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REVIEW 4 major objections 5 minor 1 cited by

INN-FF: A Scalable and Efficient Machine Learning Potential for Molecular Dynamics

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2505.18141 v1 pith:5WOKPANI submitted 2025-05-23 cond-mat.mtrl-sci physics.chem-ph

Taskin Mehereen , Sourav Saha , Intesar Jawad Jaigirdar , Chanwook Park This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-ph
keywords INN-FFmachinelearninginteratomicpotentialinterpolatingneuralnetworkstensordecompositionforcefieldmoleculardynamicsdataefficiencyliquidwater
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [Section 3.2, Eq. (2)] 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.
  2. [Section 7] 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.
  3. [Tables 1 and 2] 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.
  4. [Section 4.2.2, Table 2] 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.
minor comments (5)
  1. [Section 4.1, Figure 3] 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.
  2. [Appendix A.2.1 / Appendix A.3] 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.
  3. [Section 5] 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.
  4. [Appendix A.4] 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.
  5. [Table 2] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the benchmark claims rest on external DFT labels and held-out test splits, and the architecture self-citations are not load-bearing.

full rationale

The central claimed result is that the INN architecture, when trained on external DFT labels, achieves low energy and force errors on held-out water and rMD17 configurations. The reported benchmark quantities are fitted to external reference data (revPBE0-D3 for bulk water, DFT for rMD17) and are evaluated on held-out test splits: 159 of 1,593 water configurations for testing, and 1,800 unseen rMD17 configurations for testing. No equation in the paper reduces a reported benchmark number to a parameter fitted from that same benchmark; the INN interpolation functions are specified by the explicit C-HiDeNN construction in Appendix A.1 (Eqs. 3-14), not by citation alone. Self-citations to Refs. [18]-[23] identify the architectural origin of INN, but the central claim is independently supported by the paper's own experiments against external baselines. The absence of a defined atomic-coordinate descriptor and the admitted lack of explicit symmetry enforcement in Section 7 are correctness and generalization concerns, not circularity: they do not make the reported test errors equivalent to the training inputs. Therefore no circular step can be exhibited from the paper's own equations or citation chain, and the circularity score is 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several unstated or weakly justified choices: the number of INN segments and TD modes (grid-searched), the choice of activation basis and patch size (not reported), and, most critically, the assumption that the unspecified input representation works without symmetry enforcement. No new entities are introduced.

free parameters (6)
  • segments per input dimension (number of nodes J) = 9 (water), 2 (rMD17)
    Grid-searched hyperparameter that controls the resolution of the 1D interpolation on each input coordinate.
  • number of TD modes M = 4 (water), 1 (rMD17)
    Grid-searched rank of the CP decomposition; higher M increases parameters linearly.
  • patch size s = not reported
    Sets the support domain of the interpolation functions; never specified for any experiment.
  • activation basis A_p(x) = not reported
    Table 3 lists six possible families (polynomial, sinusoidal, exponential, sigmoid, tanh, GELU) but the paper does not say which was used.
  • dilation parameter a in cubic spline = not reported
    Appears in Eq. (5); its value is not given.
  • training hyperparameters = not reported
    Learning rate, optimizer, number of epochs, and energy/force loss weights are omitted from Appendix A.3.
assumptions (4)
  • standard math The C-HiDeNN moment matrix G in Eq. (11) is invertible for the chosen nodes and basis functions.
    Appendix A.1 says 'Assuming it is invertible' before computing the coefficients in Eq. (12).
  • domain assumption The molecular potential energy surface is representable by a CP decomposition of products of 1D interpolations as in Eq. (2).
    The paper assumes low-rank structure in the high-dimensional energy map without evidence.
  • ad hoc to paper The unspecified input coordinates are a sufficient and physically meaningful representation of an atomic configuration.
    Section 3 never defines the input vector; without rotational and translational invariance this representation cannot generalize across orientations.
  • domain assumption Published NequIP and MACE numbers are comparable to INN-FF trained on 50 rMD17 configurations.
    Table 2 compares to literature results that used the standard 1000-configuration protocol; this comparability is unstated and likely false.

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Cite this review

Pith. "Pith review of INN-FF: A Scalable and Efficient Machine Learning Potential for Molecular Dynamics." pith.science (2026). https://pith.science/paper/5WOKPANI

@misc{pith2026250518141,
  author       = {Pith},
  title        = {Pith review of: INN-FF: A Scalable and Efficient Machine Learning Potential for Molecular Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5WOKPANI}},
  note         = {Machine review of arXiv:2505.18141}
}
read the original abstract

The ability to accurately model interatomic interactions in large-scale systems is fundamental to understanding a wide range of physical and chemical phenomena, from drug-protein binding to the behavior of next-generation materials. While machine learning interatomic potentials (MLIPs) have made it possible to achieve ab initio-level accuracy at significantly reduced computational cost, they still require very large training datasets and incur substantial training time and expense. In this work, we propose the Interpolating Neural Network Force Field (INN-FF), a novel framework that merges interpolation theory and tensor decomposition with neural network architectures to efficiently construct molecular dynamics potentials from limited quantum mechanical data. Interpolating Neural Networks (INNs) achieve comparable or better accuracy than traditional multilayer perceptrons (MLPs) while requiring orders of magnitude fewer trainable parameters. On benchmark datasets such as liquid water and rMD17, INN-FF not only matches but often surpasses state-of-the-art accuracy by an order of magnitude, while achieving significantly lower error when trained on smaller datasets. These results suggest that INN-FF offers a promising path toward building efficient and scalable machine-learned force fields.

Figures

Figures reproduced from arXiv: 2505.18141 by the authors.

Figure 1
Figure 1. INN interpolation functions in 1D input space for linear (a) and nonlinear (b) cases. The [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. INN network architecture for 1D input variable (a) and 2D input variables (b). TD: Tensor [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Trainable parameters vs. epochs. INNs trained on bulk water dataset [ [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Training Energy Mean Absolute Error (MAE) for bulk water dataset [ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Learning curves for INN and MACE models trained on bulk water dataset [ [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Comparison of training time and GPU memory usage between INN-FF and MLP models [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Training MAE loss (mean std) over 5 runs for INN-FF architectures on the bulk water[ [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

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Forward citations

Cited by 1 Pith paper

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    A C++/pybind11 shared-memory plugin layer exposes VASP SCF and ionic data as NumPy arrays so Python can modify structure, forces, local potential, and occupancies in place.

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Reviewed August 7, 2026 · model on record in the stance chip above.