highly symmetric domains.' Consequently, even if Tables 1 and 2 are numerically correct, they were obtained on fixed-orientation, fixed-ordering datasets and do not demonstrate transferability to rotated, translated, or permuted configurations that occur in molecular dynamics. A model without symmetry invariance is not a usable interatomic potential, and the missing input definition also prevents reproduction or independent verification. This is a load-bearing correctness risk, not a stylistic omission.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes INN-FF, a machine-learned interatomic potential built from Interpolating Neural Networks (INNs), which combine finite-element-style interpolation and CP tensor decomposition. The authors claim that INN-FF achieves state-of-the-art or better accuracy on the bulk water and rMD17 benchmarks while using far fewer trainable parameters and less GPU memory than standard MLPs, and that it is particularly data-efficient when trained on small datasets. The manuscript reports energy and force errors in Tables 1 and 2, describes the INN architecture in Section 3, and discusses limitations in Section 5 and Appendix A.4, including the fact that full molecular dynamics simulations have not yet been performed and that physical symmetries are not explicitly enforced.","tokens_in":10295,"tokens_out":4703,"duration_ms":38923,"significance":"Data-efficient machine-learned force fields are an important goal, and the INN-FF architecture, based on C-HiDeNN interpolation and CP tensor decomposition, is cleanly formulated and offers linear scaling of parameters with input dimension. The inclusion of learning curves and an explicit limitations section is commendable. However, as written, the central claims are not supported: the atomic input representation is never defined, the architecture does not enforce the physical symmetries required of an interatomic potential, and the benchmark comparisons are not sufficiently controlled. These issues are load-bearing because they affect whether the reported accuracy numbers are meaningful and reproducible, and whether the model can function in molecular dynamics at all.","major_comments":[{"comment":"The paper never specifies how an atomic configuration (atomic species, positions, simulation cell, periodic boundary conditions) is mapped to the generic input vector x in Eq. (2). Section 3.2 defines the INN approximation for an abstract I-dimensional function, and Appendix A.3 provides only segment/mode counts and training splits. Without this mapping, the benchmark numbers in Tables 1 and 2 are not reproducible, and the claim that the model learns interatomic interactions cannot be verified.","section":"Section 3.2, Eq. (2)"},{"comment":"The text explicitly states that \"the architecture does not explicitly enforce physical symmetries, which may affect generalization in highly symmetric domains.\" A machine-learned interatomic potential for MD must assign identical energies to configurations related by rotation, translation, and permutation of identical atoms; Eq. (2), combined with an unspecified input representation, provides no such invariance. Therefore, the fixed-orientation benchmark errors do not demonstrate that INN-FF is usable as a force field. A concrete test would be to evaluate energies on randomly rotated, translated, and permuted copies of the test configurations and report the resulting errors.","section":"Section 7"},{"comment":"The benchmark results are reported as single point estimates with no error bars or uncertainty quantification. Appendix A.5 shows that training variability across five runs is non-negligible for loss curves, so the headline energy RMSE of 0.133 meV/H2O in Table 1 and the rMD17 MAEs in Table 2 need confidence intervals to support the claim of state-of-the-art accuracy, especially given the stated sensitivity to hyperparameter choices in Section 5.","section":"Tables 1 and 2"},{"comment":"The comparison with NequIP and MACE on rMD17 is not controlled. The text states that INN-FF was trained on 50 configurations, but it is not established that the cited baseline numbers in Table 2 were obtained under the same training-set size, validation split, and test set. If the baseline values are taken from the literature with different data regimes, the conclusion that INN-FF \"achieves or surpasses state-of-the-art accuracy\" is not supported. The paper should either retrain the baselines under identical protocols or clearly report the original data conditions for each cited number.","section":"Section 4.2.2, Table 2"}],"minor_comments":[{"comment":"The caption \"Trainable parameters vs. epochs\" is ambiguous: the figure appears to show two panels (parameters and epochs), but neither axis labels nor units are described in the caption. Please clarify what is plotted.","section":"Section 4.1, Figure 3"},{"comment":"The dataset description says the water dataset contains 1,593 configurations, but the training/validation/test split in Appendix A.3 sums to 1274 + 159 + 159 = 1,592. Please reconcile the total count.","section":"Appendix A.2.1 / Appendix A.3"},{"comment":"The paper is titled \"...for Molecular Dynamics\" but the text concedes that \"the model has not yet been evaluated in full molecular dynamics simulations.\" This is a significant gap for the claimed applicability; either add MD stability tests or temper the title and abstract accordingly.","section":"Section 5"},{"comment":"The statement that full code cannot be shared due to pending patent and proprietary restrictions is important for reproducibility and should be disclosed in the main text or at least in the abstract, not only in an appendix.","section":"Appendix A.4"},{"comment":"The rMD17 dataset contains ten molecules, but Table 2 lists only eight; the paper should state whether the two omitted molecules were excluded and why, or include them for completeness.","section":"Table 2"}],"recommendation":"reject","confidential_remarks":"The manuscript relies heavily on the authors' own C-HiDeNN and INN papers, and while this is not circularity in the forbidden sense, the novelty of INN-FF relative to those prior works is not clearly delineated. The absence of any defined input representation and the admitted lack of symmetry invariance are fundamental issues that would require a substantial redesign of the method and a complete re-evaluation of the benchmarks, rather than a local revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a promising way to apply the INN architecture to interatomic potentials, but the manuscript as written does not support its headline claims. The central missing piece is the descriptor: the paper never says how atomic positions, species, and cell are encoded into the x_i in Eq. (2). Without that, nobody can reproduce the results or even check whether the model has a chance of being a valid potential. Section 7 concedes that physical symmetries are not enforced; for a force field used in MD, invariance to rotations, translations, and atom permutations is a hard requirement, not a nice-to-have. Fixed-orientation benchmark accuracy does not transfer to MD.\n\nWhat is good: the INN architecture is genuinely compact—linear parameter scaling with input dimension, low GPU memory, and fast training on the water dataset. The authors are also upfront in the limitations section: no long-timescale MD, no charged or multi-component systems, no code release. That honesty matters.\n\nThe soft spots are load-bearing. The rMD17 comparison likely mixes training set sizes: Table 2 says 50 configurations for INN-FF, while the NequIP and MACE numbers appear to be from models trained on the standard 1000-point protocol. No error bars on any benchmark table, and the Appendix shows error bars only for training loss. The abstract's 'order of magnitude' claim is not supported by the evidence as presented.\n\nWould I referee it? Yes, if I were an editor I'd send it to review with a strong request for major revision: define the descriptor, add symmetry handling (e.g., use a local environment descriptor or enforce equivariance), give error bars and a fair comparison, and release code or a detailed I/O spec. The idea is worth engaging with, but the current version is not a usable MLIP.","headline":"The numbers look too good to be true, and the paper gives us no way to verify them: it never defines the atomic input representation, so the headline claims are not supported.","tokens_in":10816,"tokens_out":2449,"would_cite":false,"duration_ms":20654,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"INN-FF is a machine-learning force field that combines compact-supported interpolation functions with tensor decomposition to reach benchmark accuracy from 50 training configurations and with orders of magnitude fewer parameters.","keywords":["INN-FF","machine learning interatomic potential","interpolating neural networks","tensor decomposition","force field","molecular dynamics","data efficiency","liquid water"],"falsifier":"Take any rMD17 test configuration, apply a rigid rotation and a random permutation of identical atoms, and feed all versions to a trained INN-FF model: if the predicted energy or forces change by more than numerical precision, the potential is not invariant under the symmetries molecular dynamics requires.","tokens_in":9870,"feed_emoji":"⚛️","tokens_out":12017,"duration_ms":69918,"temperature":0.7,"pith_summary":"The paper proposes INN-FF, a machine-learning interatomic potential built from interpolating neural networks that merge locally supported interpolation functions with CP tensor decomposition. The central claim is that this single-hidden-layer architecture learns quantum-mechanical energies and forces from far fewer training configurations and trainable parameters than standard multilayer perceptrons or published graph-based baselines. On liquid water, INN-FF reports an energy RMSE of 0.133 meV per water molecule, roughly an order of magnitude below several published models; on rMD17 molecules trained on only 50 configurations, it reports force MAEs near 20 meV/Å. If these numbers survive actual molecular dynamics, the method would lower both the data-generation and hardware costs of building accurate force fields.","feed_headline":"New force field learns molecular dynamics from 50 configurations","feed_subtitle":"Interpolation plus tensor decomposition cuts parameters and memory while matching or beating published accuracy on water and rMD17.","key_machinery":"The central object is the interpolating neural network built from C-HiDeNN interpolation functions, i.e., compact-supported convolution patches $W^{(k)}_j(x)$ assembled from radial basis functions $R_k(x)$ and $P$ activation functions $A_p(x)$, with nodal values as the trainable parameters. These give the 1D edge functions finite-element-like properties: compact support, partition of unity, Kronecker delta, and reproducing conditions. For multivariate systems the network uses CANDECOMP/PARAFAC (CP) tensor decomposition, writing a $d$-input function as $\\sum_{m=1}^M \\prod_{i=1}^d N_i(x_i) u_i^{(m)}$, so the total parameter count is $M d J$, linear in the number of inputs. This linear scaling is the mechanism claimed to deliver data efficiency and low memory cost, and it is what separates INN-FF from deep MLPs and graph-based message-passing potentials.","core_discovery":"INN-FF is a force-field architecture in which each input dimension is processed by a learnable one-dimensional interpolation function, a compact-supported shape function with tunable nodal values, and the univariate responses are combined by CP tensor decomposition rather than deep-layer composition. The resulting network has only one hidden layer, and its parameter count scales linearly with the number of input variables, $M I J$, whereas MLPs and KANs scale quadratically with layer width. The paper reports that this architecture converges in fewer epochs with orders of magnitude fewer parameters, uses under 300 MB of GPU memory where an MLP baseline uses about 10 GB, and achieves state-of-the-art benchmark accuracy: an energy RMSE of 0.133 meV per water molecule and a force RMSE of 42.3 meV/Å on the bulk-water dataset, and force MAEs around 20 meV/Å on rMD17 molecules trained from 50 configurations.","pith_inferences":["A direct test the paper does not perform is to rotate, translate, and permute a held-out configuration and check that predicted energies and forces are unchanged; if they are not, the benchmark numbers are not yet evidence of an MD-ready potential.","The mesh-compatible interpolation functions hint at a tighter coupling with finite-element or isogeometric simulation codes than typical graph-based potentials, since the same shape functions could discretize both the physics and the learned potential; the paper only gestures at this in its conclusion.","The nearly flat force learning curve down to 100 water samples suggests the practical data floor may be below what was tested, so probing 10 to 50 configurations per molecule would reveal whether the small-data advantage is general."],"forward_implications":["Training sets of roughly 50 configurations could suffice for small organic molecules, shrinking the cost of DFT label generation for new targets.","On the bulk-water benchmark, the reported energy RMSE of 0.133 meV per water molecule is about ten times smaller than several published values, so an energy surface fit this tightly would give a smoother starting point for sampling.","The linear parameter scaling and sub-300 MB GPU memory footprint mean training can run on a single consumer GPU, making MLIP development practical without large compute clusters.","Because the architecture is compact, inference is cheap enough to embed in molecular dynamics engines; the paper identifies ASE as a target but has not yet run such simulations."],"supporting_citations":[{"why":"supplies the bulk-water dataset of 1,593 revPBE0-D3 configurations and the BP-NN baseline numbers used in Table 1.","marker":"[24]"},{"why":"supplies the rMD17 benchmark trajectories and the 50/50/1800 train/validate/test regime used for the molecule experiments.","marker":"[32]"},{"why":"MACE baseline used for the water learning-curve comparison and for the rMD17 accuracy table.","marker":"[15]"},{"why":"NequIP baseline used in the rMD17 accuracy table.","marker":"[33]"},{"why":"defines the interpolating neural-network architecture, including the 1D edge functions and the activation-function menu.","marker":"[23]"},{"why":"introduces the C-HiDeNN convolution patch functions and the four interpolation conditions that the INN basis satisfies.","marker":"[20]"},{"why":"provides the GPU-accelerated C-HiDeNN formulation used to compute the compact-supported interpolation functions.","marker":"[21]"},{"why":"supplies the CANDECOMP/PARAFAC tensor decomposition that combines univariate INNs into a multivariate approximation.","marker":"[22]"},{"why":"supplies the cubic-spline radial basis function used inside the C-HiDeNN convolution patches.","marker":"[35]"}],"fun_headline_variants":["INN-FF: ML force field from just 50 configurations","Interpolation + tensor decomposition cut parameters for ML force fields","INN-FF: one hidden layer, orders fewer parameters","ML potential from 50 configs beats state-of-the-art","Interpolation + tensor decomposition: force field from 50 configs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a network with no explicit symmetry constraints, trained on fixed-orientation snapshots, will assign the same energy and forces to physically equivalent configurations once atoms rotate, translate, or reorder, so the reported benchmark accuracy carries over to real molecular dynamics.","fun_headline_variants_meta":{"raw":{"variants":["INN-FF: ML force field from just 50 configurations","Interpolation + tensor decomposition cut parameters for ML force fields","INN-FF: one hidden layer, orders fewer parameters","ML potential from 50 configs beats state-of-the-art","Interpolation + tensor decomposition: force field from 50 configs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00138,"raw_usage":{"total_tokens":5585,"prompt_tokens":936,"completion_tokens":4649,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":4562}},"tokens_in":552,"tokens_out":4649,"duration_ms":33628,"temperature":1.0,"reasoning_tokens":4562,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:34:27.632692+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take any rMD17 test configuration, apply a rigid rotation and a random permutation of identical atoms, and feed all versions to a trained INN-FF model: if the predicted energy or forces change by more than numerical precision, the potential is not invariant under the symmetries molecular dynamics requires.","supporting_citations":[{"cited_title":"A., Behler, J., Dellago, C","cited_arxiv_id":null,"evidence_quote":"supplies the bulk-water dataset of 1,593 revPBE0-D3 configurations and the BP-NN baseline numbers used in Table 1."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the rMD17 benchmark trajectories and the 50/50/1800 train/validate/test regime used for the molecule experiments."},{"cited_title":"P., Simm, G., Ortner, C","cited_arxiv_id":null,"evidence_quote":"MACE baseline used for the water learning-curve comparison and for the rMD17 accuracy table."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"NequIP baseline used in the rMD17 accuracy table."},{"cited_title":"Convolution hierarchical deep-learning neural networks (c-hidenn): finite elements, isogeometric analysis, tensor decomposition, and beyond","cited_arxiv_id":null,"evidence_quote":"introduces the C-HiDeNN convolution patch functions and the four interpolation conditions that the INN basis satisfies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the GPU-accelerated C-HiDeNN formulation used to compute the compact-supported interpolation functions."},{"cited_title":"explanatory","cited_arxiv_id":null,"evidence_quote":"supplies the CANDECOMP/PARAFAC tensor decomposition that combines univariate INNs into a multivariate approximation."},{"cited_title":"K., Jun, S","cited_arxiv_id":null,"evidence_quote":"supplies the cubic-spline radial basis function used inside the C-HiDeNN convolution patches."}],"review_version":1}